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PTI 2006-04

VIEWS: 18 PAGES: 79

									FACTORS AFFECTING MOTOR CARRIER
CRASH RISK


Prepared for
Federal Motor Carrier Safety Administration




FINAL REPORT




September 30, 2005




By P. P. Jovanis, S.-W. Park, K.-Y. Chen, F. Gross and A. Mukherjee




PENNSTATE


    Pennsylvania Transportation Institute   The Pennsylvania State University
                                            Transportation Research Building
                                            University Park, PA 16802-4710
                                            (814) 865-1891 www.pti.psu.edu
1. Report No.                             2. Government Accession No.          3. Recipient’s Catalog No.

4. Title and Subtitle                                                          5. Report Date
Factors Affecting Motor Carrier Crash Risk                                     September 30, 2005
                                                                               6. Performing Organization Code

7. Author(s)                                                                   8. Performing Organization Report No.
Paul P. Jovanis, Sang-Woo Park, Ko-Yu Chen, Frank Gross                        PTI 2006-04
and Aviroop Mukherjee

9. Performing Organization Name and Address                                    10. Work Unit No. (TRAIS)
The Pennsylvania Transportation Institute
Transportation Research Building                                               11. Contract or Grant No.
The Pennsylvania State University                                              DTMC75-3-C-00011
 University Park, PA 16802-4710

12. Sponsoring Agency Name and Address                                         13. Type of Report and Period Covered

Federal Motor Carrier Safety Administration                                    Final Report
400 Seventh Avenue                                                             1/1/2003—8/30/2005
Washington, DC 20590-0001
                                                                               14. Sponsoring Agency Code

15. Supplementary Notes
COTR: Chuck Rombro

16. Abstract

There is a need to understand the relationship between commercial truck driver hours of service and the risk of a
crash, particularly correlations with federal hours of service regulations. A series of time-dependent logistic
regression models are used to analyze crash and operations data from two distinct time periods: the mid 1980s and
2004. The findings consistently reveal a relatively flat risk for the first 1-5 hours, then a non-linear increase in risk
through hours 10 or 11. Multi-day driving, particularly during night and early morning hours, is also frequently
associated with increased risk, of nearly the same magnitude as driving 9-11 hours. These findings help to provide
a baseline estimate of crash risk relationships for the new hours of service policy initiated in 2004.




17. Key Words                                                                  18. Distribution Statement
driving crash risk, crash analysis, hours of service, multi-day driving,       No restrictions. This document is
driving schedules, sleeper operations                                          available from the National Technical
                                                                               Information Service, Springfield, VA
                                                                               22161
19. Security Classif. (of this         20. Security Classif. (of this page)    21. No. of Pages           22. Price
report)                                Unclassified                            72
Unclassified
                   FACTORS AFFECTING MOTOR CARRIER CRASH RISK


                                       FINAL REPORT



                                          Prepared for

                          Federal Motor Carrier Safety Administration




                                              By

                                       Paul P. Jovanis
                                       Sang-Woo Park
                                         Ko-Yu Chen
                                         Frank Gross
                                             and
                                      Aviroop Mukherjee



                           The Pennsylvania Transportation Institute
                              The Pennsylvania State University
                              Transportation Research Building
                               University Park, PA 16802-4710



                                      September 30, 2005



                                         PTI 2006-04


This work was sponsored by the Federal Motor Carrier Safety Administration, U.S. Department
of Transportation. The contents of this report reflect the views of the authors, who are
responsible for the facts and the accuracy of the data presented herein. The contents do not
necessarily reflect the official views or policies of either the Federal Motor Carrier Safety
Administration or the U.S. Department of Transportation at the time of publication. This report
does not constitute a standard, specification, or regulation.
                                         TABLE OF CONTENTS

                                                                                                                          Page

Executive Summary ...........................................................................................................1

1. INTRODUCTION ........................................................................................................3
   1.1 Background ............................................................................................................3
   1.2 Structure of the report ............................................................................................4

2. METHODOLOGY .......................................................................................................5
   2.1 Modeling crash risk................................................................................................5
   2.2 Deriving multi-day driving schedules...................................................................6
   2.3 Time of day ...........................................................................................................7
   2.4 Experience.............................................................................................................7
   2.5 Sleeper operations.................................................................................................7
   2.6 Circadian effects and night operations..................................................................7

3. DATA DESCRIPTION AND ANALYSIS – DATA SET 1........................................8
   3.1 Data description ....................................................................................................8
   3.2 Identification of Multi-day Driving Schedule.......................................................9
   3.3 Model results and interpretation .........................................................................13
        3.3.1 Interpretation of Model 1 .........................................................................14
        3.3.2 Interpretation of Model 2 .........................................................................15
   3.4 Discussion ...........................................................................................................17
   3.5 Conclusions – data set 1......................................................................................19

4. DATA DESCRIPTION AND ANALYSIS – DATA SET 2......................................20
   4.1 Data description ..................................................................................................20
   4.2 Model results and interpretation .........................................................................21
       4.2.1 Model A ....................................................................................................21
       4.2.2 Model B ....................................................................................................23
       4.2.3 Model C ....................................................................................................25

5. DATA DESCRIPTION AND ANALYSIS – DATA SET 3.....................................27
   5.1 Data description ..................................................................................................27
   5.2 Data analysis for data set 3 .................................................................................29
       5.2.1 Discussion of Model D: Pooled model with all data ...............................29
       5.2.2 Discussion of Model E: Non-sleeper berth operations ............................31
       5.2.3 Discussion of Model F Results: Sleeper berth operations .......................33
       5.2.4 Discussion of Model G and H: Interaction terms only ............................35

6. SUMMARY OF FINGINDS ......................................................................................40

7. REFERENCES ...........................................................................................................41



                                                                 iv
                            TABLE OF CONTENTS (Continued)

                                                                                                                          Page

APPENDIX A..................................................................................................................44
APPENDIX B ..................................................................................................................48
APPENDIX C ..................................................................................................................49




                                                                  v
                                            LIST OF TABLES

                                                                                                                 Page

Table 1. Manually-identified driving schedules .............................................................11
Table 2. Description of driving schedules derived from cluster analysis .......................14
Table 3. Model 1 estimates: effect of driving time........................................................15
Table 4. Model 2: Driving time and multi-day schedule ...............................................16
Table 5. Data summary for Model A ..............................................................................21
Table 6. Omnibus tests of model coefficients.................................................................21
Table 7. Estimation results: Model A ............................................................................22
Table 8. Data summary for Model B ..............................................................................24
Table 9. Omnibus tests of model coefficients Model B..................................................24
Table 10. Estimation results: Model B ..........................................................................24
Table 11. Data summary for Model C ............................................................................26
Table 12. Omnibus tests of model coefficients: Model C .............................................26
Table 13. Estimation results: Model C ..........................................................................26
Table 14. Sample size for data set 3 ...............................................................................27
Table 15. Summary of data concerning driving time – data set 3 ..................................28
Table 16. Test of Model D coefficients ..........................................................................30
Table 17. Model D summary ..........................................................................................30
Table 18. Variables in the equation for Model D: pooled model and all data...............31
Table 19. Test of Model E coefficients...........................................................................32
Table 20. Model E summary...........................................................................................32
Table 21. Variables in the equation Model E: non-sleeper berth operations.................33
Table 22. Test of Model F coefficients...........................................................................34
Table 23. Model F summary...........................................................................................34
Table 24. Variables in the equation for Model F ............................................................35
Table 25. Likelihood ratio test: Model E and F .............................................................35
Table 26. Variables in the equation for Model G: non-sleeper berth interaction ..........37
Table 27. Variables in the equation for Model H: sleeper berth interaction only .........38
Table 28. Summary of results for interaction term models ............................................39




                                                             vi
                                              LIST OF FIGURES

                                                                                                                             Page
Figure 1. Example of regular multi-day driving schedule – start driving at 10 AM for
2 days prior to day of interest ..........................................................................................10
Figure 2. Example of irregular schedule – initiate driving 10 PM one day prior and
7 PM two days prior to day of interest.............................................................................12
Figure 3. Example of schedule derived from cluster analysis ........................................13
Figure 4. Detailed analysis of crash risk during daytime and night/early morning
Driving schedules.............................................................................................................18
Figure 5. Effect of driving time by hour for Model A ....................................................23
Figure 6. Relative risk with hours driving: Model B .....................................................25
Figure 7. Relative risk with hours driving: Model C .....................................................26
Figure 8. Driving schedule based on start time...............................................................28
Figure 9. Crash odds and driving time with Model D ....................................................32




                                                                vii
Executive Summary

The detailed analysis of pre-existing crash and non-crash data representing an estimated 16
million vehicle miles of travel has revealed strong consistency between crash analysis using
data from the 1980s and field experiments conducted in the 1990s. Time of day of driving is
associated with crash risk: night and early morning driving has elevated risk in the range of
20-70% compared to daytime driving. Overall, 16 of 27 night and early morning driving
schedules had elevated risk. Irregular schedules with primarily night and early morning
driving had relative risk increases of 30-80%.

In addition, there remains a persistent finding of increased crash risk associated with hours
driving, with risk increases of 30-over 80% compared to the first hour of driving. These
increases are less than previously reported and are of similar magnitude to the risk increases
due to multi-day schedules. Finally, there is some evidence, although it is far from
persuasive, that there may be risk increases associated with significant off-duty time, in some
cases in the range of 24-48 hours.

A time dependent logistic regression model using data collected from 3 carriers in 2004
indicates that crash risk is statistically similar to the first hour of driving (except for an
increase in the second hour), then increases non-linearly after the 6th hour of driving. The
highest crash risk relative to the 1st hour of driving is hour 11 with a risk more than 3 times
the first hour. These results are qualitatively similar to those obtained in a recent research
paper by the team (Park, et al., 2005) using data from the 1980’s. These findings, using data
20 years apart, establish a consistent pattern of increased crash risk with hours driving. It is
important to note, however, that the confidence intervals for the estimates of the odds ratios
in the 9th, 10th and 11th hours are increasing; this is as a result of the loss of non-accident trips
as trips are successfully completed without a crash. The point estimate of a nearly 3 times
increase in crash odds is thus comparatively uncertain; at the extremes of the confidence
interval, the odds may be as large as 10 times the risk or as small as an approximate 10%
increase. Table 2 indicates that only 4 crash trips and 30 non-crash trips remain in this last
hour; the confidence interval is a reflection of the uncertainty that results from this reduced
sample size.

Certain multi-day driving schedules are also associated with crash risk increases. Consistent
with findings from the recent research using 1980’s data, the risk connected with the multi-
day patterns is statistically significant and of comparable magnitude to driving time. These
findings, using data 20 years apart, indicate that driving crash risk is associated with both
multi-day driving schedules and time on task (i.e. driving time).

A series of models indicate that the pattern of crash risk is different for non-sleeper
operations than for sleeper schedules. Models of non-sleeper operations indicate that crash
risk is strongly associated with multi-day driving, somewhat stronger than with driving time
(i.e. many parameter values for multi-day driving are significant and their magnitude is
generally larger then the parameters for driving time). Driving time shows elevated risk in
hours 2, 3, and 5 in addition to an increase in risk in hours 7 and 9. Models of sleeper
operations indicate strong association of crash risk and driving time, with particularly
increased risk in the 8th, 10th and 11th hours. Interestingly, within sleeper berth operations,
there is much less association of crash risk with regular schedules and substantial risk
associated with irregular schedules. One tentative conclusion is that the rigors of sleeper
operations appear to result in a greater decline in performance at extended driving hours than
for comparable non-sleeper operations. The team would feel more confident in this
conclusion if other studies supported this finding as well. Statistical tests confirm that
models of crash risk are different for sleeper and non-sleeper operations. This implies that
subsequent modeling should treat these operations distinctly, to the extent possible.

Detailed models aimed at exploring the association between crash risk and time of day (see
Table 28 for summary) indicate that crash risk appears highest when extended driving occurs
during the evening rush hour and late afternoons. While other time periods and driving times
also have significant association with elevated risk (e.g. some early morning driving), there is
a strong association with daytime and early evening driving. Consistent with other models,
sleeper berth users have particularly strong association of crash risk and driving time,
especially when the driving schedule is irregular.




                                               2
1. INTRODUCTION

1.1 Background

Despite several important studies, analysts have only a limited understanding of the factors
affecting commercial motor vehicle crashes, including especially the role of driver fatigue
and hours driving. This shortcoming inhibits an analyst’s ability to develop rules, policies,
and enforcement strategies that will have an impact on commercial motor vehicle crashes.
Many aspects of the motor carrier industry have changed over the last 50-60 years including
increasing economic pressure and the need for just-in-time shipments, increasing levels of
traffic congestion, and increasing levels of safety management (Freund, 1999). These
changes argue for an update of the safety studies as an establishment of current baseline
conditions concerning safety and hours of service. This report and study respond to that
need.

During the late 1980’s and early 1990’s, there were several safety studies conducted at
Northwestern University and University of California, Davis using carrier-based data (e.g.
Jovanis et al., 1991; Kaneko and Jovanis, 1992; Lin, Jovanis and Yang, 1993; Lin, Jovanis
and Yang, 1994. The research team collected both crash and non-crash data from carriers
and developed and tested a number of statistical techniques, focused on carrier -available
data including driver attributes such as age and experience, trip attributes such as time of day
and characteristics of the duty cycle undertaken by the driver.

Recent research in this area was a study conducted for FMCSA by the University of
Michigan Transportation Research Institute (UMTRI), using exposure and fatal crash data
from a variety of sources (Campbell, et al., 2000). The primary objective of this work was to
separate the estimates of fatigue-related accidents by the driver/operational subsets identified
in the hours of service options under consideration at the time. Fatigue was derived from a
variable coded in the Fatality Analysis Reporting System (FARS) as a “driver related factor”.
Of interest is the fact that no driver factor was coded in 60% of the crashes. The study
included the influence of the following driver and carrier attributes on crash risk: type of
firm, one way trip distance, the number of hours driving, and time of day. Time of day
analyses indicate a particularly high level of fatigue-related relative risk during early morning
hours.

Several additional studies from around the world address other aspects of hours of service. A
literature review was conducted for Transport Canada focusing on the efficacy of a 36-hour
restart policy (Smiley and Heslegrave, 1997). The conclusion was that there was limited
scientific evidence, either in the highway safety or other scientific literature, to support such
a policy. An additional study using self-reported data from a truck driver survey found that
falling asleep at the wheel was associated with several independent factors including more
arduous schedules characterized by more hours of work and fewer hours off duty (McCartt et
al., 2000). This study also contained a very thorough literature review. Research from
Finland regarding responsibility for fatal two-vehicle crashes found that truck drivers were
responsible in only 16% of the crashes (Hakkanen and Summala, 2001). Young driver age



                                               3
and driving during evening hours were principally associated with truck driver responsibility
in crashes. Prolonged and early morning driving was not associated with a significant effect
on responsibility. Lastly, an Australian-based study compared fatigue impairments with
those due to alcohol consumption in an effort to develop quantitative guidelines for driving
impairment due to fatigue (Williamson, et al. 2001). The European Union has also been
active in the area, recently considering changes in their regulations (Usdaw, 2004).

While there are many reasons why managing service hours is a challenging task, one of the
most perplexing aspects is the inconsistency in research findings concerning the effect of
driving schedules on driver performance and safety. A recent major study sponsored by
USDOT (Wylie, et al., 1996), using instrumented vehicles, off-line tests of driver
performance, video recording of driver faces on the road, physiological monitoring and a
series of driver ratings through surveys, found that the principle factor associated with a
decline in driving performance was time of day. Number of hours driving (time on task) and
cumulative number of days driving were not strong or consistent predictors. The study was
one of the most extensive field studies of its kind involving 80 drivers measured for
performance during revenue-producing runs for a carrier operating in both the US and
Canada (in order to allow legal driving for up to 12 hours consecutively).

These findings stand in contrast to work with carrier crash data conducted over several years
(Jovanis, et al., 1991; Kaneko and Jovanis, 1992; Lin et al., 1993; Lin, et al., 1994), in which
driving time has been most strongly associated with increases in crash risk, and night driving,
while significantly associated with crash risk in some situations, was neither consistently of
the same magnitude nor significance. Others have noted that the use of different
performance measures often yield different findings; the search for convergent validity is
important (Wylie et al., 1996).

The objective of this project was to examine the effect of driving schedule and other factors
(e.g. multi-day driving and continuous driving) on crash risk. The study has used a variety of
data to explore this issue, including some from the 1980’s and some collected during 2004.
In addition, reference is frequently made to the findings of other studies, notably the Driver
Fatigue and Alertness Study (DFAS) which was conducted in the mid-1990s. This is a
deliberate attempt to seek convergent validity: from data sets separated in time and from
different carriers, some using different measures of safety and driving performance.
Regardless, the nature of the driving task is similar and physiological capabilities of humans
are similar.

1.2 Structure of the report

The report is structured to describe each of the separate analyses undertaken with the range
of data involved. The next chapter of the report describes the common statistical approach
applied to the data: time dependent logistic regression. Each of the subsequent chapters
describes the 3 separate analyses undertaken during the study including a description of the
data used, analyses completed, and findings and conclusions. Results of statistical
estimations are included in the chapter only to the extent that they support an understanding
of the findings. Additional statistical material is contained in the appendix.



                                               4
2. METHODOLOGY

2.1 Modeling crash risk

One of the most important aspects of early studies of safety and hours of service (e.g. Harris,
et al., 1972; Mackie and Miller, 1978) is the need to characterize continuous driving by using
the notion of “survival”. Specifically, a driver who has a crash after driving 9 hours, for
example, has successfully “survived” the first 8. Any model that attempts to characterize the
probability of a crash as a discrete outcome must recognize in its statistical formulation that
most drivers can thus be considered to have multiple outcomes during a crash-involved trip:
the survival for hours prior to the crash and a crash outcome (i.e. a failure) for the time period
of the crash. Early statistical models of driving time crash risk proposed the use of survival
theory in recognition of this phenomenon (Jovanis and Chang, 1989; Chang and Jovanis,
1990).

        Subsequent research (e.g. Lin, et al., 1993) used a data replication scheme and logistic
regression to capture the survival effect. In the case described earlier of a driver having a
crash in the ninth hour of driving, there is a need to have each prior hour coded individually
with an outcome of a non-accident; this would occur for each of the 8 hours prior to the crash
event. In addition, the 9th hour would be coded as the alternate outcome, a crash. Similarly a
9 hour trip without a crash would need to be replicated for all 9 hours with a non-accident
outcome. It is only through this replication that the logistic regression is able to account for
the survival phenomenon. There is evidence in the statistical literature to support the use of
this type of model (e.g. Abbott, 1985; Brown, 1975; Efron, 1988; Hosmer and Lemeshow,
1989). The model is thus:

                                Pit = P(Yti = 1Yt 'i = 0 for t ′ < t , X i ) =
                                            exp [ g ( X i , t , β )]                        (1)
                                          1 + exp [ g ( X i , t , β )]
The model is interpreted as the probability that driver i has an accident (outcome Y = 1) at
time t, given survival until that time (i.e. an outcome Y = 0, for all time periods t΄ prior to
time period t) is given by the familiar logistic function with time t, predictor variables, X, and
estimated parameters, β. A linear addition function is assumed for g(X, t, β):

                   r
g ( X i , t , β ) = ∑ β j X ji                                                              (2)
                  j =0



The X ji ( j = 0,..., r ) , are the values of the r covariates for the driver i. The value of X oi = 1 so
that β o represents an intercept parameter in the regression model.

Equation 2 can be expanded to:

                          r               T −1                 s −1
     g ( X i , t , β ) = ∑ β j X ji + ∑ β r + k X *ki + ∑ β r + (T −1) + n X ni (ti )       (3)
                         j =0              k =1                n =1




                                                                      5
The first term of the right-hand side of Equation 5 represents time-independent covariates,
the effects of which are assumed to be independent of time. The second term represents the
time main effect (in this application, driving time), and X *ki represents the kth time interval
for driving time. A trip with a length of k time intervals would be represented by a series of
indicator variable with X *ki = 1 . The last term represents the time-dependent covariate (in
this application, time of day). The parameters β r +(T −1) + n are a series of coefficients
associated with the s intervals used as categories for the time-dependent covariate (Lin,
Jovanis and Yang, 1994).

2.2 Deriving multi-day driving schedules

The effect of multi-day driving on crash is a challenging phenomenon to quantify. The
elements of such an analysis must recognize that driving occurs with the following sources of
variability: different times of day; for trips of potentially differing durations; in differing
sequences involving off-duty time and off-duty days (i.e. drivers may be off-duty for one
more days before returning to the driving task). In particular, there may be an interaction
between the duration of driving and time of day. Statistical models attempt to capture this
phenomenon by using interaction terms between driving time and driving schedule to
identify a range of times during the day when crash risk may be high or low.

Multi-day driving is characterized as an attribute of each individual driver. As such it is
included as a driving attribute in the logistic regression model. Drivers are grouped into
common schedules (identified through different procedures depending on the data set). Each
driver is assigned to one and only one group; depending on the outcome of the model
estimation, each driver in a group is assigned the same risk for multi-day driving. Groups
vary in size from the low 20’s to several hundred.

There are several techniques that need to be applied to the data to facilitate the modeling of
driving hours and accident risk. A unique method has been developed (Kaneko and Jovanis,
1992) to group multi-day driving patterns into a smaller more manageable set that can be
used for crash risk modeling. The procedure uses the driving pattern for an individual driver,
described as the driving status for the individual on the day of the crash for each 15 minutes
of that day. In addition, the status of the driver is recorded for each 15 minutes of the prior 7
days. Given 24 hours in a day, four 15-minute periods in an hour and 7 days of interest, this
yields 24 times 4 times 7 or 672 dichotomous variables, coded as a 1 if the driver was on-
duty or driving and a 0 if not. This dichotomous characterization attempts to capture the
effect of the hours of service that regulate hours-on-duty over multiple days. The research
team explores several clustering approaches to determine if other types of carriers with
different operations may require different numbers of driving patterns to characterize their
operations. The driving pattern number to which the driver is a member is then used as a
predictor of crash risk in the subsequent crash model (e.g. Jovanis, Kaneko and Lin, 1991;
Lin, Jovanis and Yang, 1993, 1994).




                                                6
An extension of this technique uses manually extracted common schedules observed in the
data, classifying about half the data set. The remaining drivers are then classified using
cluster analysis. This method is applied in the first set of models using data from the 1980’s.

The second method breaks the day into 7 approximately equal time periods and allocates
drivers into one of these time periods if they drive a regular schedule over the 3-4 days prior
to the day of interest. Drivers without regular schedules are then checked for an advancing
schedule (one with periodicity less than 24 hours), a delaying schedules (one with periodicity
greater than 24 hours) and highly irregular (one with no apparent pattern at all).

2.3 Time of day

The time of day of travel is also included as a predictor. Previous research (Lin et al., 1993),
because of data limitations, divided the day into 12 2-hour time periods. This research uses a
4-hour window for time of day.

2.4 Experience

While an attempt was made to include driver experience, this variable proved very difficult
to collect as these data were maintained at the driver’s home terminal, not the centralized
location where crash data were located. As a result, experience was not used as a predictor
variable in this study.

2.5 Sleeper operations

The safety implications of sleeper berth operations are investigated by adding information
about crashes occurring with sleepers and a sample of non-accident sleeper trips. Sleeper
operations shall then be used as a dichotomous variable: 1 if a crash or non-accident
exposure trip involves a sleeper and 0 if not. Interaction terms can be used to determine if
the time-dependant risks change at all based upon the type of driver operation; separate
models of sleeper operations are also tested to explore if the underlying crash risk of
operation differs from non-sleeper terminal to terminal operations.

2.6 Circadian effects and night operations

A review of the comments received during the hours of service Notice of Proposed
Rulemaking (NPRM) indicates that late night and early morning operations may be related to
driver safety. Sleep research suggests that operations that span times of typical low alertness
due to circadian effects (approximately 4-6AM) pose particular challenges to safe operations.

The Penn State team used several statistical approaches to conduct this comparison,
including interaction terms. To the extent possible, specific comparisons are made of crash
risk vs. hours driving for trips that would have their last few hours occurring during 4-6AM.
This risk was compared to that of other times of day.




                                               7
3. DATA DESCRIPTION AND ANALYSIS – DATA SET 1

3.1 Data description

All crash data are obtained from a national less-than-truckload firm from 1984 to 1985. At
the time of data collection, the company conducted operations from coast to coast, with no
sleeper berths. The findings are thus not intended to typify the trucking industry as a whole.
The carrier undertook scheduled service between its own terminals, with significant
knowledge of the time to be taken to complete trips and safety supervisors in the field to
verify driver behavior. This reduces the incentive for drivers to misstate driving hours on
their logs. While an independent assessment of driving hour data was not feasible, given the
type of service provided and the steps taken by the company to adhere to U.S Department of
Transportation (U.S. DOT) service hour regulations, the researchers believe the driving hour
data reflect operations that adhere to HOS regulations in existence at the time.

The analyses presented in this paper use data from 1984 through 1985. The data set consists
of accident-involved drivers and non-accident-involved drivers. For accident involved
drivers, the day of the crash serves as the starting point for additional data collection (this day
can be called the day of interest). For each crash-involved driver, driving logs are assembled
and coded which represent the duty status of the driver on the accident-involved day as well
as the previous 7 days. These data are used to develop a detailed characterization of the
driving status of the accident-involved drivers for each 15 minutes of each day for an eight
day period (the accident day and 7 prior days). This data structure corresponds to the hours
of service policy in effect at the time of operations (maximum multi-day driving or on-duty
time of 70 hours in eight days).

In addition to the crash data, a data set of 2 non-accident-involved drivers was assembled by
having a person from the trucking firm randomly select 2 sets of driver logs from the same
terminal as each accident-involved driver. In this way, 2 non-accident drivers are selected as
controls for each crash involved driver, where the selection from the common terminal serves
as a mechanism to help control for driving environment. A day and a trip within the day
were selected at random for each non-crash driver so there would be a starting point of a
randomly selected trip that would be comparable to the accident trip for the crash-involved
drivers (again, this day that begins the measurement of the driving schedule is referred to as
the day of interest).

The data set includes 954 accident-involved drivers and 1506 non-accident drivers in 1984;
887 accident drivers, and 1604 non-accident drivers in 1985 for a total sample size of 5050
drivers. This is a large data set for a truck safety study, estimated to encompass
approximately 16 million vehicle miles of travel (assuming an average of 8 hours driving
over the 8-day period and an average speed of 50 mph). There are many possible schedules
for drivers over an eight-day period; it is only through the use of a large data set that common
schedules can be identified for enough drivers to allow statistical estimation of crash risk.




                                                8
Under the hours-of-service regulation enforced during the time of data collection, drivers
could drive for a maximum of ten hours followed by a mandatory minimum eight-hour off
duty period. Driving time was divided into 10 one-hour periods, starting with the first hour.

3.2 Identification of multi-day driving schedule

Previous research (Jovanis et al., 1991; Kaneko and Jovanis, 1992; Lin, et al., 1993; Lin, et
al., 1994) used cluster analysis on a small subset of the study data (either 6 months or 1 year
of crash and non-crash data). As a result, only 10 sets of driving schedules were identified.
For this analysis, data for a full 2 years were used. As a starting point, the Driver Fatigue and
Alertness Study was carefully reviewed and an attempt made to extract driving schedules
from the data set that included those from DFAS (Wylie, et al., 1996; p 3-6 to 3-7). In
particular, an attempt was made to identify drivers with regular and irregular schedules over
multiple days. It was not possible to identify drivers with 12 hour driving times, as used in
the DFAS, but the pattern of day and night driving and irregularity of schedules were
specifically sought within the crash data.

Drivers were manually grouped based upon their multi-day schedule by searching through
the record of the 5050 drivers to find those who started driving at approximately the same
time every day; for example, starting to drive at 10AM the day before the crash (or more
generally the day of interest). An accuracy of plus or minus 2 hours was used to group
drivers with similar driving schedules. The set of drivers starting at 10AM on the day before
the day of interest was then searched further for those drivers who started driving at 10AM
the previous day (2 days before the crash). This process was continued for 3 and 4 days
before the crash as well. While searching back in time from the day of interest, the sample
size of drivers was successively reduced, so in some cases it was only possible to go back
one or two days (see Table 1 for summary of manually extracted driving schedules and their
sample sizes). The occurrence of a crash on the day of interest was irrelevant to this search;
the driving schedules on the days prior to the crash (or randomly selected matching trip) were
the only information used to form the schedules.

Figure 1, an example of one manually derived driving schedule, helps illustrate the method
and the outcome of the driver grouping. The figure illustrates the percentage of drivers
within the group that are on duty or driving for every 15 minutes for 7 days prior to the day
of interest (here time zero is midnight). Each day is represented by 24 hours, so hour 168 is
midnight on the beginning of the eighth day (the day of interest). In this particular driving
schedule, over 90% of the drivers are on duty or driving starting at around 10AM for the 2
days prior to the day of interest. Prior to these 2 days, the drivers have a less well-structured
pattern of driving, with at most 40% of the drivers on duty at any one time. Note also that
there is virtually no early morning driving for the 2 days prior to the day of interest. This
grouping then represents drivers with a regular, largely daytime driving schedule for 2
consecutive days. The figure contains 2 very similar lines, one representing data from 1984
and one from 1985, even though the procedure would not necessarily lead to this outcome.




                                                9
                                                    Cluster 22
                            1
                           0.9            84
                                          85
                           0.8
   Proportion of drivers




                           0.7
                           0.6
                           0.5
                           0.4
                           0.3
                           0.2
                           0.1
                            0
                                 0   24        48   72     96    120   144   168
                                                          Time

Figure 1. Example of regular multi-day driving schedule – Start driving at 10AM for 2 days
prior to day of interest.


Table 1 summarizes all 23 manually-developed driving schedules; these schedules are
labeled C21 through C43. Note that schedules C21 through C28 are regularly scheduled
drivers who started driving at either 10AM or midnight for 1-4 days before the crash (Figure
1 represents schedule C22). These particular times were selected because they match the
time of day used in the regularly scheduled driver in DFAS. In addition to time of day, there
is an interest in the off duty status of drivers. Drivers who had one or more days off duty and
regular driving on previous days are represented in driving schedules C29 to C35.

Irregularly scheduled drivers were first extracted based upon the irregular schedules driven in
DFAS. Schedules C36 and C37 were derived from the description of the irregular schedule
in the DFAS report. Additional irregular schedules included:
    • drivers who alternated the start of driving between 7PM and 10PM (schedules C38
        through C41),
    • drivers starting driving at 10PM the day before the crash and had progressively early
        start times on each day previously (e.g. 7 PM two days before the crash and then 4PM
        3 days previously),
    • drivers with no driving the 2 days prior to the crash and very infrequent driving
        previous to those days; these drivers were grouped in schedule C43.
An example of irregularly scheduled driver group C39 is shown in Figure 2. As in Figure 1,
the 2 lines representing separate years of data are very similar.




                                                         10
Table 1. Manually-identified Driving Schedules

   Schedule Number          4 Days           3 Days           2 Days       1 Day Prior
     (Sample Size)      Prior to Crash   Prior to Crash   Prior to Crash     to Crash

       C1-C20                       Created using cluster analysis software
       C21 (481)                -                -                -            10 am
       C22 (125)                -                -             10 am           10 am
       C23 (28)                 -             10 am            10 am           10 am
       C24 (19)               10 am           10 am            10 am           10 am
       C25 (517)                -                -                -            12 am
       C26 (134)                -                -             12 am           12 am
       C27 (52)                 -             12 am            12 am           12 am
       C28 (17)               12 am           12 am            12 am           12 am
       C29 (32)                 -                -             10 am          Off-Duty
       C30 (20)                 -             10 am            10 am          Off-Duty
       C31 (41)                 -                -             12 am          Off-Duty
       C32 (19)                 -             12 am            12 am          Off-Duty
       C33 (11)               12 am           12 am            12 am          Off-Duty
       C34 (29)                 -             10 am          Off-Duty         Off-Duty
       C35 (25)               10 am           10 am          Off-Duty         Off-Duty
       C36 (83)                 -                -            3:30 pm          11 am
       C37 (20)                 -             7 pm            3:30 pm          11 am
       C38 (657)                -                -                -            10 pm
       C39 (113)                -                -              7 pm           10 pm
       C40 (67)                 -             10 pm             7 pm           10 pm
       C41 (24)               7 pm            10 pm             7 pm           10 pm
       C42 (20)                 -              4 pm             7 pm           10 pm
       C43 (362)                -                -           Off-Duty         Off-Duty




                                            11
                                                     Cluster 39
                              1
                            0.9            84
                                           85
    Proportion of drivers



                            0.8
                            0.7
                            0.6
                            0.5
                            0.4
                            0.3
                            0.2
                            0.1
                              0
                                  0   24        48   72     96    120   144   168
                                                           Time

Figure 2. Example of irregular schedule – Initiate driving 10PM one day prior and 7PM two
days prior to day of interest


After allocation to the 23 manually derived groups, there remained approximately 2500
drivers unallocated. Cluster analysis was used to allocate these remaining drivers to one of
20 clusters using the same procedure as the previous research (e.g. Kaneko and Jovanis,
1991). Schedules derived from cluster analysis were assigned schedule numbers C1 through
C20. Table 2 contains a qualitative description of the nature of the driving schedule for each
of the 20 clusters, including the sample size. Figure 3 is an example of a schedule identified
through cluster analysis, Schedule C7. It shows:
        • The drivers in this schedule (109 in all) drive during the night and early morning
            hours starting 4 days and continuing during the 3rd day before the day of interest.
        • Two days before the day of interest (around hour 144) there is little driving with
            most drivers seeming to be off duty during this time.
        • On the day before the day of interest, drivers again start to drive, but a bit earlier
            than before, starting at times more like late afternoon and early evening.
        • Around the night of the 4th day before the crash day, 90% or more of the drivers
            are on duty; there are also very few times when no drivers are on duty. This is in
            contrast to the manually derived schedules which are more “precise” in the sense
            that they have more well-defined peaks and troughs.

Table 2 contains a qualitative description of the nature of the driving schedule for each of the
20 clusters, including the sample size.




                                                          12
                                            Cluster 20-7
                                             Cluster 7
                1
                         com-84
                         com-85
               0.9


               0.8


               0.7


               0.6
  Proportion




               0.5


               0.4


               0.3


               0.2


               0.1


                0
                     0   24       48   72          96      120        144       168        192
                                                  Time




Figure 3. Example of schedule derived from cluster analysis


3.3 Model results and interpretation

Two sets of models were estimated with the data. Model 1 is developed to assess the effect
of driving time where the time is divided into 10, one-hour periods with the first hour
(designated T0) serving as the baseline. The second model retains driving time and adds as
covariates the 43 driving schedules manually derived and developed by cluster analysis. The
interpretation of the model is that a parameter being statistically different from zero implies
that a driver with that characteristic has a significantly higher crash risk, compared to the first
hour. In this way the model estimates the relative risk of a crash, compared to the baseline.
The baseline for multi-day driving schedules is schedule C22, which consists of daytime
driving for 2 days prior to the day of interest; changes in risk for driving schedules are
relative to this baseline risk.




                                                  13
Table 2. Description of Driving Schedules Derived from Cluster Analysis.

 Cluster                                 Description                                  Sample
    #                                                                                  Size
   C1       Regular night, AM driving; 3 days before day of interest                     86
   C2       Consistent regular daytime driving for all 7 prior days                     200
   C3       Afternoon and night driving 1 day prior; day off 2 days prior, and          146
            afternoon and night driving previous days
    C4      Little driving 2 days prior; consistent daytime driving prior days          114
    C5      Little driving 1 day prior; daytime driving 2-3 days prior                   63
    C6      Early morning to noon driving consistently for all days                     152
    C7      Little driving 1 day prior; night and early morning driving                 109
            consistently for 4 – 5 days prior to day off.
    C8      Night and early AM driving; most drivers on duty 5 days prior to            121
            day of interest; decreasing numbers on duty to 1 day prior
    C9      3-4 days off duty just prior to day of interest, but night and early         97
            morning prior to that
   C10      Consistent day driving 4 days prior; little driving 6-7 days prior          123
   C11      Night and early AM driving 2-3 days prior; day off 4 days prior;            101
            consistent night and early morning driving before that
   C12      Consistent afternoon and late night driving for 2 days prior; little        182
            driving for 3-5 days prior
   C13      Evening and night driving day before, with some drivers on duty 2           146
            days before; little driving 3-5 days prior
   C14      Late night driving night before; some off duty 2 days before, but           113
            very consistent night and early morning driving 3-7 days before
   C15      Intermittent daytime driving 1-3 days before; very consistent                86
            daytime driving 4-7 days before
   C16      Consistent afternoon and night driving for 4 days prior                     156
   C17      Night and early morning driving for 3 days prior; almost no                 148
            driving 5-7 days prior
   C18      Very consistent daytime driving 1-2 days prior; day driving before           97
            that but not with high % of drivers
   C19      Daytime driving 2 days before; minimal driving 3-7 days prior               138
   C20      Night and early morning driving 3-4 days prior; 5 days prior is off         104
            duty; 6-7 days prior night and early morning



3.3.1 Interpretation of Model 1

As seen in Table 3, the positive parameter in each covariate represents an increase in the log
of the odds ratio or, more simply, an increase in the probability of accidents among the
drivers in the specific driving time category compared to the drivers in the baseline category
(i.e. the first hour). All driving hour variables are significant at α =0.05, which leads to the
rejection of the hypothesis of constant hazard over time. The crash risk increases slightly,


                                               14
but significantly, as driving time increases through the fourth hour of driving. Statistical tests
of equality of the parameters 1 through 4 fails to reject the null hypothesis that the parameters
are equal. Parameters for hours 5-10, however, are all significantly higher than the baseline
first hour, and significantly higher than hours 2-4, but are unable to be differentiated from
each other in additional statistical tests. One may thus infer that crash risk appears to
increase only slightly between the first and 4th hour of driving, increases significantly in the
fifth hour, and is sustained at a higher level through hour ten. Importantly, the risk trend with
driving time differs in comparison to earlier findings (e.g. Lin, et al., 1993): the risk increase
after hour 4 (variable T5) is not nearly as steep, particularly in the last hour of driving. While
unable to statistically differentiate the crash risk, the trend in risk is a general increase from
hours 5 through 10.

            Table 3. Model 1 Estimates: effect of driving time
                               coefficient       S.E.          Sig.        Exp(B)
               Constant          -1.238          .707          .080         .290
              D.H. < 1*                                                     1.000
             1 ≤ D.H. < 2         .229           .113          .043         1.257
             2 ≤ D.H. < 3         .348           .111          .002         1.417
             3 ≤ D.H. < 4         .287           .114          .011         1.333
             4 ≤ D.H. < 5         .623           .107          .000         1.865
             5 ≤ D.H. < 6         .601           .109          .000         1.825
             6 ≤ D.H. < 7         .608           .111          .000         1.837
             7 ≤ D.H. < 8         .678           .112          .000         1.969
             8 ≤ D.H. < 9         .555           .122          .000         1.741
               9 ≤ D.H.           .746           .135          .000         2.108
            * baseline category


3.3.2 Interpretation of Model 2

Estimation results for model 2 are summarized in Table 4. All the driving time variables are
significant and have similar relative magnitudes and interpretation to those in model 1.

The pattern of significance for the multi-day driving schedules is of particular interest. In
keeping with the recommendations of others in the safety field (e.g. Hauer, 2004) the
discussion of each parameter will be conducted without a strict use of null hypothesis tests of
significance; a very liberal level of significance (any with alpha less than .25) will be used to
screen driving schedules and identify those of possible interest, a procedure consistent with
the research being exploratory in nature.




                                               15
Table 4. Model 2: Driving time and Multi-day Schedule
                 B          S.E.        Sig.       Exp(B)
   Constant    -3.688       .186        .000       .025
     T1          .230       .113        .041       1.259
     T2          .351       .111        .002       1.421
     T3          .292       .114        .010       1.339
     T4          .632       .107        .000       1.882
     T5          .612       .109        .000       1.844
     T6          .625       .111        .000       1.867
     T7          .700       .112        .000       2.014
     T8          .581       .122        .000       1.788
     T9          .786       .135        .000       2.194
     C1          .284       .247        .251       1.328
     C2         -.271       .223        .225       .763
     C3          .197       .222        .373       1.218
     C4          .238       .233        .307       1.269
     C5          .172       .275        .532       1.188
     C6          .129       .222        .560       1.138
     C7          .404       .230        .079       1.498
     C8          .363       .226        .109       1.437
     C9          .301       .235        .200       1.352
     C10         .080       .236        .735       1.083
     C11         .166       .243        .495       1.180
     C12         .240       .210        .252       1.272
     C13         .262       .219        .232       1.299
     C14         .086       .238        .716       1.090
     C15        -.229       .283        .418       .796
     C16         .286       .215        .182       1.332
     C17         .254       .217        .243       1.289
     C18         .150       .245        .540       1.162
     C19        -.039       .233        .866       .962
     C20         .289       .235        .219       1.334
     C21         .059       .192        .759       1.061
     C23         .251       .451        .579       1.285
     C24        -.480       .534        .368       .619
     C25         .311       .183        .090       1.365
     C26         .115       .226        .609       1.122
     C27         .370       .295        .210       1.447
     C28        -.283       .535        .597       .754
     C29        -.150       .420        .721       .861
     C30        -.457       .534        .392       .633
     C31        -.567       .418        .175       .567
     C32         .608       .384        .114       1.837
     C33        -.472       .736        .522       .624
     C34         .513       .332        .123       1.670
     C35         .451       .367        .219       1.570
     C36        -.099       .274        .717       .905
     C37        -.294       .484        .544       .745
     C38         .647       .182        .000       1.909
     C39         .482       .231        .037       1.619
     C40         .605       .248        .015       1.831
     C41         .337       .366        .357       1.401
     C42         .764       .370        .039       2.146
     C43         .479       .197        .015       1.614




                            16
Using the screening criteria of alpha less than 0.25, there are twenty one schedules identified
for further exploration (specifically C1, C2, C7-C9, C12, C13, C16, C17 and C20 derived
from the cluster analysis; C25, C27, C31, C32, C34, C35, C38-C40, C42, and C43 derived
manually). Importantly, 16 of the 21 involve increased crash risk associated with night and
early morning driving, irregular schedules or both. Closer examination indicates that 16 of
the 27 night and early morning driving schedules (specifically C1, C7-C9, C12, C13, C16,
C17, C20, C25, C27, C 32, C38-C40, C42) have elevated crash risk compared to the baseline.

The exceptions to the general trends are also of interest. There is a reduction in risk for
schedule C2, consistent regular daytime driving for all 7 days, further evidence of the safety
benefits of regular driving schedules. Schedule C31, drivers who started driving at midnight
2 days prior to the day of interest but had a day off in between, is one of the few driving
schedules that showed a decrease in crash risk associated with a day or more off-duty.
However, schedules C34 and C35 indicate increased risk for daytime driving, immediately
after 2 full days off duty, as does schedule C32 for drivers starting at midnight after 2 days
off duty.

Lastly, schedule C43 consists of drivers who are off duty for the 2 days prior to the day of
interest and prior to that are infrequently driving. This schedule may be reflecting drivers
from the “extra board” who may differ in some other fundamental ways from other drivers at
the firm; for that reason they are separated from the other schedules.

Taken as a whole, Model 2 shows rather conclusively that night and early morning driving
results in increased crash risk relative to daytime driving, and that irregular schedules during
night also have elevated risk. The benefits of extended off-duty time are unclear: in some
cases there are risk decreases, but there are also several cases of risk increases.

Comparison of parameter scale for driving schedule and driving time indicate that many
schedules have a relative risk increase comparable to driving time. For example, clusters
C32, C34, C38, C40, and C42 all have parameters in the range of 0.5 to 0.7, indicating a
relative risk increase of 60 to 90% compared to the baseline (see Table 4, column 5);
previous modeling did not indicate risk increases of nearly these magnitudes.

3.4 Discussion

Among the schedules that involved night driving and no days off immediately prior to the
day of interest, 9 (schedules C1, C12, C13, C16, C17, C20, C25, C27, C38) out of 12
schedules have elevated risk (see Figure 4 for summary). Drivers with one or two days off
immediately prior to the day of interest have elevated risk in 3 (C7, C8, C32) of 7 cases; and,
drivers with irregular schedules have elevated risk in 4 (C9, C39, C40, C42) of 8 cases.
These detailed comparisons further highlight the elevated risk posed by night driving
compared to the baseline regular daytime driving.

There is also evidence that even as much as a 24 hour off-duty period may not be sufficient
to alleviate the elevated risk of night and early morning driving. Driving schedules C7 to C9




                                               17
           Daytime                                                         Nighttime and Early Morning




                                        Number of Driving Schedules
                                                                                    12

                                                                      Unable to
                                                                       Detect
                                                                       Change

                 9                                                                  9

                                                                                                                             8

                                                                                                        7
                                                                                                               Unable to
                                                                                                                Detect
    Unable to                                                                            Unable to              Change
     Detect                         5                                                     Detect
                                                                      Increase in
     Change                                                                               Change
                                                                      Crash Risk
                       Unable to                                                                                             4
                        Detect
                        Change                                                                          3
                                                                                                               Increase in
                                    2
                                                                                         Increase in              Risk
                      Increase in                                                           Risk
                 1
                         Risk
     Decrease

    Driving on                                                        Driving on
                      1 or 2 Days                                                        1 or 2 Days            Irregular
    Day Before                                                        Day Before
                          Off                                                                Off                Schedule
      Crash                                                             Crash

         Unable to Detect Change                                      Decrease in Risk                 Increase in Risk

Figure 4. Detailed analysis of crash risk during daytime and Night/Early morning driving
schedules


(averaging about 100 drivers in each group) involve drivers with night and early morning
driving and include large amounts of off-duty time one or two days prior to the day of
interest; all show elevated crash risk. A similar result appears for schedule C32, although the
sample size is only 19 drivers. These findings raise questions about the efficacy of a
“restart” period (Smiley and Heslegrave, 1997); there appears to be evidence from this
analysis that 24 and perhaps 48 hours may be insufficient, particularly for night and early
morning driving. Further, the elevated risk associated with schedules C34 and C35 indicate
that two days off duty prior to driving may actually elevate risk, compared to more regular
schedules even for day time driving. This may be due to the relative unfamiliarity of driving
a heavy vehicle again, or other personal factors, but the evidence exists for those driving at
night as well as during the day.

These results differ from those in the DFA study in that they show the continued importance
of driving time (time on task) as a significant correlate of crash risk. This result has been


                                                                          18
consistently obtained by one of the co-authors, admittedly using partially overlapping data
sets. It is interesting to recall, however, that increases in crash risk beyond the 4th hour was
also observed in the 1970’s (Harris, et al. 1972). This remains an area of additional study.

Examining the findings in the context of the HOS regulations implemented in 2004 in the US,
there appears to be support for the changes in regulations that sought more regular schedules.
Several of the driving schedules with the highest relative crash risk (e.g. C38, C39 and C40)
involved irregular schedules. While the sample size in each group was small, the increase in
relative risk was large and significant. Previous studies using smaller crash data sets were
unable to identify this important effect.

3.5 Conclusions – data set 1

The detailed analysis of drivers representing an estimated 16 million vehicle miles of travel
has revealed a stronger consistency between field experiments, such as DFAS, and crash data
analysis than has previously been reported. In particular:
    a. The time of day of driving is significantly associated with increased crash risk:
       drivers with predominately night and early morning schedules have crash risk 20-
       70% higher than drivers in the baseline regular daytime driving schedule.
    b. Drivers with irregular schedules also have elevated risk, again in the 30-80% range.

These findings of convergent validity are an important independent verification of some of
the DFAS findings.

In addition, there remains a persistent finding of increased crash risk associated with hours
driving, with risk increases of 30 - 100% compared to the first hour of driving. These
increases are less than previously reported and are of similar magnitude to the risk increases
due to multi-day schedules. Finally, there is some evidence, although it is far from
conclusive, that there may be risk increases associated with significant off-duty time, in some
cases in the range of 24-48 hours.

Areas for additional research are many, including further studies of crash risk associated with
extended off-duty time, closer examination of irregular schedules that better reflect truckload
operations and analysis of irregular schedules with primarily daytime driving (largely non-
existent in this data set) to further explore the effect of variability. These findings, taken as a
whole, support the case for continued research and evaluation of HOS along with other truck
safety regulatory actions.




                                                19
4. DATA DESCRIPTION AND ANALYSIS – DATA SET 2

4.1 Data description

The objective of this analysis is to explore a number of questions regarding the safety
implications of various aspects of HOS policy.

Crash data are collected from 2 national carriers operating a mix of sleeper berth and
terminal-to-terminal operations. Fed Ex Ground and ABF supplied data for the study. In
keeping with the confidentiality agreements with the firms, all models and data will be
reported as aggregate findings.

The data set consists of accident-involved drivers and non-accident-involved drivers. For
accident involved drivers, the day of the crash serves as the starting point for additional data
collection (this day can be called the day of interest). For each crash-involved driver, driving
logs are assembled and coded which represent the duty status of the driver on the accident-
involved day as well as the previous 7 days. These data are used in the estimates of 11th hour
usage through out the year. This data structure corresponds to the hours of service policy
currently in effect for these firms: drivers are permitted a maximum multi-day driving or on-
duty time of 70 hours in eight days.

In addition to the crash data, a data set of 2 non-accident-involved drivers was assembled by
a random draw of 2 sets of driver logs from the same terminal as each accident-involved
driver. In this way, 2 non-accident drivers are selected as controls for each crash involved
driver, where the selection from the common terminal serves as a mechanism to help control
for driving environment. A day and a trip within the day were selected at random for each
non-crash driver so there would be a starting point of a randomly selected trip that would be
comparable to the accident trip for modeling the effect of driving time on crash risk. At Fed
Ex, the draw was conducted from boxes of driving logs by Penn State students. At ABF, it
was performed by their staff. The data at hand represent a total of 122 crash-involved drivers
and 243 controls.

The modeling approach is the same as that used in section 3 of this report. Time-dependent
logistic regression is used as the basic model to assess crash odds. The three crash risk
models developed during this phase of the research include:
    • Model A: This explores the effect of driving time by coding each hour of driving as a
        separate variable. This allows us to fully explore non-linearity in the effect of driving
        time. The first hour is selected as the baseline (no parameter is estimated for this
        variable), so all effects of driving time are relative to the baseline. Sleeper berth
        operations are denoted for both crash-involved and non-crash trips, allowing us to test
        the hypothesis of a constant increase of decrease in risk due to sleeper operations.
    • Model B: This model aggregates the last 10 hours of driving into 2-hour increments,
        retaining the first hour as the baseline. This more parsimonious model has fewer
        degrees of freedom and likely greater statistical significance. Sleeper berth
        operations are coded as in Model A.



                                               20
   •   Model C: This model aggregates the first 10 hours of driving into five 2-hour
       increments, with the 11th hour being modeled as a single hour. This model was
       developed in response to issues arising with Model B, and also in response to a desire
       to estimate the relative risk of the 11th hour separately. Sleeper berth operations are
       modeled as in A and B.

4.2 Model results and interpretation

4.2.1 Model A

        The results of the estimation for Model A are summarized below. The first table
provides details about the coding of the driving time, and the sample size of crashes in each
time period. In addition, the non-accident column reports the number of non-accident trips
which terminated during that time period (e.g. there were 88 driving trips which safety
completed their travel during time period T9). Table 6 indicates that the model as a whole is
marginally significant (the “sig.” column is .146, while it is conventional for it to be .05 or
less for statistical significance).

Table 5. Data Summary for Model A
                                       Non-                                                Non-
    Driving Time (hr)     Accident                     Driving Time (hr)       Accident
                                      Accident                                            Accident
    D.H. < 1       (T1)      10           0           6 ≤ D.H. < 7     (T7)       9         30
   1 ≤ D.H. < 2    (T2)      11           0           7 ≤ D.H. < 8     (T8)      15         49
   2 ≤ D.H. < 3    (T3)      13           2           8 ≤ D.H. < 9     (T9)       7         88
   3 ≤ D.H. < 4    (T4)      14           0           9 ≤ D.H.<10      (T10)      9         78
   4 ≤ D.H. < 5    (T5)      14           8           10≤ D.H. ≤11     (T11)      7         61
   5 ≤ D.H. < 6    (T6)      12          27                  Total               121        243



Table 6. Omnibus Tests of Model Coefficients
                  Chi-square      df                     Sig.
 Step 1 Step            15.877        11                        .146
         Block          15.877        11                        .146
         Model          15.877        11                        .146


        Table 7 indicates, perhaps not surprisingly, that most variables are not statistically
significant (“Sig.” for each parameter is greater than the conventional .05) except for T8, T10
and T11. These results are depicted graphically in Figure 5. Note that all the estimates in
Figure 1 show error bars that include 1 (i.e. the baseline) except the 3 time periods with
elevated relative risk. Based upon this model, the first 7 hours of driving have
indistinguishable risk; the risk increases in hour 8, drops in hour 9 and then increases again in
hours 10 and 11. The magnitude of the relative risk increases seem reasonable, however with



                                                 21
the 8th and 10th hours indicating risk increases of about 20% while the 11th hour is 113%.
This is rather different than previous driving time findings (e.g. Lin et al., 1993) and
indicates a model that has too many parameters. The response is to estimate Model B, which
aggregates the driving time for hours 2-11 into 2-hour increments.

Table 7. Estimation Results: Model A.
                   B        S.E.    Wald      df    Sig.     Exp(B)    95.0% C.I. for EXP(B)
                                                                         Lower       Upper
   T2             .217      .435     .248     1     .618     1.242        .530        2.912
  T3              .484      .415    1.360     1     .244     1.623        .719        3.664
  T4              .465      .421    1.218     1     .270     1.592        .697        3.635
  T5              .350      .435     .646     1     .422     1.419        .605        3.330
  T6              .328      .444     .547     1     .460     1.389        .582        3.317
  T7              .352      .455     .600     1     .439     1.422        .583        3.468
  T8              .967      .412    5.498     1     .019     2.629       1.172        5.899
  T9              .184      .525     .122     1     .726     1.202        .430        3.359
  T10            1.117      .473    5.582     1     .018     3.057       1.210        7.724
  T11            1.779      .522    11.633    1     .001     5.925       2.131       16.469
  S_B             .100      .196     .260     1     .610     1.105        .753        1.623
  Constant       -3.602     .327   121.149    1     .000      .027




                                             22
                   17
                   16
                   15
                   14
                   13
                   12
                   11
   Relative Risk




                   10
                    9
                    8
                    7
                    6
                    5
                    4
                    3
                    2
                    1
                    0
                        t2   t3   t4     t5      t6       t7      t8      t9      t10     t11
                                        Driving Hour Categories

Figure 5. Effect of Driving Time by Hour for Model A
Note: Standard errors are depicted by error bars about point estimates.


4.2.2 Model B

Tables 8-10 summarize the estimation of Model B. Table 9indicates that the model is
significant, while Table 10 indicates that all driving times after the first hour show elevated
relative risk with particularly high risk in the T5 and T6 time periods, representing driving
during hours 8 through 11. The last 2 columns show the 95% confidence interval, which is
shown graphically along with the point estimate of the parameter in Figure 6.

Note that each time period now shows a significantly elevated risk compared to Model A.
The relative risk is 200% higher in hours 2-7, 270% higher in time hours 8-9 and nearly
500% in hours 10-11. These estimates certainly seem high; confidence intervals are also
large (see Figure 2). While these results are statistically significant, they seem a bit
unreasonable. It does not seem reasonable that crash risk would increase by 200% by driving
1 or 2 additional hours. As a result, an additional model was estimated, Model C, which
aggregated the first 10 driving hours and left the last hour (the 11th) as a single hour.




                                               23
Table 8. Data Summary for Model B
                                        Non-                                                  Non-
   Driving Hour (hr)      Accident                      Driving Hour (hr)         Accident
                                       Accident                                              Accident
    D.H. < 1      (T1)         10         0            5 ≤ D.H. < 7        (T4)     21         39
  1 ≤ D.H. < 3    (T2)         27         2            7 ≤ D.H. < 9        (T5)     22         97
  3 ≤ D.H. < 5    (T3)         26         8            9 ≤ D.H. ≤ 11       (T6)     16         97
                                                                 Total              122        243

                  Table 9. Omnibus Tests of Model Coefficients: Model B
                                          Chi-
                                         square             df            Sig.
                     Step 1    Step      23.106             6             .001
                               Block     23.106             6             .001
                               Model     23.106             6             .001

Table 10. Estimation Results: Model B.
                                                                                     95.0% C.I. for
 Variable        B            S.E.     Wald            df         Sig.     Exp(B)       EXP(B)
                                                                                    Lower   Upper
  T2              1.073        .378      8.048              1      .005     2.923    1.393     6.132
  T3              1.123        .380      8.720              1      .003     3.074    1.459     6.479
  T4              1.011        .393      6.633              1      .010     2.749    1.273     5.934
  T5              1.313        .391     11.270              1      .001     3.719    1.727     8.007
  T6              1.760        .419     17.629              1      .000     5.814    2.556   13.223
  S_B              .150        .199       .569              1      .451     1.162     .787     1.714
  Constant       -3.619        .328    121.828              1      .000      .027




                                                  24
                   14
                   13
                   12
                   11
                   10
                    9
   Relative Risk




                    8
                    7
                    6
                    5
                    4
                    3
                    2
                    1
                    0
                        t2         t3              t4              t5              t6
                                        Driving Hour Categories

Figure 6. Relative Risk with Hours Driving: Model B.


4.2.3 Model C

The model estimation results for this model are shown in Tables 11-13 and Figure 7. Table
11 shows the revised definitions of the driving time variables with the first 10 hours driving
divided into five 2-hour time periods. Table 12 shows that the overall model fit is poor, with
significance level of .378. Despite the relatively poor fit, the model estimates seem more
reasonable than in Model B. Relative risk increases from the first to last driving hour, and
magnitudes vary between a 24% increase in hours 4-6 to a 250% increase in hour 11.
Graphically in Figure 7, risk rises slightly above 1 with a strong increase in the last hour.
The point estimates are much more consistent with the magnitudes obtained in the recent
TRB paper, with an older but much more extensive data set (Park, et al. 2005). This suggests
that the point estimates from the current data set may be reasonable, although the standard
errors are large because of the smaller sample size (compared to the TRB paper). As in all
previous models, the effect of the sleeper berth variable is positive, but unable to be
differentiated from zero.




                                              25
Table 11 Data Summary for Model C
                                               Non-                                                              Non-
   Driving Hour (hr)              Accident                             Driving Hour (hr)        Accident
                                              Accident                                                          Accident
   D.H. < 2               (T1)      22              0              6 ≤ D.H. < 8        (T4)       26              51
  2 ≤ D.H. < 4            (T2)      29              2              8 ≤ D.H. < 10       (T5)       15              120
  4 ≤ D.H. < 6            (T3)      23             29          10 ≤ D.H. ≤ 11          (T6)        7              41
                                                                               Total              122             243

                        Table 12 Omnibus Tests of Model Coefficients: Model C
                                    Chi-square           df                 Sig.
                         Step         6.418              6                  .378
                         Block        6.418              6                  .378
                         Model        6.418              6                  .378

Table 13 Estimation Results: Model C
                            B       S.E.          Wald         df             Sig.     Exp(B)          95.0% C.I. for EXP(B)
                                                                                                         Lower         Upper
  T2                      .364      .293       1.543               1          .214     1.440              .810         2.558
  T3                      .215      .309       .484                1          .487     1.240              .677         2.270
  T4                      .552      .302       3.340               1          .068     1.736              .961         3.138
  T5                      .329      .348       .893                1          .345     1.389              .703         2.747
  T6                      .949      .467       4.137               1          .042     2.584             1.035         6.449
  S_B                     .131      .200       .427                1          .514     1.139              .770         1.685
  Constant               -2.789     .230      146.987              1          .000     .061


                    7

                    6

                    5
    Relative Risk




                    4

                    3

                    2

                    1

                    0
                            t2               t3                        t4              t5                  t6
                                                   Driving Hour Categories

  Figure 7. Relative Risk with Hours Driving: Model C


                                                              26
5. DATA DESCRIPTION AND ANALYSIS – DATA SET 3

5.1 Data description

Data set 2 constrained the analyses that could be undertaken for the project because of
limitations in sample size. The team was able to enhance the data set by adding additional
data from Fed Ex and ABF and also successfully engaging Schneider national to share data.

Table 14 summarizes the data set which was used for the modeling and analysis during this
final phase of the project. While enhancing the sample size of data set 2, several additional
tasks were undertaken. The team spent significant effort error checking and verifying the
accuracy of our data. Several problems were identified, most often missing driver logs.
These problems were corrected to the extent possible by working with the involved carriers,
but several crash records were lost as a result of inadequate and missing driver logs.
Whenever a crash record was incomplete, we did not use the non-crash logs collected as
controls for that crash. This further attenuated our data set. Positively, the data are now very
thoroughly checked, particularly data received from carriers in the last few months. The
sample size is nearly twice that used in developing models in data set 2. This has allowed us
to develop much better models of driving time and the effect of multi-day work schedule.
This allowed the team to study the crash risk implications of these operations for the first
time.

          Table 14. Sample size for data set 3.
           Type of                             # of Observations
           Operation               Crash          Non-Crash              Total
           Non-Sleeper              115               213                328
           Sleeper                  116              249                 365
                                    231               462                693

The data collection and modeling approach are the same as described for data set 2. We
continue to use the time-dependent logistic regression model as the basic model for our study.

Table 15 summarizes the data broken down by driving time. The first and fourth columns
indicate the categories used for driving time; note specifically that the last category
represents driving in excess of 10 hours. This category is used to reflect any change in risk
associated with driving the 11th hour, added in the January 2004 HOS regulations. Note also
that there are 106 and 105 non-accidents trips which end in hours 9 and 10 respectively,
greatly reducing the sample size during the 11th hour.




                                              27
  Table 15. Summary of data concerning driving time – data set 3
     Driving Hour                            Non-             Driving Hour                          Non-
                             Accident                                           Accident
         (hr)                               Accident               (hr)                            Accident
       D.H. ≤ 1                28              1               6 < D.H. ≤ 7         24                62
     1 < D.H. ≤ 2              31              6               7 < D.H. ≤ 8         24                73
     2 < D.H. ≤ 3              29              9               8 < D.H. ≤ 9         16               106
     3 < D.H. < 4              19              7               9 < D.H. ≤10         12               105
     4 < D.H. ≤ 5              22             29              10 < D.H. ≤11         4                30
     5 < D.H. ≤ 6              22             34                   Total           231               462

Figure 8 contains definitions of the driving schedules used in this modeling; they were
developed based upon a review of the safety and driving schedule literature. In order to
capture the effect of driving during different times of day, a scheme was developed to
allocate each driver to a unique time of day based upon the time when they started to drive
(i.e. first driving after at least the mandatory 10 hours off duty). In all, 11 schedules were
used, 7 regular and 4 irregular. Given sample size constraints, this approach allows the
model to be sensitive to multi-day driving, while not as detailed as in a recent TRB paper by
the authors (Park, et al., 2005).


                 Pattern 1                  Pattern 3               Pattern 5                 Pattern 7

                                Pattern 2               Pattern 4               Pattern 6

 Midnight 2 AM               6 AM       9 AM      Afternoon      3 PM       6 PM            9 PM     Midnight


 Regular driving schedule:
 Pattern 1: DP1: drivers started driving during early morning (i.e. 2 AM to 6 AM)
 Pattern 2: DP2: drivers started driving during morning (6 AM to 9 AM)
 Pattern 3: DP3: drivers started driving during late morning (9 AM to 12 PM)
 Pattern 4: DP4: drivers started driving during afternoon (12 PM to 3 PM)
 Pattern 5: DP5: drivers started driving during late afternoon (3 PM to 6 PM)
 Pattern 6: DP6: drivers started driving during early night (6 PM to 9 PM)
 Pattern 7: DP7: drivers started driving during late night (9 PM to 2 AM)
Irregular driving schedule:
 Pattern 8: DP8: Advancing driving schedule (i.e. a schedule with periodicity less than 24
            hours; the driver starts driving progressively earlier each day)
 Pattern 9: DP9: Delaying driving schedule (i.e. a schedule with periodicity greater than 24
            hours; the driver starts driving later each day)
 Pattern 10: DP10: Alternating driving schedule (i.e. a schedule which alternates between 2
            start times every other day)
 Pattern 11: DP11: Highly irregular schedule (i.e. a schedule with no apparent pattern)

Figure 8. Driving schedule based on start time



                                                        28
5.2 Data Analysis for data set 3

While many models were developed and tested, five models are included in this report
because they are readily interpretable and represent the most refined models developed to
date. The models include consideration of driving time, driving schedule and whether the
operation was conducted in a sleeper berth or regular tractor. The five models developed for
this report and a brief discussion of their rationale are described below:

       Model D – This model includes all the driving schedules shown in Figure 8 as
       predictors, along with driving time, as defined in Table 14. Notice that the last
       driving time is the 11th hour of driving, the “new” hour added in the new HOS rules
       implemented in January 2004. All variables are categorical. Note we are starting
       with Model D to distinguish these models from the Models A-C described in the first
       interim report.
       Model E – This model is identical to Model D, but is estimated with crash and non-
       crash data from operations other than sleeper berth.
       Model F – This model is identical to Model D and E, but estimated with sleeper berth
       data only. The rationale for this approach requires additional discussion.
       While we included sleeper berth as a predictor in several previous models, the
       variable never achieved statistical significance. We were concerned that representing
       sleeper operations as a fixed effect may not be the best representation. Review of the
       raw data also revealed the possibility that patterns of crash occurrence were different
       with sleepers than non-sleepers. After the tables illustrating the results of the
       modeling, there is a discussion of additional statistical tests that seek to determine if
       Models E and F are significantly different from Model D. This is essentially a test of
       a hypothesis that the factors associated with crash risk in sleeper operations are
       different than those in non-sleeper operations.
       Models G and H – Finally, models are estimated with only interaction terms between
       driving pattern and driving time. This is intended to explore how driving time and
       time of day are related to crash risk. Separate models are again developed for non-
       sleeper and sleeper operations.


5.2.1 Discussion of Model D: Pooled model with all data

Tables 16 and 17 indicate that the model fits the data acceptably at normal levels of
significance. The last column in Table 18 quantifies the magnitude of the effect of the
variable on the crash risk, relative to the baseline for that variable. For driving time, the
baseline is the first hour of driving. For driving schedules, the baseline is pattern 6, initiating
driving during early night (6 PM to 9 PM). So, for example, the seventh driving hour has a
55% higher risk than the first hour (i.e. Exp (β) =1.555).




                                                29
                     Table 16. Test of Model D Coefficients
                                         Chi-square      df         Sig.
                      Step 1     Step     33.579         20         .029
                                 Block    33.579         20         .029
                                 Model    33.579         20         .029


                       Table 17. Model D Summary
                                    -2 Log     Cox & Snell    Nagelkerke
                                  likelihood    R Square       R Square
                         Step1     1831.168       .007           .022


The model in Table 18 has several important attributes beyond a statistically significant fit to
the data:
    • With the exception of the jump in relative risk in hour 2, the driving time has a risk
        indistinguishable from the baseline through the 6th hour, but then a steady, non-linear
        increase in risk thereafter. In the 11th hour of driving, the risk is more than 3 times
        that in the baseline first hour. This is the now familiar increase in relative risk with
        time-on-task. For ease of interpretation, the crash odds reflected by each parameter
        are plotted with their standard errors in Figure 9. Note that the standard errors
        increase with driving time, particularly during hours 10 and 11.
    • It is useful to compare the parameter values in this model with Model A, a
        comparable model using data set 2. The relative risk in Model A is much higher, but
        our experience with these models led us to believe that a larger sample would lead to
        a model with reduced risk at the margin. This belief is supported by Model D. While
        the underlying trend is similar to the models contained in the recent TRB paper (Park,
        et al., 2005), the level of risk is higher. Model D indicates risk increases of more than
        200%, whereas the TRB paper, drawing on a larger sample size, shows gradual
        increases of 70-100%. The authors believe the TRB paper results, derived from
        1980’s data, are better estimates of the relative risk; Model D is, however, a distinct
        improvement compared to the models from data set 3.
    • Another interesting aspect of Model D is the scale and significance of the parameters
        for multi-day driving schedule. All the regular schedules and all but one of the
        irregular schedules have crash risk greater than the baseline 6-9PM start time.
        Further, the scale of the parameters is in the same range as the parameter estimates for
        driving time; in fact, parameter values exceed the estimates of all but that for the 11th
        driving hour. This is a strong indication of the importance of multi-day driving on
        crash risk (one of the important findings of the recent TRB paper).




                                                30
5.2.2 Discussion of Model E: Non-sleeper berth operations

Tables 19 and 20 indicate a significant model fit at conventional levels of significance. Table
21 indicates that there are several important changes in the pattern of variable significance
compared to Model D:
    • The driving time risk increases in time periods 2, 3 and 5 as well as later time periods
       7 and 9. While the increases are of marginal statistical significance (p values of .117
       to .235) the parameter values are quite large.
    • The significance of driving time varies from 2-11 hours, likely reflecting the reduced
       sample of crash and non-crash data available for modeling.
    • The last driving time period contains no crash data, so the parameter value is not
       meaningful
    • All the fixed driving time patterns have coefficients that are significantly different
       from the baseline and of a magnitude higher than the driving time in the model. This
       is the first time we have seen consistent parameter estimates for multi-day driving
       patterns which are higher then driving time.
    • Irregular driving also has elevated crash risk, particularly schedules 10 (an alternating
       driving schedule) and 11 (a highly irregular schedule with no discernable pattern).


    Table 18. Variables in the Equation for Model D: Pooled model with all data.
                            B        S.E.       Wald         df        Sig.       Exp(B)
            T2            .418       .271       2.370        1         .124        1.518
            T3            .290       .282       1.058        1         .304        1.337
            T4           -.083       .313       .070         1         .791        .920
            T5            .121       .301       .161         1         .689        1.128
            T6            .227       .302       .566         1         .452        1.255
            T7            .441       .296       2.227        1         .136        1.555
            T8            .672       .297       5.127        1         .024        1.959
            T9            .569       .332       2.938        1         .086        1.766
            T10           .901       .367       6.036        1         .014        2.463
            T11          1.250       .573       4.761        1         .029        3.491
           DP1            .790       .428       3.401        1         .065        2.203
           DP2           1.045       .364       8.262        1         .004        2.844
           DP3            .628       .428       2.158        1         .142        1.874
           DP4            .713       .527       1.833        1         .176        2.040
           DP5           1.038       .411       6.376        1         .012        2.825
           DP7           1.014       .417       5.914        1         .015        2.756
           DP8            .510       .369       1.911        1         .167        1.665
           DP9            .477       .557       .733         1         .392        1.611
           DP10           .914       .386       5.620        1         .018        2.494
           DP11           .991       .346       8.222        1         .004        2.695
          Constant      -4.124       .377      119.714       1         .000        .016




                                              31
                           11


                           10


                           9


                           8
  Relative Accident Risk




                           7


                           6


                           5


                           4


                           3


                           2


                           1


                           0
                                t1   t2         t3       t4          t5        t6            t7       t8      t9   t10   t11

                                                                  Driving Hour Variable

Figure 9 Crash odds and driving time with Model D


                                          Table 19 Test of Model E Coefficients.

                                                                Chi-square              df            Sig.
                                           Step      Step         35.097              20              .020
                                            1        Block        35.097              20              .020
                                                     Model        35.097              20              .020




                                           Table 20. Model E Summary.

                                                         -2 Log           Cox & Snell         Nagelkerke R
                                            Step        likelihood         R Square               Square
                                            1                880.522                .015               .046




                                                                          32
        Table 21. Variables in the Equation Model E: Non-sleeper berth operations
                           B          S.E.          Wald     df     Sig.      Exp(B)
               T2        .596         .389          2.348    1      .125      1.815
               T3        .617         .393          2.460    1      .117      1.853
               T4        .171         .436           .153    1      .696      1.186
               T5        .491         .414          1.408    1      .235      1.634
               T6        -.132        .493           .072    1      .789       .876
               T7        .759         .409          3.440    1      .064      2.135
               T8        .331         .476           .484    1      .487      1.393
               T9        .800         .465          2.958    1      .085      2.224
              T10        .450         .671           .450    1      .502      1.569
              T11       -17.839    13251.707         .000    1      .999       .000
              DP1        1.258        .540          5.429    1      .020      3.519
              DP2        1.205        .511          5.568    1      .018      3.336
              DP3        1.047        .552          3.602    1      .058      2.850
              DP4        1.315        .730          3.241    1      .072      3.724
              DP5        1.127        .518          4.736    1      .030      3.087
              DP7        1.494        .500          8.929    1      .003      4.454
              DP8        .233         .514           .206    1      .650      1.263
              DP9       -17.374     5204.543         .000    1      .997       .000
             DP10        .996         .492          4.102    1      .043      2.708
             DP11        .905         .460          3.868    1      .049      2.471
            Constant    -4.233        .508          69.312   1      .000       .015
Baseline: Pattern 6→ drivers started driving during 6 PM to 9 PM (3hrs) – Early Night


5.2.3 Discussion of Model F Results: Sleeper berth operations

The results in Tables 22-2 indicate the sleeper berth models fit the data very well overall and
have several variables that are significantly associated with changes in crash risk. Among
the important findings of Model F are:
    • Driving time has the more traditional patterns of increased risk with driving time.
       The risk is particularly high in driving hours 8, 10 and 11.
    • Interestingly, the regular driving schedules appear to have relatively small association
       with crash risk, except for patterns 2 and 5.
    • Irregular driving has a very significant association with crash risk as all irregular
       schedules are significantly higher than the baseline. All irregular schedules have
       coefficients higher than that for the 11th driving hour reflecting a very significant
       association with increased relative crash risk.




                                               33
•   Both the magnitude and the pattern of parameter significance for this model are quite
    different from Model E. This leads us to suspect that crash risk has a different
    underlying pattern of association between the 2 types of operations.
•   Table 25 summarizes the results of a chi-squared test conducted to compare Models
    D, E and F. The null hypothesis is that the non-sleeper berth model is similar to the
    sleeper berth model (i.e. that Model E and F are indistinguishable from the pooled
    Model D). The alternate hypothesis is that the non-sleeper berth model has
    parameters that are not equal to the sleeper berth model. Since the chi-squared value
    (41.78) is greater than the critical value (31.41) the null hypothesis is rejected and we
    conclude that the set of coefficients are statistically different. The pooled model is
    inappropriate.



                 Table 22. Test of Model F Coefficients.

                                        Chi-square          df           Sig.
                  Step 1     Step          39.601           20           .006
                            Block          39.601           20           .006
                            Model          39.601           20           .006




                    Table 23. Model F Summary.
                               -2 Log         Cox & Snell        Nagelkerke R
                     Step     likelihood       R Square            Square
                     1          908.864              .015                .049




                                               34
        Table 24. Variables in the Equation for Model F
                           B        S.E.       Wald       df     Sig.      Exp(B)
                  T2      .244      .382       .407       1      .523       1.276
                  T3     -.064      .418       .024       1      .878       .938
                  T4     -.328      .457       .515       1      .473       .720
                  T5     -.283      .457       .383       1      .536       .754
                  T6      .488      .389       1.571      1      .210       1.629
                  T7      .101      .443       .052       1      .820       1.106
                  T8      .937      .387       5.874      1      .015       2.552
                  T9      .376      .481       .610       1      .435       1.457
                  T10    1.170      .455       6.623      1      .010       3.223
                  T11    1.637      .620       6.966      1      .008       5.141
                  DP1    1.005     1.128       .793       1      .373       2.731
                  DP2    1.847     1.029       3.221      1      .073       6.341
                  DP3    1.023     1.105       .858       1      .354       2.782
                  DP4    1.186     1.166       1.034      1      .309       3.274
                  DP5    1.709     1.108       2.379      1      .123       5.521
                  DP6     .860     1.128       .582       1      .446       2.364
                  DP8    1.553     1.033       2.260      1      .133       4.725
                  DP9    1.895     1.109       2.920      1      .088       6.650
               DP10      1.638     1.071       2.339      1      .126       5.143
               DP11      1.916     1.021       3.521      1      .061       6.796
              Constant   -4.909    1.043      22.146      1      .000       .007
Baseline: Pattern 7: drivers started driving during 9 PM to 2 AM (5hrs) – Late Night



 Table 25. Likelihood Ratio Test: Model E and F.
                         N_S_B Model           S_B Model             Pooled Model
 -2LL                    880.522               908.864               1831.168
 Chi Square              41.782                [1831.168 – (880.522 + 908.864)
 DF                      20
 Critical Value          31.41                 P=0.05


5.2.4 Discussion of Model G and H: Interaction terms only

In order to develop a better understanding of the interaction of driving time and multi-day
schedule, a final pair of models was developed with only interaction terms and no main
effects. The objective was to develop a model that would quantify the effect of time of day
on crash risk. It was recognized that by constructing interaction terms between driving



                                             35
schedule and driving time, it would be possible to isolate a particular narrow range of time of
day crash probability. The process followed in developing the models:
   • For each significant multi-day driving pattern, a series of models are built with an
       interaction with driving time. For example, for the non-sleeper berth drivers, driving
       schedules DP 1-7 and DP 10 and 11 were used to interact with driving time.
   • Each of the significant interactions in each of these models was identified for use in a
       subsequent model.
   • Table 26 summarizes the model results for the non-sleeper berth operations. The
       baseline is all drivers who are not members of one of the interaction groups. For
       example, the coefficient for DP 1 and T2 is interpreted as a more than 5 times
       increase in crash risk experienced by drivers using schedule 1 during the second hour
       of driving compared to all other drivers not otherwise represented in the table.
       Similar interpretations can be given to parameters in Table 27 for sleeper operations.
   • Results from the 2 models are summarized in a more interpretable form in Table 28.
       Because each driving schedule has a range of time of day when the driver starts to
       drive, we are able to identify a range of times of day when the crash risk significantly
       rises (these are shown in Table 28 in columns headed “likely time range”). It is not
       possible to identify a likely range for the irregular patterns, but it is for the regular
       schedules.
   • Notice that the increase in risk, while occasionally occurring during the early morning
       hours, is much more likely to occur during rush hour periods (e.g. DP 2 and T9 and
       T10; DP 5 and T2). While there are clearly some early morning times with increased
       risk, there are also many other times that occur outside the early morning.
   • Further, the pattern of interactions is quite different for non-sleeper operations
       compared to sleeper operations. This reinforces the notion that the underlying pattern
       of association between the 2 operations is different.
   • Relatively speaking, irregular schedules increase risk somewhat more frequently for
       sleeper operations than non-sleepers.




                                              36
Table 26. Variables in the Equation for Model G: Non-sleeper berth interaction.
                         B        S.E.          Wald     df         Sig.     Exp(B)
      DP1 by T2        1.672      .767          4.746     1        .029       5.322
      DP1 by T4        2.250      .659         11.668     1        .001       9.490
      DP1 by T9        2.181      1.109         3.871     1        .049       8.857
      DP2 by T1        1.754      .637          7.575     1        .006       5.776
      DP2 by T9        2.287      .800          8.165     1        .004       9.841
      DP2 by T10       3.098      .883         12.313     1        .000      22.143
      DP3 by T2        2.056      .649         10.032     1        .002       7.815
      DP3 by T3        1.776      .772          5.292     1        .021       5.905
      DP3 by T9        2.538      .820          9.584     1        .002      12.653
      DP4 by T2        2.181      1.109         3.871     1        .049       8.857
      DP4 by T5        2.404      1.131         4.519     1        .034      11.071
      DP4 by T6        2.692      1.167         5.319     1        .021      14.762
      DP5 by T2        1.393      .758          3.375     1        .066       4.026
      DP5 by T3        1.488      .761          3.823     1        .051       4.429
      DP5 by T5        1.651      .767          4.633     1        .031       5.210
      DP5 by T7        1.845      .775          5.666     1        .017       6.327
      DP5 by T10       2.181      1.109         3.871     1        .049       8.857
      DP7 by T1        1.348      .757          3.174     1        .075       3.851
      DP7 by T2        1.439      .759          3.591     1        .058       4.218
      DP7 by T3        1.539      .763          4.073     1        .044       4.662
      DP7 by T5        1.711      .769          4.949     1        .026       5.536
      DP7 by T6        1.845      .775          5.666     1        .017       6.327
      DP7 by T9        1.845      1.083         2.903     1        .088       6.327
      DP8 by T7        1.226      .623          3.870     1        .049       3.407
      DP8 by T9        1.488      .761          3.823     1        .051       4.429
      DP10 by T2       1.651      .556          8.828     1        .003       5.210
      DP10 by T5       1.522      .630          5.834     1        .016       4.581
      DP10 by T7       1.711      .636          7.244     1        .007       5.536
      DP10 by T8       1.711      .769          4.949     1        .026       5.536
      DP11 by T3       1.894      .396         22.838     1        .000       6.643
      DP11 by T4       .846       .617          1.884     1        .170       2.331
      DP11 by T5       1.207      .546          4.885     1        .027       3.342
      DP11 by T7       1.821      .468         15.136     1        .000       6.179
       Constant        -3.791     .171         491.814    1        .000           .023




                                          37
Table 27. Variables in the Equation for Model H: Sleeper berth interaction only
                          B         S.E.         Wald      df        Sig.         Exp(B)
       DP1 by T8        1.761       .775         5.157     1         .023         5.819
      DP1 by T10        2.167      1.126         3.702     1         .054         8.728
       DP2 by T1        1.404       .421        11.107     1         .001         4.073
       DP2 by T6        1.155       .539         4.587     1         .032         3.174
       DP2 by T8        1.284       .621         4.274     1         .039         3.612
      DP3 by T10        1.607      1.077         2.224     1         .136         4.987
       DP5 by T8        1.607      1.077         2.224     1         .136         4.987
       DP6 by T8        1.681       .771         4.750     1         .029         5.371
      DP8 by T10        2.329       .526        19.592     1         .000         10.268
       DP9 by T3        1.943       .786         6.111     1         .013         6.982
       DP9 by T9        2.454      1.162         4.457     1         .035         11.637
      DP10 by T8        2.349       .672        12.223     1         .000         10.474
      DP10 by T9        1.473      1.069         1.899     1         .168         4.364
      DP10 by T11       3.553      1.421         6.255     1         .012         34.912
      DP11 by T2        1.080       .416         6.743     1         .009         2.944
      DP11 by T4        1.082       .446         5.888     1         .015         2.950
      DP11 by T7        .760        .610         1.552     1         .213         2.137
      DP11 by T8        1.041       .615         2.861     1         .091         2.831
      DP11 by T9        1.681       .554         9.220     1         .002         5.371
      DP11 by T11       2.454       .827         8.797     1         .003         11.637
       Constant         -3.553      .134        699.457    1         .000          .029




                                           38
Table 28. Summary of results table for interaction term models

         Non Sleeper Berth Users                           Sleeper Berth Users
 Interaction    Accident    Likely Time        Interaction    Accident     Likely Time
    terms        Risk          Range              terms        Risk           Range
   DP1 by T2      5.322     3am< ≤ 8am         DP1 by T8        5.819      8am< ≤ 2pm
   DP1 by T4      9.490     5am< ≤10am         DP1 by T10       8.728     10am< ≤ 4pm
   DP1 by T9      8.857     10am< ≤ 3pm        DP2 by T1        4.073     6am< ≤ 10am
   DP2 by T1      5.776     6am< ≤ 10am        DP2 by T6        3.174     11am< ≤ 3pm
   DP2 by T9      9.841     2pm< ≤ 6pm         DP2 by T8        3.612     1pm< ≤ 5pm
  DP2 by T10     22.143     3pm< ≤ 7pm         DP3 by T10       4.987     6pm< ≤ 10pm
   DP3 by T2      7.815     10am< ≤ 2pm        DP5 by T8        4.987     10pm< ≤ 2am
   DP3 by T3      5.905     11am< ≤ 3pm        DP6 by T8        5.371      1am< ≤ 5am
   DP3 by T9     12.653     5pm< ≤ 9pm         DP8 by T10      10.268            n/a
   DP4 by T2      8.857     1pm< ≤ 5pm         DP9 by T3        6.982            n/a
   DP4 by T5     11.071     4pm< ≤ 8pm         DP9 by T9       11.637            n/a
   DP4 by T6     14.762     5pm< ≤ 9pm         DP10 by T8      10.474            n/a
   DP5 by T2      4.026     4pm< ≤ 8pm      DP10 by T9          4.364            n/a
   DP5 by T3      4.429     5pm< ≤ 9pm      DP10 by T11        34.912            n/a
  DP5 by T5       5.210    7pm< ≤ 11pm         DP11 by T2       2.944            n/a
  DP5 by T7       6.327     9pm< ≤ 1am         DP11 by T4       2.950            n/a
  DP5 by T10      8.857    12am< ≤ 4am         DP11 by T7       2.137            n/a
   DP7 by T1      3.851      9pm< ≤ 3am     DP11 by T8          2.831            n/a
   DP7 by T2      4.218     10pm< ≤ 4am     DP11 by T9          5.371            n/a
   DP7 by T3      4.662     11pm< ≤ 5am     DP11 by T11        11.637            n/a
   DP7 by T5      5.536     1am< ≤ 7am
   DP7 by T6      6.327     2am< ≤ 8am
   DP7 by T9      6.327     5am< ≤11am
   DP8 by T7      3.407          n/a
   DP8 by T9      4.429          n/a
  DP10 by T2      5.210          n/a
  DP10 by T5      4.581          n/a
  DP10 by T7      5.536          n/a
  DP10 by T8      5.536          n/a
  DP11 by T3      6.643          n/a
  DP11 by T4      2.331          n/a
  DP11 by T5      3.342          n/a
  DP11 by T7      6.179          n/a




                                          39
6. SUMMARY OF FINDINGS

Crash and operations data sets collected 20 years apart have been analyzed using time-
dependent logistic regression to assess the safety implications of aspects of hours of service
regulations. The analyses focus on driving time, multi-day driving schedules (including the
effect of schedule regularity and time of day), time off duty and interactions among these
variables. Important consistencies have emerged across the data sets as well as in
comparison of the data sets with other hours of service research such as the Driver fatigue
and Alertness Study (DFAS).

Crash odds (compared to a baseline of the first hour of driving) increase non-linearly with
driving time. There is a remarkable consistency in estimates of crash odds when driving 6
hours or longer as summarized below:

Driving Duration (hours)        1983-84 Odds            2004 Odds
       6-7                           1.8                   1.6
       7-8                           2.0                   2.0
       8-9                           1.7                   1.8
       9-10                          2.1                   2.5

The crash odds in the 11th hour, available only from the 2004 data set, were 3.5. The
implication is that extension of continuous driving time should be considered very cautiously.
Even though the HOS were changed in 2004 to extend the minimum off duty time from 8 to
10 hours, the odds of a crash remained similar. Economic benefits associated with extending
the driving hours may, however, mitigate the odds increase from the perspective of benefits
and costs.

Time of day of driving and regularity of schedule are associated with crash odds in both the
1983-84 and 2004 data sets.: In the 1983-84 data set night and early morning driving has
elevated odds in the range of 20-70% compared to daytime driving. Overall, 16 of 27 night
and early morning driving schedules had elevated risk, while this was true of only 3 of 14
day time schedules. Irregular schedules with primarily night and early morning driving had
relative risk increases of 30-80%. The risk increases with night driving existed in 3 of 7
schedules in which the driver had 1-2 days off duty. The crash odds associated with multi-
day driving are of comparable magnitudes to those of continuous driving time. Data analyses
from 2004 indicate that multi-day driving contributes more to crash odds increases than
driving time, a finding consistent with the DFAS study of the 1990s. Finally, there is some
evidence, although it is far from conclusive persuasive, that there may be risk increases
associated with significant off-duty time, in some cases in the range of 24-48 hours.

Comparisons of crash odds for sleeper berth and non-sleeper operations have revealed
statistically significant and practically important findings. For non-sleepers crash odds are
strongly associated with multi-day driving, somewhat stronger than with driving time (i.e.
many parameter values for multi-day driving are significant and their magnitude is generally
larger then the parameters for driving time). Driving time shows elevated risk in hours 2, 3,
and 5 in addition to an increase in risk in hours 7 and 9. Sleeper operations indicate strong



                                              40
association of crash risk and driving time, with particularly increased risk in the 8th, 10th and
11th hours (similar to the odds increases from the 1983-84 data). Interestingly, within sleeper
berth operations, there is much less association of crash risk with regular schedules and
substantial risk associated with irregular schedules. One possible conclusion is that the rigors
of sleeper operations appear to result in a greater decline in performance at extended driving
hours than for comparable non-sleeper operations. The research team would feel more
confident in this conclusion if other studies supported this finding as well. Statistical tests
confirm that models of crash risk are different for sleeper and non-sleeper operations. This
implies that subsequent modeling should treat these operations distinctly, to the extent
possible.

Detailed analyses of the association between crash risk and time of day using the 2004 data
confirm crash odds appear highest when extended driving occurs during the evening rush
hour and late afternoons. While other time periods and driving times also have significant
association with elevated risk (e.g. some early morning driving), there is a strong association
with daytime and early evening driving. Consistent with other models, sleeper berth users
have particularly strong association of crash risk and driving time, especially when the
driving schedule is irregular.

Experience obtained during this study offers the opportunity to identify several areas of
promising additional research including:
    1. There is a need for more extensive study of the crash odds correlates for sleeper
        operations. This area has increased potential importance with the 2005 change in
        HOS governing these operations.
    2. There is a need to collect data from many more firms, particularly those operating
        sleepers to verify the findings that were limited due to sample size restrictions.
        Sufficient assets should be available to construct a data base of 1500-2000 crashes
        and the equivalent non-crash sample.
    3. Greater economies for data collection will be realized if crash data reflected all DOT-
        reportable crashes for the involved firms. Given that data collection involves manual
        assembly and coding, it is cost-efficient to generally capture as much data as possible
        when the initial assembly (at the carriers headquarters) occurs.
    4. Assessment of safety implications of multi-day driving, including the 34 hour restart
        policy, would benefit greatly from assembly of 2 weeks of driving data for each
        driver. Eight days is not enough of a record to identify restarts for a large driver pool.
The study team believes such research could be undertaken very quickly and, over the next
12 -24 months, yield very important information about the safety implications of HOS
regulations.

7. REFERENCES

Abbott, R.D., Logistic regression in survival analysis, American Journal of Epidemiology,
Vol. 121, No.3, pp465-471, 1985.

Brown, C.C., On the use of indicator variables for studying time-dependence of parameters
in a response-time model, Biometrics, 31, pp 863-872, 1975.



                                               41
Campbell, K. L., M. H. Belzer, Hours of Service Regulatory Evaluation Analytical Support,
Task 1: Baseline Risk Estimates and Carrier Experience, UMTRI, UMTRI 2000-11, Ann
Arbor Michigan, 2000.

Efron, B., Logistic regression, survival analysis and the Kaplan-Meier curve, Journal of the
American Statistical Association, Vol. 83, No. 3, pp 414-425, 1988.

Freund, D. M., An Annotated Literature Review Relating to Proposed Revisions to the
Hours-of-Service Regulation for Commercial Motor Vehicle Drivers, DOT-MC-99-129,
Office of Motor Carrier Safety, U.S.D.O.T., 156p, November, 1999.

Hakkanen, H., and H. Summala, “Fatal Accidents among trailer truck drivers and accident
causes as viewed by truck drivers”, Accident Analysis and Prevention, Vol. 33, pp 187-196,
March 2001.

Harris, W., R. Mackie, C. Abrams, D. Buckner, A. Harabedian, J. O’Hanlon and J. Starks, A
study of the relationships among fatigue, hours of service, and safety of operations of truck
and bus drivers, BMCS-RD-71-2, Bureau of Motor Carrier Safety, Federal Highway
Administration, Washington, D.C., 1972, 232p.

Hosmer, D.W., and S. Lemeshow, Applied Logistic Regression, John Wiley and Sons, Inc.,
N. Y. 1989.

Jovanis, P.P., T. Kaneko, and T. Lin. “Exploratory Analysis of Motor Carrier Accident Risk
and Daily Driving Pattern,” Transportation Research Record 1322, Transportation Research
Board, Washington, D.C., pp. 34-43, 1991.

Jovanis, Park, Chen, Gross, “On the Relationship of Crash Risk and Driver Hours of
Service”, 2005 Truck & Bus Safety & Security Symposium, Alexandria, VA., November,
2005. (In preparation)

Kaneko, T. and P.P. Jovanis. “Multi-day Driving Patterns and Motor Carrier Accident Risk:
A Disaggregate Analysis,” Accident Analysis and Prevention, Vol. 24, No. 5, pp. 437-456,
October 1992.

Lin, T.D., P.P. Jovanis and C.-Z. Yang. “Modeling the Effect of Driver Service Hours on
Motor Carrier Accident Risk Using Time Dependent Logistic Regression,” Transportation
Research Record 1407, Transportation Research Board, Washington, D.C., pp. 1-10, January
10-14, 1993

Lin, T.D., P.P. Jovanis, and C.-Z. Yang. “Time of Day Models of Motor Carrier Accident
Risk,” Transportation Research Record 1467, Transportation Research Board, Washington,
D.C., pp. 1-8, 1994.




                                             42
Mackie, R., J. Miller, Effects of hours of service, regularity of schedules, and cargo loading
on truck and bus driver fatigue, Report U.S.D.O.T HS-803 799, Human Factors Research,
Inc., Goleta, California, 286 p, 1978

McCartt, A. T., J.W. Rohrbaugh, M.C. Hammer, and S.Z. Fuller, “Factors associated with
falling asleep at the wheel among long-distance truck drivers”, Accident Analysis and
Prevention, Vol. 32, pp. 493-504, 2000.

Park, S-W, A. Mukherjee, F. Gross, P. P. Jovanis, “Safety Implications of Multi-day Driving
Schedules for Truck Drivers: Comparison of Field Experiments and Crash Data Analysis”,
Transportation Research Board Annual Meeting CD, January 2005, in press, Journal of the
Transportation Research Board.

Smiley, A., and R. Heslegrave, A 36-Hour Recovery Period for Truck Drivers: Synopsis of
Current Scientific Knowledge, TP 13035E, Transportation Development Centre, Safety and
Security Group, Transport Canada, 1997, 27p.
Williamson, A.M., A. Feyer, R.P. Mattick, R. Friswell and S. Finlay-Brown, “Developing
measures of fatigue using an alcohol comparison to validate the effects of fatigue on
performance”, Accident Analysis and Prevention, Vol. 33, pp 313-326, 2001.
.
Wylie c.d., Schultz, T., Miller, J.C., Mitler, M.M., Mackie, R.R., Commercial Motor Vehicle
Driver Fatigue and Alertness Study: Technical Summary, MC-97-001, Federal Highway
Administration, Washington, D.C., 1996.




                                              43
                                       Appendix A

                        Other analyses requested of the team

Utilization of 11th hour driving throughout 2004
In support of another FNCSA contractor, we were asked to explore whether there was any
trend in the use of the 11th hour driving throughout 2004. In response to this request we used
our entire data set from ABF and Fed Ex and identified every driving trip whether crash or
non-crash throughout all 8 days for all drivers. The results indicate that there is not pattern
apparent through the year. For example in one of the early months of the year there was 19%
usage of the 11th hour, but 3 months later there was only 9% usage. Usage was generally
much heavier by Fed Ex than by ABF, perhaps tied to the greater use of sleeper and long
distance driving by Fed Ex.




Data 1




                                              44
Period Serial # Year Hours On-Duty
     1         1 2003              45.00
     1         2 2003              41.75
     1         3 2003              41.00
     1         4 2003              52.50
     1         5 2003              36.75
     1         6 2003              50.25
     1         7 2003              47.50
     1         8 2003              41.75
     1         9 2003              35.25
     1       10 2003               43.00
     1       11 2003               43.75
     1       12 2003               42.00
     1       13 2003               51.25
     1       14 2003               59.00
     1       15 2003               40.25
     1       16 2003               56.50
     1       17 2003               36.75
     1       18 2003               46.00
     1       19 2003               39.50
     1       20 2003               45.25
       Mean                        44.75
       Standard Deviat              6.46

Period Serial # Year Hours On-Duty
     2       21 2004               34.75
     2       22 2004               48.75
     2       23 2004               50.00
     2       24 2004               47.50
     2       25 2004               48.00
     2       26 2004               49.50
     2       27 2004               52.25
     2       28 2004               27.00
     2       29 2004               47.50
     2       30 2004               62.50
     2       31 2004               62.00
     2       32 2004               53.50
     2       33 2004               61.50
     2       34 2004               27.00
     2       35 2004               62.50
     2       36 2004               55.00
     2       37 2004               58.75
     2       38 2004               47.00
     2       39 2004               60.00
     2       40 2004               62.75
       Mean                        50.89
       Standard Deviat             10.94

Period Serial # Year Hours On-Duty
     3       41 2004               42.50
     3       42 2004               53.00
     3       43 2004               68.25
     3       44 2004               60.75
     3       45 2004               56.25
     3       46 2004               66.00   45
     3       47 2004               64.50
     3       48 2004               45.25
     3       49 2004               41.00
Off duty analysis




                    46
The table lists numbers of drivers with 1, 2, and 3 days off-duty prior to the accident day
driving pattern.
                            Carrier                       ABF                       FedEx                   Schneider        Total
                           # of Driver                     135                       293                      264            692
Accident/Non-Accident                               A            NA             A          NA           A           NA       Total
                           # of A/NA                45           90          97            196          88          176      692
Accident/Non-Accident                               A            NA             A          NA           A           NA       Total
                            # of NA                 36           79          83            170          80          176      624
  # of 1Day Off-Duty                                3             8             4          12           4            0           31
  # of 2Day Off-Duty                                4             2             7           9           4            0           26
  # of 3Day Off-Duty                                2             1             3           5           0            0           11




The graph plots the proportion of drivers with 1 day off-duty prior to the accident day
over time.

                                                         1 day Off-Duty prior to Accident Day Pattern


                           0.7


                           0.6


                           0.5
   Proportion of Drivers




                           0.4


                           0.3


                           0.2


                           0.1


                           0.0
                                 1       65   129        193      257     321       385     449   513        577     641   705
                                                                             Time (15mins)




                                                                                47
                                          Appendix B

                         Table B1 Variance-Covariance Matrix Model B

                         t2            t3              t4              t5              t6
     t2                0.1429        0.1028          0.1028          0.1028          0.1028
     t3                0.1028        0.1446          0.1028          0.1028          0.1028
     t4                0.1028        0.1028          0.1542          0.1028          0.1028
     t5                0.1028        0.1028          0.1028          0.1531          0.1028
     t6                0.1028        0.1028          0.1028          0.1028          0.1758

       Table A2 Summary of Tests of Significance Between Coefficients: Model B

                  t2            t3              t4              t5              t6
t2                                   -0.17471        0.204966        -0.79823         -2.0428
t3                                                   0.366868        -0.62607        -1.88005
t4                                                                   -0.94699        -2.12359
t5                                                                                   -1.27299
t6

Numbers in Table A2 calculated from t-test for significant difference between two
parameters in a model using the test statistic:

       βi − β j
t=
     var(β i − β j )
Where:
Var (βi – βj) = Var (βi) + Var (βj) – 2 Cov (βi βj) and βi and βj are parameters to be tested for
difference.




                                                48
               Appendix C
Graphical Summaries of clusters from data set 1




                      49
Cluster membership
Cluster Number   4th Day       5th Day         6th Day           7th Day
1 to 20                    Cluster from SPSS using cluster analysis
21               -             -               -                 10 am
22               -             -               10 am             10 am
23               -             10 am           10 am             10 am
24               10 am         10 am           10 am             10 am
25               -             -               -                 12 am
26               -             -               12 am             12 am
27               -             12 am           12 am             12 am
28               12 am         12 am           12 am             12 am
29               -             -               10 am            Off duty
30               -             10 am           10 am             Off duty
31               -             -               12 am             Off duty
32               -             12 am           12 am             Off duty
33               12 am         12 am           12 am             Off duty
34               -             10 am           Off duty          Off duty
35               -             12 am           Off duty          Off duty
36               -             -               3:30 pm           11 am
37               -             7 pm            3:30 pm           11 am
38               -             -               -                 10 pm
39               -             -               10 pm             10 pm
40               -             10 pm           10 pm             10 pm
41               10 pm         10 pm           10 pm             10 pm
42               -             4 pm            7 pm               10 pm
43               -             -               Off duty          Off duty




                                       50
Cluster 1st

                                                     Cluster 20-1

                1
                                       com-84
                                       com-85



               0.8




               0.6
  Proportion




               0.4




               0.2




                0
                     0   24   48                72          96      120   144   168   192
                                                            Time




Cluster 2nd

                                                     Cluster 20-2

                 1
                              com-84
                              com-85


               0.8




               0.6
  Proportion




               0.4




               0.2




                 0
                     0   24   48                72          96      120   144   168   192
                                                           Time




                                                           51
Cluster 3rd

                                            Cluster 20-3

                1
                         com-84
                         com-85



               0.8




               0.6
  Proportion




               0.4




               0.2




                0
                     0     24     48   72          96      120   144   168   192
                                                  Time




Cluster 4th

                                            Cluster 20-4

                1
                         com-84
                         com-85



               0.8




               0.6
  Proportion




               0.4




               0.2




                0
                     0     24     48   72           96     120   144   168   192
                                                   Time




                                                  52
Cluster 5

                                                Cluster 20-5

               1
                                                                           com-84
                                                                           com-85



              0.8




              0.6
 Proportion




              0.4




              0.2




               0
                    0   24            48   72           96     120   144            168   192
                                                       Time




Cluster 6

                                                Cluster 20-6

               1
                             com-84
              0.9            com-85


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24            48   72          96      120   144            168   192
                                                      Time




                                                      53
Cluster 7

                                               Cluster 20-7

               1
                            com-84
                            com-85
              0.9


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0       24       48   72          96      120   144   168   192
                                                     Time




Cluster 8

                                               Cluster 20-8


               1
                        com-84
                        com-85
              0.9


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0       24       48   72          96      120   144   168   192
                                                      Time




                                                     54
Cluster 9

                                           Cluster 20-9

               1
                                                                             com-84
              0.9                                                            com-85


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0       24   48   72          96       120   144   168            192
                                                  Time




Cluster 10

                                           Cluster 20-10

                1
                        com-84
                        com-85
              0.9


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


                0
                    0       24   48   72          96       120   144   168            192
                                                 Time




                                                  55
Cluster 11

                                               Cluster 20-11

               1
                        com-84
              0.9       com-85


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0      24    48     72             96      120   144   168   192
                                                      Time




Cluster 12

                                               Cluster 20-12

               1
                                      com-84
                                      com-85
              0.9


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0      24    48      72            96      120   144   168   192
                                                      Time




                                                      56
Cluster 13

                                           Cluster 20-13

               1
                        com-84
                        com-85
              0.9


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24       48   72           96      120   144   168            192
                                                  Time




Cluster 14

                                           Cluster 20-14

               1
                                                                             com-84

              0.9                                                            com-85



              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24       48   72           96      120   144   168            192
                                                  Time




                                                  57
Cluster 15

                                           Cluster 20-15

               1
                                                                       com-84

              0.9                                                      com-85



              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0     24     48   72           96      120   144            168   192
                                                  Time




Cluster 16

                                           Cluster 20-16

               1

                        com-84
              0.9       com-85


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0     24     48   72           96      120   144            168   192
                                                  Time




                                                  58
Cluster 17

                                              Cluster 20-17

               1
                           com-84

              0.9          com-85



              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0       24      48   72           96      120   144   168   192
                                                     Time




Cluster 18

                                              Cluster 20-18

               1
                        com-84

              0.9       com-85



              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0       24      48   72           96      120   144   168   192
                                                     Time




                                                     59
Cluster 19

                                              Cluster 20-19

               1
                        com-84
                        com-85
              0.9


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0      24       48   72           96      120   144   168   192
                                                     Time




Cluster 20

                                              Cluster 20-20

               1

                           com-84
              0.9          com-85


              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0      24       48   72           96      120   144   168   192
                                                     Time




                                                     60
Cluster 21

                                                                   84-85-7th-10am


                               1


                           0.9
                                            84-Com
                                            85-Com
                           0.8


                           0.7


                           0.6
              Proportion




                           0.5


                           0.4


                           0.3


                           0.2


                           0.1


                               0
                                   0    24               48   72            96        120   144   168    192
                                                                            Time




Cluster 22

                                                                   84-85-7-6th-10am

                           1


                 0.9
                                               84-Com
                                               85-Com
                 0.8


                 0.7


                 0.6
 Proportion




                 0.5


                 0.4


                 0.3


                 0.2


                 0.1


                           0
                               0       24               48    72            96        120   144    168    192
                                                                           Time




                                                                           61
Cluster 23

                                           84-85-5-7th-10am

               1


              0.9       84-Com
                        85-Com
              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24       48   72            96        120   144   168   192
                                                   Time




Cluster 24

                                           84-85-4-7th-10am

               1


              0.9
                        84-Com
                        85-Com
              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24       48   72            96        120   144   168   192
                                                   Time




                                                   62
Cluster 25

                                                                         84-85-7th-12am

                  1


              0.9

                                        84-Com
              0.8                       85-Com


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


                  0
                            0           24               48        72            96           120         144         168         192
                                                                                Time




Cluster 26


                                                                         84-85 6-7th 12am
                                1


                            0.9


                            0.8
                                                  1984
                                                  1985
                            0.7


                            0.6
               Proportion




                            0.5


                            0.4


                            0.3


                            0.2


                            0.1


                                0
                                    0        24               48        72             96           120         144         168         192
                                                                                       Time




                                                                                63
Cluster 27

                                                                     84-85 5-7th 12am
                            1

                    0.9

                    0.8                       1984
                                              1985
                    0.7

                    0.6
  Proportion




                    0.5

                    0.4

                    0.3

                    0.2

                    0.1

                            0
                                0       24           48        72                96         120     144     168     192
                                                                                Time




Cluster 28

                                                                         84-85 4-7th 12am
                                1


                            0.9                      1984
                                                     1985
                            0.8


                            0.7


                            0.6
               Proportion




                            0.5


                            0.4


                            0.3


                            0.2


                            0.1


                                0
                                    0        24           48        72             96         120     144     168     192
                                                                                  Time




                                                                                64
Cluster 29

                                             7th-off-duty 6th-1000 (regular)

               1


              0.9
                             84-Com
              0.8            85-Com


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24              48    72              96               120   144   168   192
                                                             Hour




Cluster 30

                                                   7-5th 10am (regular)

               1


              0.9
                               84-Com

              0.8              85-Com


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24              48    72              96               120   144   168   192
                                                             Hour




                                                             65
Cluster 31

                                                      7th-off-6th-12 am

                     1


                    0.9            84-Com
                                   85-Com
                    0.8


                    0.7


                    0.6
      Proportion




                    0.5


                    0.4


                    0.3


                    0.2


                    0.1


                     0
                          0   24            48   72              96         120   144   168   192
                                                                Hours




Cluster 32

                                                      7th-off-5-6th 12 am

                    1


                   0.9        84-Com
                              85-Com
                   0.8


                   0.7


                   0.6
 Proportion




                   0.5


                   0.4


                   0.3


                   0.2


                   0.1


                    0
                         0    24            48   72              96         120   144   168   192
                                                               Hours




                                                                66
Cluster 33

                                                7-4th midnight (regular)

               1


              0.9                                                                      84-Com

                                                                                       85-Com
              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24            48   72                96            120   144        168   192
                                                            Hour




Cluster 34

                                                7-6th-off-duty-5th-10am

               1


              0.9
                             84-Com
                             85-Com
              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24            48   72                96            120   144        168   192
                                                            Hours




                                                            67
Cluster 35

                                                       7-6th-off-5th-mid

               1

                         84-Com
              0.9
                         85-Com

              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24        48              72             96               120   144   168    192
                                                                Hours




Cluster 36

                                                84-85-1100-1530 driving pattern

               1


              0.9                      84-Com
                                       85-Com
              0.8


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24        48             72             96                120   144   168   192
                                                               Hours




                                                                68
Cluster 37

                                                                     84-85-5-7th driving pattern

                        1


              0.9
                                                     84-Com
              0.8                                    85-Com


              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


                        0
                                      0         24            48     72             96             120   144      168      192
                                                                                  Hours




Cluster 38

                                                                   Driving on 7th day 10 pm 84-85              1984     1985


                                            1
                                          0.9
                                          0.8
              Proportion of drivers




                                          0.7
                                          0.6
                                          0.5
                                          0.4
                                          0.3
                                          0.2
                                          0.1
                                            0
                                             2
                                             8
                                             4
                                             0
                                             6
                                             2
                                             8
                                             4
                                             0
                                             6
                                             2
                                             8
                                             4
                                             0
                                             6
                                            12
                                            18
                                            24
                                            30
                                            36
                                            42
                                            48
                                            54
                                            60
                                            66
                                            72
                                            78
                                            84
                                            90
                                            96
                                             0
                                             6




                                           10
                                           10
                                           11
                                           12
                                           12
                                           13
                                           13
                                           14
                                           15
                                           15
                                           16
                                           16
                                           17
                                           18
                                           18




                                                                                         Time




                                                                                   69
Cluster 39

                                                                          84-85 6-7th 10pm
                                       1

                         0.9

                                                    1984
                         0.8
                                                    1985
                         0.7

                         0.6
  Proportion




                         0.5

                         0.4

                         0.3

                         0.2

                         0.1

                                       0
                                           0   24          48        72             96       120   144     168     192
                                                                                   Time




Cluster 40

                                                                Driving on 5th day 10 pm 84-85
                                                                                                         1984    1985


                                           1
                                       0.9
                                       0.8
               Proportion of drivers




                                       0.7
                                       0.6
                                       0.5
                                       0.4
                                       0.3
                                       0.2

                                       0.1
                                           0
                                             2
                                             8
                                             4
                                             0
                                             6
                                             2
                                             8
                                             4
                                             0
                                             6
                                             2
                                             8
                                             4
                                             0
                                             6
                                            12
                                            18
                                            24
                                            30
                                            36
                                            42
                                            48
                                            54
                                            60
                                            66
                                            72
                                            78
                                            84
                                            90
                                            96
                                             0
                                             6




                                           10
                                           10
                                           11
                                           12
                                           12
                                           13
                                           13
                                           14
                                           15
                                           15
                                           16
                                           16
                                           17
                                           18
                                           18




                                                                                    Time




                                                                                  70
Cluster 41

                                                      84-85 4-7th 10pm
                  1


                 0.9
                                  1984
                                  1985
                 0.8


                 0.7


                 0.6
    Proportion




                 0.5


                 0.4


                 0.3


                 0.2


                 0.1


                  0
                       0   24            48      72               96         120     144     168         192
                                                                Time




Cluster 42

                                              84-85 5-7th driving pattern

                   1


                 0.9
                           1984
                 0.8
                           1985

                 0.7


                 0.6
    Proportion




                 0.5


                 0.4


                 0.3


                 0.2


                 0.1


                   0
                       0    24           48     72             96           120    144     168     192
                                                              Time




                                                             71
Cluster 43

                                                      7-6th-off-duty-only

               1


              0.9


              0.8
                             84-Com Proportion
                             85-Com-Proportion
              0.7


              0.6
 Proportion




              0.5


              0.4


              0.3


              0.2


              0.1


               0
                    0   24              48       72              96         120   144   168   192
                                                               Hours




                                                                72

								
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