Transcript Approaches for Risk Estimation: Epidemiologic Measures

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 CaliforniaBerkeley 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
Animals
2°
Trans.
Food
Recreational Waters
or
Wastewater reuse
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, placebocontrolled 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
Incidencetapwater  Incidenceactive
 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
IncidenceComm  Incidenceactive
 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
Cryptosporidium
Model
Giardia
Viruses
1. Source water
Concentration
(organisms per liter)
(Normal Mean (SD)*)
2.68 (24.20)
0.93 (3.00)
0.40
0.40
0.48
3.84 (0.59)
3.84 (0.59)
0
3.5 (2.93)
4 (2.93)
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
Recovery rate
1.06 (2.24)
2. Treatment efficiency
(logs removal)
Sedimentation and
filtration (Mean (SD)*)
Chlorination (Mean (SD)
3. Water Consumption
1.99 (0.52)
in liters (mean (SD) ‡)
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
Mean
Percentile
(2.5, 97.5)
Cryptosporidium
2.1
(0.8, 3.5)
Giardia
Enteric viruses
(disinfection = 4
log removal)
Enteric viruses
(disinfection = 4
log removal)
3.4
(0.6, 15.5)
8.4
(0.2, 18.7)
0
(0, 0.2)
Approaches for Risk Estimation: Comparison/Conclusions
Table 3. Comparison of risk assessment and intervention trials
Risk Assessment
Intervention Trials
Not relevant
Low
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
Sensitivity
Causal evidence
*
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  kd 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
Animals
2°
Trans.
Food
Recreational Waters
or
Wastewater reuse
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
S

I
W
•
•
•
•
•
•
•
•
•
d
R
ENVIRONMENT
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
X
0+ (W)
Y
λ
W
(ρ)
ρ
Z
μ
σ
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
X
0+ (W)
Y
λ
W
(ρ)
ρ
Z
μ
σ
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)
r
S(t)
Susceptible
 + S
E1
p
E2
p
... p
Ek
Latently Infected
Infectious
(asymptomatic)
p
d
1r
IS(t)
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
R(t)
Removed
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
Frequency
500
400
300
200
100
0
0
0.1
0.2
0.3
Percent attributable risk
0.4
0.5
Model 2
Goal:
To examine the role of person-environmentperson 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)
r
S(t)
Susceptible
 + S
E1
p
E2
p
... p
Ek
Latently Infected
Infectious
(asymptomatic)
p
d
1r
IS(t)
R(t)
Removed
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
Log Likelihood
-2455
-2460
-2465
-2470
-2475
-2480
0
5
10
15
20
Days
25
30
35
40
Preventable Fraction As a
Function of Delay Time
Predicting the public health benefits of moving the
drinking water inlet
0.9
Preventable Fraction
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
Days
30
35
40
45
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-waterperson 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 colinearity.
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