BSC 417

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Lecture 11

• BSC 417

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Outline

• More on sensitivity analysis
• Spreadsheet on website
• Examples and in-class exercise
• Case analysis
• Discussion of Eisenberg et al. (2002) paper
• Eisenberg presentation on model
• Translating the model to Stella

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Assessing Risk from Environmental Exposure to
Waterborne Pathogens Use of Dynamic,
Population-Based Analytical Methods and
Models26 February 2008
The following 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
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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

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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

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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

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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

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The Disease Transmission Process

• Risk estimation depends on transmission dynamics
  and exposure pathways

Transport to other water sources
Agricultural Runoff
Drinking Water
Recreational Waters or Wastewater reuse
Animals
2 Trans.
Food
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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.

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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.

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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)

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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

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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.

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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

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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

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Approaches for Risk Estimation Epidemiologic
Measures

• Attributable Risk (AR)
• Incidence in exposed Incidence in unexposed
• Interpretation There are 6 excess cases of
  disease per 100 subjects receiving tap water

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Approaches for Risk Estimation Epidemiologic
Measures

• Attributable Risk Percent (AR)
• Excess cases in exposed
• Incidence in exposed
• Interpretation 33 of the cases of disease in
  the tap water group are due to water

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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

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Approaches for Risk Estimation Epidemiologic
Measures

• Population attributable risk
• Incidence in the communityincidence in the
  unexposed
• Interpretation In the community, 2 excess cases
  of disease per every 100 subjects in the community

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Approaches for Risk Estimation Epidemiologic
Measures

• Population attributable risk percentage
• Excess cases in the community
• Incidence in the exposed
• Interpretation 14 of the cases of disease in
  the community are due to tap water

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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

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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?

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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

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Approaches for Risk Estimation Risk Assessment
Model
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Approaches for Risk Estimation Risk Assessment
Model
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Approaches for Risk Estimation Risk Assessment
Results

• Overall risk estimate 14 cases/10,000/yr

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Approaches for Risk Estimation
Comparison/Conclusions
Table 3. Comparison of risk assessment and
intervention trials
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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.

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Microbial Risk Assessment

• Chemical risk paradigm
• Hazard identification, exposure assessment, dose
  response, risk characterization
• Model structure
• where P probability that a single individual,
  exposed to N organisms, will become infected or
  diseased.
• Exposure calculation

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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 or Wastewater reuse
Animals
2 Trans.
Food
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Microbial Risk AssessmentEisenberg 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

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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

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The SIR model key details

• There are two sets of variables
• Variables describing the states people are in
• Ssusceptible
• Iinfectious
• Rnon-infectious/asymptomatic
• Variables describing how many people are moving
  between these states (parameters)
• Example ?Fraction of people in state R who move
  to state S

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The SIR Model
g
?
d
I

• S Susceptible
• I Infectious (symptomaticasymptomatic)
• R Non-infectious
• W Concentration of pathogens in the environment
• ß Infection rate due to exposure to pathogen
• d Fraction of people who move from state I to
  state R
• ? 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

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The SIR Model slightly different version
g
dµ

• 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

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The SIR Model slightly different version (cont)
dµ

• The parameters
• ? fraction in state Y who move to state D
• a Fraction in state Y who move to state Z
• s Fraction in state D who move to state Z
• ? Fraction in state Z who move to state X
• d Fraction in state D who die
• µ Fraction who die of natural causes
• ? Numbers of pathogen shed per
  infectious/asymptomatic individual
• ß0 Baseline transmission rate
• ß Infection rate due to pathogen

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Dynamic Modeling of Disease Transmission an
example

• 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

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Dynamic Modeling of Disease Transmission an
example

• a number of susceptible individuals migrating
  into the population
• ?Z 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
• ß0X number of susceptible individuals who become
  infected and drop out of the susceptible
  population
• ß(W)X number of susceptible people becoming ill
  due to pathogen exposure and drop out of the
  susceptible population

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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

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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

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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

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Cryptosporidium Outbreak - Model Diagram
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
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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 bs0 then obtaining a random draw of the
  posterior.
• The attributable risk associated with secondary
  transmission was I1- I0

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Risk Attributable to Secondary Transmission

• 10 , 95 CI 6, 21

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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

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Cryptosporidium Outbreak- Model Diagram
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
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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

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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)

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Preventable Fraction As a Function of Delay Time

• Predicting the public health benefits of moving
  the drinking water inlet

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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

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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

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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.

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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