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
Animals
AgriculturalRunoff
DrinkingWater
2°Trans.
Recreational Waters
orWastewater reuse
Transport to other water sources
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 groupIncidence 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
Interpretation: There are 6 excess cases of disease per 100 subjects receiving tap water
06.012.018.0 activetapwater IncidenceIncidence
Approaches for Risk Estimation:
Epidemiologic Measures
Attributable Risk Percent (AR%) Excess cases in exposedIncidence in exposed
Interpretation: 33% of the cases of disease in the tap water group are due to water
33.018.006.0
tapwater
tapwater
IncidenceCasesExcess
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
Interpretation: In the community, 2 excess cases of disease per every 100 subjects in the community
02.012.014.0 activeComm IncidenceIncidence
Approaches for Risk Estimation: Epidemiologic
Measures Population attributable risk percentage
Excess cases in the communityIncidence in the exposed
Interpretation: 14% of the cases of disease in the community are due to tap water
14.014.002.0
tapwater
Comm
IncidenceCasesExcess
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 TrialComparing 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 (organisms per liter) (Normal Mean (SD)*)
1.06 (2.24)
2.68 (24.20)
0.93 (3.00)
Recovery rate 0.40 0.40 0.48 2. Treatment efficiency (logs removal)
Sedimentation and filtration (Mean (SD)*)
3.84 (0.59)
3.84 (0.59) 1.99 (0.52)
Chlorination (Mean (SD) 0 3.5 (2.93) 4 (2.93)
3. Water Consumption
in liters (mean (SD) ‡)
0.094 (0.42)
0.094 (0.42)
0.094 (0.42)
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
Table 2. Summary of risk estimates (cases/10,000,yr)
Cases of Illness
Mean Percentile (2.5, 97.5)
Cryptosporidium 2.1 (0.8, 3.5) Giardia 3.4 (0.6, 15.5) Enteric viruses (disinfection = 4 log removal)
8.4 (0.2, 18.7)
Enteric viruses (disinfection = 4 log removal)
0 (0, 0.2)
Overall risk estimate: 14 cases/10,000/yr
Approaches for Risk Estimation: Comparison/Conclusions
Risk Assessment Intervention Trials
Sensitivity Not relevant Low Causal evidence Indirect Direct Pathogen inclusion Few Many Model Specification Adds uncertainty Not relevant
Transmission processes
Can be included* Only in a limited way
Distribution System effects
Can be included* Was included
Examining alternative control strategies
Yes No
Expense Low High Time Fast Slow *Was not included in this study
Table 3. Comparison of risk assessment and intervention trials
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
where P = probability that a single individual, exposed to N organisms, will become infected or diseased.
Exposure calculation:
))(1(1 NP
dktko
dtecVN 101
Microbial Risk AssessmentAlternative framework: risk estimates at the population level allow for the inclusion of indirect risks due to secondary transmission
Animals
AgriculturalRunoff
DrinkingWater
2°Trans.
Recreational Watersor
Wastewater reuse
Transport to other water sources
Food
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
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
• 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
ENVIRONMENTW
S R
I
The SIR Model: slightly different version
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
δ+μW
X Z0+ (W) (ρ)
Dρ σ
Y
λ
a μ
The SIR Model: slightly different version (cont)
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
δ+μW
X Z0+ (W)
(ρ)
Dρ σ
Y
λ
a μ
Dynamic Modeling of Disease Transmission: an example
XWXXZadtdX )(0
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
XWXXZadtdX )(0
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
LikelihoodTraditional 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
S(t)Susceptible E1 E2 Ek
IA(t) Infectious
(asymptomatic)
R(t) Removed
W(t)Environmental Transmission
...
Latently Infected IS(t)Infectious
(symptomatic)
+ S
S: SusceptibleW: Concentration of Pathogens in the EnvironmentIS: Symptomatic and Infectious IA: Asymptomatic and InfectiousR: Immune/ Partially ProtectedSolid: Individual Flows from State to StateDashed: Pathogen Flows
Analysis - Model 1Monte 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
Transmission10% , 95% CI [6, 21]
0 0.1 0.2 0.3 0.4 0.50
100
200
300
400
500
600
700
Percent attributable risk
Freq
uenc
y
Model 2Goal:
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
S(t)Susceptible E1 E2 Ek
IA(t) Infectious
(asymptomatic)
R(t) Removed
W(t)Environmental Transmission
...
Latently Infected IS(t)Infectious
(symptomatic)
+ S
S: SusceptibleW: Concentration of Pathogens in the EnvironmentIS: Symptomatic and InfectiousIA: Asymptomatic and InfectiousR: Immune/ Partially ProtectedSolid: Individual Flows from State to StateDashed: 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
0 5 10 15 20 25 30 35 40-2480
-2475
-2470
-2465
-2460
-2455
-2450
Days
Log
Like
lihoo
d
MLE for the time between contamination of sewage and exposure from drinking water tap was 11 days
(95% CI [8.3, 19])
Preventable Fraction As a Function of Delay Time
Predicting the public health benefits of moving the drinking water inlet
0 5 10 15 20 25 30 35 40 450
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Days
Pre
vent
able
Fra
ctio
n
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: MethodsAnalyzing disease transmission models using
statistical techniquesAllows 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.
ConclusionsRisk 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
