# Ppt Birthday Templates

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```					                                                                                        Outline
• How to reason with/about time
Monitoring                          • Interpreting temporal data

6.872/HST950

Peter Szolovits

Problem                                           Time is Critical
• ICU alarms sound roughly every 30                       • Some systems have no explicit representation of
time
seconds, in a typical (full) ICU
– E.g., Internist
• Nurse takes ~minutes to resolve alarm                          • <ABDOMEN TRAUMA RECENT>
• <ABDOMEN TRAUMA REMOTE HX>
• How to resolve?                                                • <CHEST PAIN SUBSTERNAL LASTING GTR THAN 20
MINUTE <S>>
– Ignore (turn off) alarms                                     • <CHEST PAIN SUBSTERNAL LASTING LESS THAN 20
– Prioritize                                                     MINUTE <S>>

– Automate                                              • No representation of these pairs being “the
same,” but at different times.
– Make alarming algorithms more intelligent             • Note: Same problem with space; need orthogonality!

Motivating Example: Distinguishing Four
Possible Relationships                                Even Simple Models Help
Between Transfusion and Jaundice
?
abdominal
pain
• PIP’s temporal model:
blood                                                 – PAST, RECENT, NOW, SOON, FUTURE
transfusion
?
• Example:
jaundice                         – in “chronic glomerulonephritis” model, “past acute
GN”
• Post-transfusion antigen incompatibility
– (to my surprise), program hypothesized “future
hemolytic anemia                                             chronic GN” after diagnosing “now acute GN”
• Post-Transfusion Hepatitis B: Acute Hepatitis
AGN                      CGN
• G-6-PD hemolytic anemia treated by transfusion
• Post-Transfusion Hepatitis B: Chronic Active                                   past                  present      future
past                       present                  future

1
What is Time?                                                                Continuous View
d 2x
= −g
dt 2
• (Macroscopically) unidirectional                                                dx
= − gt + v 0
• Related to causality                                                            dt
• May be modeled in various ways                                                  x = − gt 2 + v 0 t + x 0

– Continuous quantity, as in differential                                     • Differential equation view of world
equations
– Discrete time points, as in discrete event                                  • States (state variables) evolve according
simulations                                                                   to their laws
– Intervals, as in ordinary descriptions of
durations, processes, etc.
… or combinations

Discrete Event View                                                     What Can Be a Time Point?
• Designated (countable) time points                                              • Calendrical point—a specific date/time
• Nothing “interesting” between events                                            • Recognizable event—e.g., “when I had my
• Events may be defined by                                                          tonsils out,” or “start of high school,” or
– Clock “ticks”                                                                 “my ninth birthday”
– Interactions among objects in universe                                      • Now—special, because it moves
– Distinguished points in representation of state
variables (e.g., highest point of cannon shell)

Discrete Events are                                                                   Constraint Propagation
Associated with State Transitions                                                            among Time Points
E.g., Beck & Pauker’s model to help compute quality-adjusted years of survival:                                            B   l, u
l, u

A           l, u              C

•   Clearly, T(A,B)+T(B,C) = T(A,C)
•   But we only know lower/upper bounds on T
•   L(A,C) = L(A,B)+L(B,C)
•   U(A,C) = U(A,B)+U(B,C)
•   and thus, we can infer relationships

2
Intervals and Points are
Interval “Overlaps” in TUPese                                                                   Alternate Representations
+                   <ANOREXIA
• “Overlaps” defined in terms of its
ε                                                                       endpoints:
<IRRITABILITY
´
+                                         Most medical history
temporal terminology                                                          +0,+∞
+                                  is expressible in                                      <Anorexia                               Anorexia>
´
+
+                                       +        statements composed                                                      +ε,+∞
+0
+0
´
-   ε                          from TUP assertions.
+ε,+∞                                     +ε,+∞
-
+ε,+∞
IRRITABILITY>
+
ANOREXIA>                                                   +0,+∞
+´   ε                                               <Irritability                             Irritability>

Initial Assertions                                                                                 Constraint
• Completing                                                 <ANOREXIA

all the                                                                                                                      <ANOREXIA
relations not                                 3 DAYS                     4 DAYS

explicitly                                    2 DAYS                     3 DAYS

asserted                                                       7 DAYS                                             3 DAYS                          3 DAYS
<IRRITABILITY                                     ANOREXIA>
5 DAYS                                             2 DAYS                          3 DAYS

Legend                                                                                         5 DAYS
<IRRITABILITY                                                ANOREXIA>
Inferred                                                                5 DAYS

Externally asserted

Propagated Constraint                                                                 Forms of Temporal Uncertainty
<ANOREXIA                                            • Lower/upper
bounds on temporal
2 DAYS                               3 DAYS
distances
2 DAYS
3 DAYS                          • Central range +
fringe
5 DAYS
<IRRITABILITY
5 DAYS
ANOREXIA>               • Continuous
• Order n2 edges in fully interconnected graph                                             distributions
• Order n3 computation
• Work to localize propagation to semantically
related events

3
Interval View                                     Allen’s Temporal Intervals
• Activities, processes take place over
extended intervals of time
• Observations are true over periods of time
• Systems remain in steady (from some
viewpoints) states over intervals

Inference among Intervals                                Temporal Control Structure.
by Composition                                             - T. Russ
Y-Z

e.g., if A starts B and B overlaps C,
what are the possible relationships
between A and C?
1. A before C
X-Y
2. A meets C
3. A overlaps C

• Processes maintaining truth of abstractions over
specified interval
• Update of past beliefs from corrections or new data.
• Actions are permanent.

Back to Monitoring                                   “Two-Point” Trend Detectors
•   Detecting Trends                                            • Restricted to hospitals with the most
•   Language for Trend Description                                complete information systems
•   Matching algorithms                                         • Rind & Safran, 1992
•   Top-down vs. bottom-up vs. both                             • Two point event detector
– rise in creatinine > 0.5 mg/dl
•   Learning trend detectors
• Therapeutic context
– Renally cleared or nephrotoxic medication
– Possible care providers
• Implementation
– M procedures linked to E-mail

4
BIH Experience (cont’d)                                                                      Are these two-point trend
• Time series trial                                                                                    detectors sufficient?
• 607 in 348
admissions during                                                                         •    If not, why not?
control periods
• 497 events in                                                                             •    Noisy data.
intervention period
•    Multi-phased processes.
584 different
physicians, 9.25
•    Uncertainty over time.
recipients per alert                                                                      •    Uncertainty over values.
• Improved response
time
• Improved outcomes

Representation
Easily implemented as an Arden Syntax
MLM

Pediatric Growth
Pediatric Growth
Issues in Trend Detection                                                          Monitoring
Monitoring
• Data:
• Defining significant trends                                                                     - heights, weights
– Multiple variables                                                                            - family history
– Multiple phases                                                                               - bone ages
– Temporal and value uncertainty                                                                - pubertal data,
stages
• Detecting trends from data                                                                      - hormone values
• Generating alarms                                                                             • Disorders show
characteristic
• Displaying, explaining results                                                                  patterns on growth
chart.
• Changing clinical context                                                                                                       Boy with constitutional
delay
--Haimowitz

Curve Fitting Approach                                                                     Describing Average Normal Growth
Describing Average Normal Growth

a1                                                                     •   Def. Z-score ≡ Number of standard deviations a patient's
parameter is from the mean for that age.
a                        a
Height(t) = + e -b             (t - c1)
+           2            +           3             •   From birth until age 2 - 3 years, height and weight vary
1                1                  1 + e -b2 (t - c2)       1 + e -b3 (t - c3)
together and establish baseline Z-scores.
Triple-logistic curve [Thissen and Bock
1990]                                              •   From then until onset of puberty, height and weight
maintain approximately the same Z-scores.
ak = component k’s contribution to mature stature
bk = a parameter proportional to the maximum growth velocity of the                        •   Throughout this time, bone age is approximately equal to
component (maximum rate of growth is (a * b) /4 centimeters per year)                          chronological age.
ck = the age in years at which the maximum growth velocity occurs

5
Trend Template for
Trend Template for
Male Average Normal Growth
Male Average Normal Growth                                                                                         Trend Template, continued
Trend Template, continued
Landmark points
Time constraints
Landmark points
Intervals
Time                                                                             Ht
constraints            Ht Z-score Ht Z-score Wt Z-score         Ht                                                Time constraints
- Wt Z-score
Value
Intervals                                                                    Peak Ht           Growth                    constraints
Puberty
onset              veloc             stops
Time                 Birth
Ht Z-score Wt Z-score                       Ht
constraints                                                                                                                                               Ht
0       2     3             10       13        12.5    14.5     17         19 Age
Ht Z-score
Value
- Wt Z-score
constraints
Chron. age
Growth
Birth           - bone age
stops                                                                 Peak height      Growth
0                                                                                                        Puberty                           stops
Birth                             onset            velocity
Pubertal
stage                                 Pubertal         Pubertal
Birth                             Pubertal       stage   Pubertal stage
1                        stage                  stage
14.5             Age
2
3                 5                     0            2          3       10      13        12.5            17   19
4
Growth
Puberty
onset                                    stops

Trend Template, continued
Trend Template, continued                                                                                         Value Constraints Have Regression Models
Value Constraints Have Regression Models
Landmark points
Constant                   Linear
Time
• Low-order                    f(D)t = K + εt
constraints                                                                                                                                                             f(D)t = a t + b + εt
Intervals                                                                                                           polynomials
Time                                  Chron. age
constraints                           - bone age
• Parameter estimates:
BirthValue                                    0                                                                     quantitative or
constraints                                                                                                    qualitative
Growth
stage                            Pubertal
Birth                                                     Pubertal
1
Pubertal        stage
stage
f(D)t = a t 2 + b t + c + εt
stage         3                 Pubertal
2                      4         stage
0                                                                 5
Puberty
onset                                                              Growth
11.5 14.5            stops

Goodness of Fit of a Hypotheses
Goodness of Fit of a Hypotheses                                                                                                                  TrenDx
TrenDx
Least-Squared          •   Matches process data to trend templates.
Value Constraint                              Error Line
Mean Absolute
% Error                                                                                                           •   Optimizes over alternate trend
chronologies.
Σ
Yt - Y’t                                                       Y’t
•   Compares best matches of competing
=       t        Yt
Yt
trends within same clinical context.
N - (no. estim. pars.)

•Hypothesis score is weighted average of value constraint
scores.

6
Linking Patient Data to Trend Template
Linking Patient Data to Trend Template                                                              Processing height and weight, 2.1 years
Processing height and weight, 2.1 years
Temporal Utility Package          • Branch to two hypotheses of average normal
Patient-1     Patient-1                            [Kohane 1987]                     growth:
Date of Birth Height
3/17/1992     4/28/1994

Ht Wt                                            Ht Wt
Patient Data                                                                                                     2.1 2.1                                          2.1 2.1
Trend Template                                                      Puberty                          (1)         Int1
(2)
onset                                                          Int2             Int1               Int2
Birth                                                                                                                                           2   2.1
2.1         3
0              2          3                                               Age
10         13

Int1
Int2

Processing data through age 4.1
Processing data through age 4.1                                                                      Maximizing Chronologies for a Trend
Maximizing Chronologies for a Trend
•First hypothesis has lower error.                                                                     Data: D1 D2 ... Dt-1 Dt
•Refining patient history from population pattern and data.                                                       time

TT normal - Chron1         TT normal - Chron2      TT normal - Chron3
Ht Wt           Ht Wt Ht Wt                                      Ht WtHt Wt Ht Wt                              0.052                0.043                    0.055
2.1 2.1         3.1 3.1 4.1 41                                   2.1 2.1 3.1 3.1 4.1 41
(1)     Int1
(2)
Int2                                Int1                      Int2
2.1 + ε        3                                              2        2.1 - ε           0.063       0.048          0.056      0.033       0.045    0.069     0.072

Score: 0.14                                     Score: 0.37

Beam search

Beam search -- soundness vs. efficiency
Beam search soundness vs. efficiency                                                                   Diagnostic Monitoring Framework
Diagnostic Monitoring Framework
•   Clinical context
Noise?                         Actual                                        •   Partition of trend templates
transition?                                   •   One normal; others faulty
Data:        1 1 1                                                                                    •   TrenDx concurrently matches to same process data
1          2             22 2
2                  2
2
•   Compare best matching hypothesis of
2
2                                               each trend template
Constant                                    2
•   Significant faulty trend match triggers
Linear (D1 -)
Phase 1                                                                                        actions
Phase 2                                               •   Alarms
•   Displays
•   Other clinical contexts

7
TrenDx Results on Growth Patient
TrenDx Results on Growth Patient
Boy with constitutional
Patient 39, Const. Delay
Exploratory Clinical Trial
Exploratory Clinical Trial
0.5                                  delay
•    30 growth records from Children’s Hospital
0.45                                                                                                                                                      H                             Endocrinology Clinic
B Normal
J Cons Delay                                                                                                                                                            •   26 have disorders; 4 normals.
0.4
H Early Puberty
0.35
•    20 growth records from general pediatrician
B                              •   All 20 declared normal
Score (% error)

0.3
B
•    Alarm based on (TTF - TTN)
0.25                                                                                                                                  H
H
B       J                              •   Single wide gap
0.2
J
J                                      •   Persistent narrower gap
J
0.15
H           H
B          H
B
J
J
B B
H H                                                                                                    Constitutional delay Early puberty
H                       H          B           J
B                       B          J
0.1
J                                                                                                          Sensitivity                                               .52                                                              .67
J
0.05
Specificity                                               .96                                                              .75
0                      H
J
B         H
J
B
0                  2                       4                       6         8                                  10                      12                        14
Age (years)

Intensive Care Unit Monitoring
Intensive Care Unit Monitoring                                                                                                                                                  TrenDx Matching to Handbagging Case
TrenDx Matching to Handbagging Case
B
B
190
190                                                                                                                                                                                                                                                                                                 B B               B B B B B
B                    B        B            B
B                                                                                                                                                                                  B B           B               B B           B B B
B BBB B B B B B B B
B
BB                                                                                                                                                              170
BB B B B
B                 BB B B    B B B BB B B B B
B
BB B BB B B BBBBB BB B B BB
BB B B B B BBB B
B BB                                                      BBB
BB          BB BB B
BB B BB B B
J       Mean Art BP
BB B BB B                                                                      B
150               1       FIO2
170
Hemodynamic                            130
H       O2 Saturation

150
B      ECG HR                                      fault                                 110
B       ECG Heart Rate

J      Mean Art BP
H      O2 Saturation
becomes                                 90      H
1
H
H
H H                           H                                                  H                                  H

130
1       FIO2
significant                             70          J                  J       J       J J           J   J       J   J     J J   J   J    J   J
J   J   J
trend.                                  50
12:20 AM            12:22 AM                 12:24 AM                  12:26 AM                  12:28 AM
J        J
12:30 AM
J
1
J
12:32 AM

110                                                                                                                                                                                                                       0.04
B
1H
H         H          H       HH
HHH H H H H
H HH H
H HH HH HH
H H
Hemodynamic Fault
H                                                  H                           H  H               H                                                                                                                             J                                                                                                            B    B
90           H                 H          HH
HH        H
HH                                              H             H                             H HH H H H H
H HHH HH                                                              0.03
H       Difference
H                                                                                                                                                                                                                                                                                B    B
Score (% Error)

0.025                                                                                                                                         H
JJ                                                                                                                                                                                                                                                                                        B
JJ J     JJJJ JJJJ    JJJ JJ J JJJJJ JJJ            JJJ J
B
70 J J                                                          J J JJ JJ JJJJ                                          JJJJJJJ J J                     J J J J J J JJJJ                                              0.02                                                                                                                                H H
J J J J J J J J J JJJJ JJ JJ J J J J J
B
JJJJ                                JJ JJ                                                                                                                                                               B
J
B B
J JJJ J                J J JJ J J J J                                                                                                                                        B B                       B
JJ J                                                                                                        0.015                                                                J J     B B
J J       B B   B
J                                                                                                                                                                                                                         J J   J J               J    J
J JJ JJJJJ
J   J               H H
JJJ                                                                                                                                                                                                                                                       J J J J               J
J J JJ                                                                                                                         0.01                                                                                                                   H
J
50
12:00 AM                 12:10 AM              12:20 AM
1
12:30 AM                 12:40 AM                    12:50 AM                   01:00 AM                                                                                        J J
B B
B
J
B
J     B
J                                                      H

0.005                                  B
J                                                                       H
H
H H

Hemodynamic fault during oxygen handbagging                                                                                                                                                                                            0
12:20:00 AM
H H H H H H H H H H H H H
J J
B B
12:22:00 AM
H H
12:24:00 AM               12:26:00 AM
Time
H
12:28:00 AM                12:30:00 AM               12:32:00 AM

Long’s Signal Segmentation
Top-Down vs. Bottom-Up
Algorithm
• Goals:
– Segment multiple data streams into a
sequence of time intervals (cover time line)
– Within each interval, characterize each signal
by a (linear) regression line
– Optimize for least total residual (greedy)
– Parameter controls maximum tolerable error
• Trades fitting error vs. number of segments

8
Segmentation                                Segmentation

Segmentation                        Multiple Data Streams

Effect of Varying Sensitivity to Change

Event Discovery in Medical
Time-Series Data

Christine L. Tsien, Ph.D.
Harvard Medical School, Boston MA
Massachusetts Institute of Technology, Cambridge MA

9
Observational Study of ICU
Overview
Alarms
• Background: Intensive Care Unit (ICU)                                 • Prospective 10-wk study at Children’s Hospital
• TrendFinder approach to event discovery                               • 2942 alarms; 298 hours
– components                                                                                            8%
6%
– performance metrics
• Applications: ICU signal artifacts, events
• Problems
• Summary                                                                  – Wider limits
Alarm
Types
– Silenced alarms
– Stress
86%

TrendFinder Approach to                                             TrendFinder Application:
Event Discovery                                               Detecting Events in the MICU
• Event: clinically-relevant systolic BP alarms
• Data collection (Children’s Hospital)
Event
Annotated      Annotated
Model       Performance      – 12 weeks
Data           Data
Identification
Collection   Preprocessing
Derivation    Evaluation
– 585 hours of 5-sec data
• Prospective alarm annotations

Annotated     Annotated
Event                                       Model         Performance
Data           Data
Identification                                Derivation      Evaluation
Collection   Preprocessing

Annotated Data Collection                                           Annotated Data Collection Program
Setup
Patient

Bedside           Bedside                 Bedside
...
device 1          device 2                device n

Spacelabs
monitor                   Alarms

Laptop                 Trained
computer               observer

Data files                    Annotations

10
Feature Attribute Derivation   Feature Attribute Derivation

Feature Attribute Derivation   Feature Attribute Derivation

maximum = 10                   minimum = 7

Feature Attribute Derivation   Feature Attribute Derivation

range = 3                      mean = 8.5

11
Feature Attribute Derivation         Feature Attribute Derivation

median = 8.5                         slope = -1

Feature Attribute Derivation         Feature Attribute Derivation

absolute value of slope = +1         standard deviation = 1.29

Feature Attribute Derivation         Feature Attribute Derivation

12
Feature Attribute Derivation   Feature Attribute Derivation

Feature Attribute Derivation   Feature Attribute Derivation

Feature Attribute Derivation   Feature Attribute Derivation

13
Feature Attribute Derivation                                Feature Attribute Derivation

Feature Attribute Derivation                                Feature Attribute Derivation

Example Decision Tree Model
Model Derivation
for BP Artifact Detection
• Data
– labeled feature vectors of derived values
bp_med3 <= 4: artifact (114.0/3.0)
– training, evaluation, test sets
bp_med3 > 4:
• Supervised machine learning methods                          bp_range3 <= 7: non-artifact (10959.0/72.5)
– Decision trees (c4.5)                                     bp_range3 > 7:
– Neural networks (LNKnet)                                           bp_med10 > 46: non-artifact (126.0/23.7)
– Logistic regression (JMP)                                          bp_med10 <= 46:
bp_std_dev3 <= 5.51: non-artifact (78.0/28.5)
• Models: labels previously unseen feature vectors as                             bp_std_dev3 > 5.51:
event or non-event                                                                       co2_low10 <= 5.3: artifact (46.0/10.1)
co2_low10 > 5.3:
hr_high5 <= 157: non-artifact (27.0/12.8)
hr_high5 > 157: artifact (21.0/8.2)

14
If temporal representation provides                                                            Time series: Arterial BP and HbO2
leverage in reasoning over time...
• What temporal representation have we                                                         50
ABP

overlooked?                                                                            g
40

H 30
m
m 20

10
0                 5                      10                    15            20            25

0.01
HbO2
0.005
.
U           0
.
A
-0.005

-0.01
0                5                      10                    15            20            25
seconds

Methods                                                                  Frequency Domain
Fourier transformation: translation from the
time domain to the frequency domain.                                temp.                    baroreflex
RR                           pulse rate
R to R
(imaginary data)                                                         150                                                                                         80
P
60
B    100
40
RR interval (s)

D     50
S                                                                                                20
P
0                                                                                          0
0         0.05   0.1   0.15       0.2         0.25   0.3    0.35     0.4        0.45       0         1.25      2.5
-5                                                                                         -6
x 10                                                                                       x 10
R    6                                                                                          3
I
N    4                                                                                          2

D    2                                                                                          1
S
Time                                               P    0                                                                                          0
0         1.25      2.5
0         0.05   0.1   0.15       0.2         0.25   0.3    0.35     0.4        0.45
(time)2/Hz

(s)                                                   0.06                                                                                      0.015

0.04                                                                                       0.01
D
S 0.02                                                                                         0.005
C
0                                                                                          0
0         0.05   0.1   0.15       0.2         0.25   0.3   0.35      0.4        0.45       0         1.25      2.5

HIGH Frequency (Hz)                                                    Hz.                                                          Hz.
LOW

Opportunities of the frequency
Summary
domain
• For new kinds of alarms
• Careful selection of temporal representations are
• Machine learning on different part of the                                   necessary to capture the aspect of interest of a
feature space                                                               biological/clinical system.
• Temporal reasoning programs have been developed but
• Informative displays                                                        are not widely used.
• Toolkit to focus on events with time-                                     • Trend detection with on-line data can be useful (low-
hanging fruit)
constants of interest
• Much can be accomplished with simple 1 and 2 point trend
detectors
• Noisy data and medically complex trends require more
sophisticated representation and reasoning mechanisms
– E.g. conversion into the frequency domain

15

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