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					Assessing Risk from Environmental
Exposure to Waterborne Pathogens:
 Use of Dynamic, Population-Based
  Analytical Methods and Models

                      May 11, 2005


This lecture is based on lecture material prepared by Prof.
Joe Eisenberg, formerly of the University of California-
Berkeley and now at the University of Michigan
Used with his permission
              Overview
Role of water in disease burden
  – Water as a route of disease transmission
Methods of risk estimation
  – Direct: intervention trials
  – Indirect: risk assessment
Population-level risks
  – Example: the Milwaukee outbreak
Importance of Waterborne Pathogens

Domestic: U.S. interest in water quality
  – 1993 Cryptosporidium outbreak
  – Increasing number of disease outbreaks
    associated with water
  – Congressional mandates for water quality
    –   (Safe Drinking Water Act)

  – Emphasis on risk assessment and regulation
Importance of Waterborne Pathogens
Worldwide: WHO interest in water quality
   – Estimating GBD associated with water,
     sanitation, and hygiene
   – Diarrheal diseases are a major cause of
     childhood death in developing countries.
   – 3 million of the 12.9 million deaths in children
     under the age of 5 attributable to diarrheal
     disease
   – Emphasis on intervention and control
    Pathways of Transmission
 Person-person
   – Mediated through fomites (e.g., phone, sink,
     etc.)
   – Often associated with hygiene practices
 Person-environment-person
   – Mediated through water, food, or soil
   – Contamination can occur through improper
     sanitation (example: sewage inflow into
     drinking water source or lack of latrines)
   – Animals are often sources (Zoonotic pathogens)
   – Exposure can occur through improper treatment
     of food or water
  The Disease Transmission Process
    Risk estimation depends on transmission
      dynamics and exposure pathways
                  Transport to other water sources
Agricultural
  Runoff


                   Drinking
                    Water
                                                Recreational Waters
 Animals                                                 or
                         2°                      Wastewater reuse
                       Trans.



                Food
Approaches to Risk Estimation

 Direct approach: The intervention trial
   – Can be used to assess risk from drinking water
     and recreational water exposures
   – Problems with sensitivity (sample size issue)
   – Trials are expensive.
 Indirect approach: Mathematical models
   – Must account for properties of infectious
     disease processes
   – Pathogen specific models
   – Uncertainty and variability may make
     interpretation difficult.
Approaches to Risk Estimation

 Combining direct and indirect
  approaches
  – Models can define the issues and
    help design studies.
  – Epidemiology can confirm current
    model structure and provide insight
    into how to improve the model.
   Approaches for Risk Estimation:
  Direct estimates of waterborne infectious illnesses

 Surveillance: count waterborne infectious illnesses
   – How can a waterborne disease outbreak be distinguished from
     other outbreak causes (food, fomites, etc.)?
   – What about endemic disease?
 Observational
   – Ecologic studies (e.g., serosurvey comparing communities
     with and without filtration).
   – Time series (e.g., correlation between turbidity and
     hospitalization data)
   Approaches for Risk Estimation:
  Distinguishing waterborne GI disease from other GI diseases


 Methods for addressing the question
   – In a single community: a randomized, blinded, placebo-
     controlled trial
   – design provides an estimate of the effectiveness of a
     drinking water intervention.
 Basic study design: two groups
    “Exposed” group = normal tap water.
    “Treated” group = use a water treatment device to
     provide water as pathogen-free as technically possible
   Approaches for Risk Estimation:
         A Tap Water Intervention Trial

 Enroll 1000 subjects
 500 receive an active home water treatment
  device (and carry drinking water to work, etc.
  when practical)
 500 receive a “placebo” home water drinking
  device (does nothing to change the water)
 Follow the subjects for one year with daily logs
  of GI illness
 Alternative design: Each household changes
  device type after 6 months.
Approaches for Risk Estimation:
       A Tap Water Intervention Trial

Placebo group (tap water):
  – 90 illnesses over course of the study
  – “Rate” = 90 / 500
     Rate in placebo group = 0.18 per person per year


Treated group (active device):
   60 illnesses in the treated group (active device)
   “Rate” = 60 / 500
     Rate in treated group = 0.12 per person per year
 Approaches for Risk Estimation:
           Epidemiologic Measures


Relative Risk (RR)
  Incidence in exposed group
  Incidence in unexposed group




  Interpretation: the risk of disease in the tap water
  group is 1.5 times higher than that of the treated group
  Approaches for Risk Estimation:
             Epidemiologic Measures


Attributable Risk (AR)
  Incidence in exposed – Incidence in unexposed

             Incidence tapwater  Incidence active
              0.18  0.12  0.06


  Interpretation: There are 6 excess cases of disease per 100
  subjects receiving tap water
  Approaches for Risk Estimation:
           Epidemiologic Measures


Attributable Risk Percent (AR%)
 Excess cases in exposed
 Incidence in exposed
         Excess Casestapwater 0.06
                                    0.33
          Incidencetapwater    0.18


Interpretation: 33% of the cases of disease
in the tap water group are due to water
     Approaches for Risk Estimation:
        Epidemiologic Measures

To generalize beyond the cohort, need an
 estimate of the community incidence.
PAR: population attributable risk
PAR%: population attributable risk %
AR compares completely protected group with
 completely unprotected group.
PAR incorporates intermediate exposure
    Approaches for Risk Estimation:
       Epidemiologic Measures
Population attributable risk

Incidence in the community–incidence in the
 unexposed

            Incidence Comm  Incidence active
             0.14  0.12  0.02


  Interpretation: In the community, 2 excess cases of
    disease per every 100 subjects in the community
    Approaches for Risk Estimation:
       Epidemiologic Measures
Population attributable risk percentage

Excess cases in the community
Incidence in the exposed
             Excess CasesComm 0.02
                                       0.14
              Incidencetapwater   0.14



  Interpretation: 14% of the cases of disease in the
  community are due to tap water
  Approaches for Risk Estimation:
           Tap Water Intervention Trials
           Trials in immunocompetent populations
 Canada (Payment)--challenged surface water
    – AR = 0.35 (Study 1), 0.14-0.4 (Study 2)
 Australia (Fairley)--pristine surface water
    – No effect
 Walnut Creek (UCB) – pilot trial
    – AR = 0.24 (non-significant effect)
 Iowa (UCB)--challenged surface water
    – No effect

               Trials in sensitive populations
 HIV+ in San Francisco (UCB)--mixed sources
 Elderly in Sonoma (UCB)--intermediate quality surface
  Approaches for Risk Estimation:
        Tap Water Intervention Trials

Davenport, Iowa study
 – Comparing sham vs. active groups
  – AR = - 365 cases/10,000/year (CI: -2555, 1825)
  – Interpretation: No evidence of a significantly
    elevated drinking water risk
  – Is the drinking water safe?
 Approaches for Risk Estimation:
   Risk Assessment vs. Intervention Trial

Comparing estimates from a risk assessment to
randomized trial results (Eienberg et al. AJE, submitted)
Data collected during the intervention trial
  –   Self-report illnesses from participants: Weekly
      diaries
  –   Source water quality: Cryptosporidium, Giardia,
      enteric viruses
  –   Drinking water patterns: RDD survey
  –   Water treatment: B. subtilis, somatic coliphage
Approaches for Risk Estimation:
    Risk Assessment Model
Approaches for Risk Estimation: Risk Assessment Model
                                                    Model
                                Cryptosporidium     Giardia       Viruses
   1. Source water
      Concentration
                                   1.06 (2.24)    2.68 (24.20)    0.93 (3.00)
      (organisms per liter)
      (Normal Mean (SD)*)
      Recovery rate                  0.40             0.40            0.48
   2. Treatment efficiency
   (logs removal)

      Sedimentation and           3.84 (0.59)     3.84 (0.59)
                                                                  1.99 (0.52)
      filtration (Mean (SD)*)

      Chlorination (Mean (SD)          0           3.5 (2.93)       4 (2.93)

   3. Water Consumption          0.094 (0.42)     0.094 (0.42)   0.094 (0.42)

    in liters (mean (SD) ‡)

   4. Dose Response §             : 0.004078      : 0.01982    ,: 0.26, 0.42

   5. Morbidity Ratio#               0.39             0.40            0.57
Approaches for Risk Estimation: Risk Assessment Results
   Overall risk estimate: 14 cases/10,000/yr
  Table 2. Summary of risk estimates (cases/10,000,yr)



                                   Cases of Illness
                                                Percentile
                            Mean                (2.5, 97.5)

 Cryptosporidium             2.1                 (0.8, 3.5)
 Giardia                     3.4                (0.6, 15.5)
 Enteric viruses
 (disinfection = 4           8.4                (0.2, 18.7)
 log removal)
 Enteric viruses
 (disinfection = 4            0                   (0, 0.2)
 log removal)
Approaches for Risk Estimation: Comparison/Conclusions
Table 3. Comparison of risk assessment and intervention trials
                                        Risk Assessment    Intervention Trials


   Sensitivity                            Not relevant            Low
   Causal evidence                          Indirect             Direct
   Pathogen inclusion                         Few                Many
   Model Specification                  Adds uncertainty      Not relevant
           Transmission                 Can be included*    Only in a limited
           processes                                              way
           Distribution System          Can be included*     Was included
           effects
   Examining alternative                      Yes                 No
   control strategies
   Expense                                   Low                  High
   Time                                       Fast                Slow
   *
       Was not included in this study
          Microbial Risk Assessment
Two classes of risk assessment models
   Individual-based
   Population-based
Individual-based estimates
   Risk estimates assume independence among
    individuals within the population
   Chemical risk paradigm
   Focus is on direct risks
   Probability of disease for a given individual
   This probability can be either daily, yearly, our lifetime.
    Microbial Risk Assessment

Chemical risk paradigm
  –Hazard identification, exposure assessment, dose
   response, risk characterization
Model structure              P  1  (1  (
                                                 N
                                                     )) 
                                                 
  where P = probability that a single individual, exposed to
   N organisms, will become infected or diseased.
Exposure calculation:

            N  V1  co  e  kt t 10  k d d
           Microbial Risk Assessment
   Alternative framework: risk estimates at the
   population level allow for the inclusion of
   indirect risks due to secondary transmission
                  Transport to other water sources

Agricultural
  Runoff

                   Drinking
                    Water
                                                     Recreational Waters
Animals                                                       or
                         2°                           Wastewater reuse
                       Trans.



                Food
           Microbial Risk Assessment
                 Eisenberg et al. AJE 2005
Transmission pathways
  – Example: a Cryptosporidium outbreak in Milwaukee Wisconsin,
    1993

Competing hypotheses on the cause
   Oocyst contamination of drinking water influent
    coupled with treatment failure
   Chemical risk paradigm may be sufficient (still need to
    consider secondary transmission)
   Amplification of oocyst concentrations in the drinking
    water influent due to a person-environment-person
    transmission process
   Chemical risk paradigm cannot address this potential
    cause of the outbreak
        A model of disease transmission:
                The SIR model
 Mathematical modeling of a population where
  individuals fall into three main categories:
    Susceptible (S)
    Infectious (I)
    Recovered (R)
 Different individuals within this population can be in one
  of a few key states at any given time
      Susceptible to disease (S)
      infectious/asymptomatic (I)
      infectious/symptomatic (I)
      non-infectious/asymptomatic; recovered (R)
 A dynamic model: individuals are moving from state to
  state over time
    The SIR model: key details
There are two sets of variables:
Variables describing the states people are in
   S=susceptible
   I=infectious
   R=non-infectious/asymptomatic
Variables describing how many people are
 moving between these states (parameters)
   Example: γ=Fraction of people in state R who move to
    state S
                       The SIR Model
                                      g

                                             d
                        S                 I          R


                                                  ENVIRONMENT
                                          W
•   S: Susceptible
•   I: Infectious (symptomatic+asymptomatic)
•   R: Non-infectious
•   W: Concentration of pathogens in the environment
•   β: Infection rate due to exposure to pathogen
•   δ: Fraction of people who move from state I to state R
•   γ: Fraction of people who move from state R to state S
•   Solid lines: Individuals moving from state to state
•   Dashed lines: Pathogen flows between individuals in different states
The SIR Model: slightly different version
                                g
 a          0+ (W)                 (ρ)               μ
     X                     Y                      Z

                       λ    ρ                       σ
              W                      D
                                                            δ+μ
     The variables
     • X: susceptible
     • Y: infectious/asymptomatic
     • Z: non-infectious/asymptomatic
     • D: infectious/symptomatic
     • W: concentration of pathogens at the source
     • a: number of new susceptible individuals migrating in
The SIR Model: slightly different version (cont)
                                   g

  a            0+ (W)                 (ρ)               μ
       X                      Y                       Z

                          λ    ρ                       σ
                 W                       D
                                                               δ+μ
 The parameters
 • ρ: fraction in state Y who move to state D
 • α: Fraction in state Y who move to state Z
 • σ: Fraction in state D who move to state Z
 • γ: Fraction in state Z who move to state X
 • δ: Fraction in state D who die
 • μ: Fraction who die of natural causes
 • λ: Numbers of pathogen shed per infectious/asymptomatic individual
 • β0 : Baseline transmission rate
 • β : Infection rate due to pathogen
         Dynamic Modeling of Disease
          Transmission: an example

           dX
           dt    a  gZ  X   0 X   (W ) X
 Remember: a derivative is a rate of change
 X= the population of individuals susceptible to a disease
 dX/dt = rate of change in the susceptible population
 The equation describes individuals moving in and out of the
  susceptible population
 Each variable represents some number of individuals moving
    into the susceptible population (+) from some other group,
    out of the susceptible population (-) to some other group
       Dynamic Modeling of Disease
        Transmission: an example

          dX
          dt    a  gZ  X   0 X   (W ) X
 a= number of susceptible individuals migrating into the
  population
 γZ =number of non-infectious/asymptomatic individuals
  migrating back into the susceptible population
 μX =Fraction of susceptible individuals who drop out of the
  susceptible population because they die of natural causes
 β0X =number of susceptible individuals who become infected
  and drop out of the susceptible population
 β(W)X =number of susceptible people becoming ill due to
  pathogen exposure and drop out of the susceptible population
Analysis of Disease Transmission
             Models
Traditional approaches to evaluating
 dynamics models are qualitative
  – Stability analysis, threshold estimates (Ro),
    qualitative fits
  – Statistics rarely used to analyze output
Methodological goal to obtain public health
 relevant estimates of the outbreak
  – Need to modify traditional statistical techniques
    to address models with large number of
    parameters, sparse data, and collinearity
  Analysis of Disease Transmission Models
                              Likelihood
 Traditional likelihood methods
   –   Difficult to find maximum likelihood point in highly parameterized
       models.
   –   Confidence intervals are often not possible in complex likelihood
       spaces
 Profile likelihood is an alternative option
   –   Fix a subset of the parameters across a grid of values.
   –   At each point in the grid the remaining parameters are maximized.

                      Bayesian techniques
 Practical for combining outbreak data with existing information about
  parameters.
 Modifications required to deal with collinearities
                        Model 1

                          Goals:
To examine the role of person-person (secondary)
 transmission

To estimate the fraction of outbreak cases associated with
 person-person (secondary) transmission
     Cryptosporidium Outbreak - Model Diagram
                                                                   IA(t)
                                                                 Infectious
                                                            r   (asymptomatic)
   S(t)                     p        p   ... p        p
                       E1       E2               Ek                              d
Susceptible    + S                                                                  R(t)
                                                          1r
                                                                    IS(t)            Removed
                            Latently Infected
                                                                 Infectious
                                                                (symptomatic)

               W(t)
          Environmental
           Transmission

      S: Susceptible
      W: Concentration of Pathogens in the Environment
      IS: Symptomatic and Infectious
      IA: Asymptomatic and Infectious
      R: Immune/ Partially Protected
      Solid: Individual Flows from State to State
      Dashed: Pathogen Flows
             Analysis - Model 1
Monte Carlo Markov Chain (MCMC) was used to
        generate a posterior distribution.
 Two step procedure was used to address collinearities
  of the parameter estimates
    –   MCMC at profiled points
    –   Second MCMC on draws from first MCMC
 Cumulative incidence, I1, was produced by a random
  draw of the posterior
 Cumulative incidence, I0, was produced by first
  setting bs=0 then obtaining a random draw of the
  posterior.
 The attributable risk associated with secondary
  transmission was I1- I0
  Risk Attributable to
Secondary Transmission
                        10% , 95% CI [6, 21]

            700

            600

            500
Frequency




            400

            300

            200

            100

              0
                  0   0.1        0.2         0.3        0.4   0.5
                            Percent attributable risk
                      Model 2
                        Goal:
To examine the role of person-environment-
 person transmission
To estimate the preventable fraction due to an
 increase in distance between wastewater outlet
 and drinking water inlet
Examine preventable fraction as a function of
 transport time parameter, d
  –   Where d is a surrogate for the potential intervention
      of moving the drinking water inlet farther from the
      wastewater outlet
 Cryptosporidium Outbreak- Model Diagram
                                                                   IA(t)
                                                                 Infectious
                                                            r   (asymptomatic)
   S(t)                     p        p   ... p        p
                       E1       E2               Ek                              d
Susceptible    + S                                                                  R(t)
                                                          1r
                                                                    IS(t)            Removed
                            Latently Infected
                                                                 Infectious
                                                                (symptomatic)

               W(t)
          Environmental
           Transmission
                                S: Susceptible
                                W: Concentration of Pathogens in the Environment
                                IS: Symptomatic and Infectious
                                IA: Asymptomatic and Infectious
                                R: Immune/ Partially Protected
                                Solid: Individual Flows from State to State
                                Dashed: Pathogen Flows
            Analysis - Model 2

Estimate the likelihood for different values of d,
 ranging from 1 - 40 days.
Estimate the attack rate (AR) for the MLE
 parameters
Estimate the AR for different values of d, keeping
 all other parameters constant at their MLE values.
Plot PFd = 1 - ARMLE / ARd
       Profile Likelihood of the
          Delay Parameter
MLE for the time between contamination of sewage
 and exposure from drinking water tap was 11 days
                  (95% CI [8.3, 19])
                          -2450


                          -2455


                          -2460
         Log Likelihood




                          -2465


                          -2470


                          -2475


                          -2480
                                  0   5   10   15    20    25   30   35   40
                                                    Days
        Preventable Fraction As a
         Function of Delay Time
Predicting the public health benefits of moving the
                drinking water inlet
                                 0.9

                                 0.8
          Preventable Fraction




                                 0.7

                                 0.6

                                 0.5

                                 0.4

                                 0.3

                                 0.2

                                 0.1

                                  0
                                       0   5   10   15   20   25   30   35   40   45
                                                          Days
               Conclusions
Secondary transmission was small.
  – Best guess is 10%, most likely less than 21%
  – Consistent with empirical findings of
    McKenzie et al.
  – Kinetics of the outbreak in Milwaukee were
    too quick to be driven solely by secondary
    transmission
                Conclusions

Person-water-person transmission as the main
 infection pathway has not been well studied
  – Few data exist that examines person-water-
    person transmission
  – Studies have demonstrated a correlation
    between cases of specific viral serotypes in
    humans and in sewage
  – Provides information on a potentially
    important environmental intervention
           Conclusions: Methods
Analyzing disease transmission models using
            statistical techniques
Allows inferences about parameters that are
 interesting and relevant
   –   Can get at posterior distribution that allows for
       calculation of relevant public health measures
Requires the modification of existing techniques
   –   Profile likelihood to deal with large numbers of
       parameters
   –   Bayesian estimation techniques to address the co-
       linearity.
             Conclusions
Risk assessments should use models that can
        integrate relevant information
 Health data
    – Epidemiology

    – Basic biology

 Environmental data
    – Water quality

    – Fate and transport

 Need a population perspective
    – Model-based approach

				
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