Quantitative Microbial Risk Assessment QMRA Workshop

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Quantitative Microbial Risk Assessment (QMRA)
Workshop

• 107th American Society for Microbiology General
  Meeting
• Toronto, Canada, May 20, 2007
• Center for Microbial Risk Assessment

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U.S. EPA and DHS Center of Excellence

• The CAMRA is an interdisciplinary research center
  stablished to develop scientific knowledge on the
  fate and risk of bioterrorist and other high
  priority infectious agents.
• (Michigan State University, Drexel University,
  University of Michigan, Carnegie Mellon
  University, Northern Arizona University,
  University of Arizona and University of
  California Berkeley)
• Homepage http//www.camra.msu.edu/

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Contents
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Introduction to Risk Analysis and Risk Assessment

• Joan B. Rose, Ph.D.
• Michigan State University

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The National Academy of Sciences Red Book
Approach
Risk Analysis
Risk Assessment
Risk Management Valuation, policy making
Risk Communication

• More recent guidance stresses involving
  interested and affected parties throughout
  process (NRC 1996)

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Definitions Used in Risk Analysis
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• Risk assessment is a method to examine
  qualitatively or quantitatively the potential for
  harm from exposure to contaminants or specific
  hazards.
• Monitoring and data are some of the keys to
  establishing risks and therefore safety goals.

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Quantitative Risk Assessment

• Tool used to estimate adverse health effects
  associated with specific hazards.
• Elicits a statistical estimate or probability of
  harm.
• Used for risk management decisions.
• Frame work for science-based assessment.

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Risk Communication

• Messages/information.
• Who is providing the information?
• Who are the stakeholders?
• What format (s) are best?
• What education need is tied to the science?
• What are the choices associated with the risk?
• What will various stakeholders do with the
  information?
• Are the risks distributed equitably?

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Risk Management

• Approaches for addressing control of the risk.
• Requires assessment and also choices of what
  people value and how they judge risks.
• Must decide what is the safety goal
• judgment ethics.
• Costs, feasibility, implementation important.
• Controls can be based on engineering approaches.
• Controls may be institutional based on policies
  to limit exposures.
• Controls may be preventative.

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Risk Management Issues

• Acceptable risk (de minimis risk) EPA has
  suggested that 1/10,000 infection annually is an
  appropriate level of safety for drinking water.
• Benefit and Cost Cost for water treatment to
  reduce cost of disease (health care costs,
  productivity time lost and suffering)

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• FDA Home Page CFSAN Home Search/Subject Index
  Q A Help
• September 16, 2006 Updated October 20, 2006
• Nationwide E. Coli O157H7 Outbreak Questions
  Answers
• FDA and the State of California announced October
  12 that the test results for certain samples
  collected during the field investigation of the
  outbreak of E. coli O157H7 in spinach are
  positive for E. coli O157H7. Specifically,
  samples of cattle feces on one of the implicated
  ranches tested positive based on matching genetic
  fingerprints for the same strain of E. coli
  O157H7 that sickened 204 people.

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    Washington-area hotel closes for
cleaning after norovirus sickens dozens of
guests The Associated PressPublished March 2,
2007 ARLINGTON, Virginia A hotel near a
Washington, D.C., airport was closed for cleaning
after as many as 150 guests were sickened by the
highly contagious norovirus, hotel and county
health officials said.
By kgw.com Staff
FAIRFAX COUNTY Senior Community Hit by Possible
Norovirus By Leef Smith Washington Post Staff
WriterSaturday, March 10, 2007 Page B02
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BioWatch Program
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BioWatch Program Model
lt 36 hrs
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Insert epi and risk sensitivity
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Risks and Water Quality Standards and Development
of Management Strategy U.S. EPA
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Water Quality Standards

• Set permissible levels of contamination (MCL)
• Establish monitoring program, sample frequency,
  and sampling sites.
• Standardize methodology, selectivity,
  sensitivity, accuracy and precision.

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Performance Criteria

• Specify the performance, treatment efficiency,
  and desirable end points.
• Define the types of treatment.
• Compliance monitoring, verification and
  reliability.

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Early History of Federal Drinking Water standards

• 1914 First standards for B. Coli
• 1925 revised the coliform standard based on
  feasibility
• 1942 required coliform monitoring in the
  distribution system, added metals.

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1962 US Public Health Service Standards

• 19,000 municipal water supplies
• Increased concern for industrial pollution
• Added nitrate, some crude organic parameters
• Binding at the federal level on 700 systems 50
  states accepted

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1969 Community WaterSupply Study

• 41 of the 969 systems surveyed did not meet
  standards
• U.S. PHS released report in 1970
• This generated congressional concern

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Increasing Concern Leads to A Federal Mandate

• As a result of the 1969 CWSS, bills were
  introduced in 1970
• 1972 EPA report on Mississippi River, 36 organic
  compounds
• 1973 GAO reports only 60 of 446 systems surveyed
  were in compliance
• Trihalomethanes, a chlorination by-product, are
  discovered.

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The Safe Drinking Water Act of 1974--Roles

• Federal standard setting, research and
  oversight of states
• States could adopt primacy for
  implementation/enforcement.
• Local must monitor and comply (responsible for
  capital and O M cost)

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Safe Drinking Water Act 1986

• Congressional concern over the rate of regulation
• Oversight hearings began in 1982.
• Increasing reports of organic contamination
• Concern for uncorrected violations
• Red Book for Risk Assessment and its role in
  policy produced by the NAS.

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SDWA 1986 -- Implementation

• EPA was required to regulated 83 contaminants by
  89
• Filtration and disinfection were required
• Monitoring for unregulated contaminants
• Lead ban Corrosion Control Rule
• Ground Water Protection Programs

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Evolution of QMRA

• lt 1980 Indicator approaches used suggesting that
  some level of contamination below which one is
  safe
• 1980s Initial Dose Response concepts
  application in development of EPA Rules
• 1988 Dose-response for Giardia, viruses in
  Water.
• 1990 Adoption for food safety WHO food and
  water consultations Dynamic model
  applications ILSI framework documents
• 2000s Air and Home Land Security applications
• Reg framework development
• Population sensitivities

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U.S. EPA Surface Water Treatment Rule 1988

• Identified Giardia, Viruses and Legionella for
  control using performance criteria.
• 1/10,000 risk identified in the preamble
• Cryptosporidium identified in the preamble
• QMRA used for Giardia
• Required 99.9 reduction of Giaridia and 99.99
  for Viruses
• BMP filtration (turbidity)
• Disinfection CT concept required for Viruses,
  Bacteria and Viruses. (However, DBP influencing
  this).

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Comparative Risks
Microorganisms Chemicals
in Water in Water
High to low dose Use of safety factors Upper 95
confidence limits
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SDWA 1986 -- Concerns

• High rate of non-compliance in small systems
• Funding shortages
• Deficiencies uncorrected
• 1991 outbreak of Cryptosporidiosis in Milwaukee

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SDWA 1996 --Changes and New Programs

• Still required 83 standards
• Eliminated 25 new regulations every 3 years
• Revised process for listing contaminants
  Contaminant Candidate List CCL
• Required cost-benefit analysis
• National occurrence data base
• Created state revolving loan fund
• Required consumer confidence reports

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The Universe of Potential Water Contaminants
Known Occurrence
Known Health Effects
I
II
III
IV
Potential to Occur
Potential Health Effects
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U.S. EPA Contaminant Candidate List

• Identify contaminants that have known or
  potential health effects AND
• Have a known or potential for occurrence in
  water.
• Develop health effects information
• Develop methods for detection
• Develop occurrence data base
• Develop rules
• HAS NOT ADDRESSED A QMRA FRAMEWORK.

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Risk Matrix
High
Low
Maximum Risk
Impact of Health Outcome
Treatability
Minimum Risk
Low
High
Exposure
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Risk Issues

• Acceptable risk (de minimis risk) EPA has
  suggested that 1/10,000 infection annually is an
  appropriate level of safety for drinking water.
• What is acceptable for recreation? (1/500, single
  swimming event).
• Benefit and Cost Cost for water treatment to
  reduce cost of disease (health care costs,
  productivity time lost and suffering)

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Current Regulatory Climate

• Major advances have been made in pollution
  control in the last 60 years.
• Further gains will require increasingly
  discriminating assessment and control of risks.
• Costs of the controls increase as high risks are
  controlled and attempts are made to control
  marginal risks
• Methods are now available to measure small levels
  of contaminants in the environment.
• Still need a framework for application of QMRA
  for microbials within EPA.

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National Academy of SciencesRisk Assessment
Paradigm

• HAZARD IDENTIFICATION
• Types of microorganisms and disease end-points
• DOSE-RESPONSE
• Human feeding studies, clinical studies, less
  virulent microbes and health adults
• EXPOSURE
• Monitoring data, indicators and modeling used to
  address exposure
• RISK CHARACTERIZATION
• Magnitude of the risk, uncertainty and
  variability

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Four Step Risk Assessment

• Hazard Identification To describe acute and
  chronic human health effects sensitive
  populations, immunology need to be understood.
• Dose-Response To characterize the relationship
  between various doses administered and subsequent
  health effects have human data sets but lacking
  appropriate animal models to increase assessment.
• Exposure Assessment To determine the size and
  nature of the population exposed and the route,
  amount, and duration of exposure. Temporal and
  spatial exposure with changes in microbial
  populations a concern.
• Risk Characterization To integrate the
  information from exposure, dose response, and
  health steps to estimate magnitude of health
  risks. Monte Carlo analysis to give distribution
  of risks and population/community models needed.

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Tools Data Needs for Microbial Risk Assessment

• Disease surveillance
• Clinical studies
• Epidemiological studies
• Methods for detection of microbials
• Transport models
• Regrowth and die-off models
• Development of occurrence data bases
• Dose-response models

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Human Health Effects

• Microbial virulence and pathogenicity factors
• Symptomatic and symptomatic infection
• Severity (duration, medical care
  hospitalization)
• Mortality
• Host immune status (role in outcome)
• Susceptible populations

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Hazard Reporting

• Sequence of events before an individual infection
  can be reported
• Individual is infected
• Did illness occur?
• Did the ill person seek medical care?
• Was the appropriate clinical test (stool, blood)
  ordered?
• Did the patient comply?
• Was the laboratory proficient?
• Was the clinical test positive?
• Was the test result reported to the health
  agency?
• Was the report timely?
• What did the health agency do with the report?

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Acute and Chronic Outcome Associated with
Microbial infections
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Dose Response Issues

• Human data sets (healthy volunteers)
• Vaccine strains or less virulent organisms
• Low doses often not evaluated
• Doses measured with mainly cultivation methods
  for bacteria and viruses (CFU PFU) for parasites
  counted under the microscope.
• Response excretion in the feces, antibody
  response and sometimes illness.
• Human subjects concerns for filling in data gaps

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Exposure Assessment and Risk Characterization

• Exposure and levels of contamination the most
  important aspect for providing input to risk
  characterization.
• Need better monitoring data, better transport
  models.
• Will need new methods, QPCR, for better
  assessment of non-cultivatible but important
  viruses and bacteria.
• Essential for Good Risk Management Decisions

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Occurrence Analysis for the Exposure Process

• Concentrations
• Frequency
• Spatial and Temporal Variations
• Regrowth and Die-off
• Transport

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New Microbiological Methodsto Inform Risk
Assessment during Exposure Assessment

• Alternative Indicators
• Pathogen Monitoring
• Source Tracking

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Watershed assessment, Flow, Transport,
Integration with Water Quality and Thus Exposure.
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Evaluation of Multiple Exposures
Pathways in the built environment
Pathways in the natural environment
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Risk Characterization

• Individual risk versus population risks.
• Static Models used predict infection NOT illness,
  thus are conservative.

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Interaction between Disease Transmission and the
Environment
?
Post - Infection
Dose-response ? b
s
?
Exposed
Susceptible
Carrier
ß
Psym
f
person - person
?
person-environment
Diseased
Exposure Assessment b
Pathogen Fate And Transport
Green boxes Epidemiological State Red box
Pathogen Source / Sink Solid Line Movement of
Population Dotted Line Movement of Pathogen
External Environment
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Linking Probability of Infection to Population
Models
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Applications for Microbial Risk Assessment

• Establish policies for protection of health using
  standards or performance based criteria
• Compare risks
• Evaluate alternative solutions
• Prioritize risks
• Identify scientific data gaps
• Develop protocols for monitoring

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PROBLEM FORMULATION
ANALYSIS
CHARACTERIZATION
of HumanHealth Effects
of Exposure
RISK CHARACTERIZATION
RISK MANAGEMENT OPTIONS
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Water Quality Data
Hazard identification



Exposure estimation
E.coli Enteroocci Coliphage levels
Sewage and


Source Tracking
Fecal Loading
Prevention Treatment Strategies
Environmental

Parasite tesing
Survival

Transport Runoff
-
Virus testing

Surface Water/ Ground Water Concentrations
Risk Estimation

Dose-response
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Water Ethics Data Access Communication Educati
on Training Networks Safety goals Sensitive
populations Shared Responsibility
Hydrogeological Setting
C L I M A T e I M P A C T s
M O N I T O R I N G
HAZ ID Transport Fate Models Exposure RISK
Prevention Early Warning Response Recovery
Watershed to the Tap HACCP WSP Decision-Support
Systems
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HACCP

• Hazards (Haz ID).
• Critical points of contamination (part of the
  exposure pathway product end point but chain
  from source and raw materials through to finished
  product).
• Controls Processes to achieve safety.
• Critical Control Points (monitoring) assurance
  monitoring.

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Challenges Water Safety PlansWHO

• Define
• Acceptable risk (Burden of disease)
• Definition (infection) Acceptable/Tolerable
  Limit Water Quality Goals for ambient waters.
• Endpoints Number of pathogens
• Critical control points Identify areas for
  control and monitoring Efficiency.
• Treatment Disinfection Needs

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Advancing Microbial Risk Assessment
The Exposure
The Hazard
The Dose-response
The Disease Dynamics
The Risk Characterization
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Exposure

• Charles P. Gerba, Ph.D.
• University of Arizona

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Quantitative Microbial Risk Assessment
Identify pathogen of concern
Dose-response data from humans
Model infection probability
Clinical data to estimate probability of disease
and mortality
Predict probability of disease from exposure
Validate model from outbreak data
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Routes of Exposure

• Ingestion
• Water
• Food
• Hand to mouth (fomites)
• Inhalation (aerosols)
• Dermal

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Percentage of Disease Due to Transmission Route
?
?
?
?
?
?
?
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Factors Important in Assessing Exposure

• Route of Exposure
• Duration of exposure
• Seconds, hours, minutes
• Number of exposures
• How many times in a day, month, year
• Degree of exposure
• Liters of water ingested
• Liters of air inhaled
• Grams of food ingested

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Import Things to Remember about Microbial
Transport Fate

• Microbes are colloids not solutes
• Log-normal or Poisson distributions
• Microbial transport is influenced by
  electrostatic and hydrophobic interactions
• Microbes are individuals
• Not all individuals behave the same

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How Important is the Environment in Disease
Transmission?

• 80 of all infections are acquired through the
  environment
• Most other infections are acquired from insect
  bites and direct personal contact (e.g. sex, hand
  shaking, kissing)

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Microbial Die-off
Number of Organisms
Time
Time
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Microbial Inactivation (die-off)

• Nt/No -kdt
• Nt microbial number at time t
• No initial microbial number
• Kd inactivation rate as a function of a
  parameter
• t time

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Factors that influence Enteric Virus and Bacteria
Survival in Surface Waters

• Temperature
• UV Light
• Organic Matter
• Seawater vs. Freshwater
• Sediments
• Antagonistic Microflora

• Longer survival at lower temperatures
• Related to amount of sunshine
• Longer survival in presence of organic matter
• Shorter survival in seawater
• Prolonged survival in sediments regrowth of
  enteric bacteria possible in sediments
• Certain marine microbes prey on bacteria or are
  antagonistic to virus survival survival is
  reduced in the presence of non-enteric
  microorganisms

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Factors that influence Enteric Virus and Bacteria
Survival at/near Soil Surface

• Temperature
• Soil Moisture
• Organic Matter
• Rate of Moisture Loss
• Antagonistic Microflora

• Longer survival at lower temperatures
• Related to amount of sunshine
• Longer survival in presence of organic matter
• The greater the evaporation rate the more rapid
  the rate of inactivation
• Certain microbes prey on bacteria or are
  antagonistic to survival survival is reduced in
  the presence of non-enteric microorganisms

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Sources of Foodborne Organisms

• Infected animal
• Cross contamination
• Cutting board to produce (vegetables)
• Irrigation water
• Handling and processing
• Hand to produce
• Wash water
• Ice

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Transport and fate of enteric viruses in the
marine environment
Aerosolization by breaking waves
Sewage outfall
Virus association with suspended solids (acts to
prolong virus survival)
Resuspension by rain, wave action,
tides, dredging, etc.
Accumulation in sediments (viruses occur in
higher concentrations in sediment than the
overlaying water)
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Uptake by crustacea and bottom feeding fish
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Viruses
Air/Water Interface
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Steps in Estimating Exposure from Pathogens in
Biosolids
A person comes into contact with the biosolids
Pathogen concentration in biosolids
Duration of exposure One day
Number of Pathogens after treatment
Amount of hand contact
Concentration after land application
Amount swallowed 50-480 mg
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Life in the 21st Century

• Most of our time is spend indoors
• More people work in offices than ever before
• We travel more than ever before
• We spend less time cleaning than the last
  generation
• We are less clean (e.g. laundry practices)
• We spend more time in public places
• We are more mobile and have more electronic
  equipment (e.g. cell phones)

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Most Common Diseases Spread Through Hand Contact

• Every three minutes, a child brings his/ her hand
  to nose or mouth
• Every 60 seconds, a working adult touches as many
  as 30 objects

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Occurrence of fecal bacteria on the hand (United
States)

• Preparing a meal Greatest
• Children after playing
• Doing the laundry Least
• Person exiting a toilet

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Disease Spread by Fomites

• Route of exposure
• Children under 12 months to their face 60 times
  per hour
• Cross contamination of foods
• Which fomites are important
• How often does hand contact occur on which
  fomites?
• Frequency of pathogens on fomites in a given
  environment
• Concentration of pathogen on a fomite

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Transmission by Fomites

• Hard surfaces
• Phones, tap handles, desk tops, door knobs,
  cutting boards, table tops
• Cleaning clothes
• Sponges, dish clothes
• Clothing
• Laundry, towels, bed sheets

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Transmission by Fomites

• Bathroom (Bano)
• Sinks, taps, bottom of the toilet seat
• Norovirus, Graidia, Cryptosporidium, Shigella
• Kitchen
• Sponge, sink, cutting board
• Salmonella, Campylobacter
• Schools
• Norovirus, rhinovirus, Salmonella

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Inactivation of Respiratory Viruses on Fomites
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Inactivation of Enteric Viruses on Fomites
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Sites by Coliform Densities
Bath Sink
Cutting Board
Kitchen Sink
Sponge
Bath Floor
Kitchen Floor
Bath Counter
Toilet Seat
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Classrooms (Grades 4-6)

• Areas most contaminated with bacteria
• Pencil sharpener
• Student desk top
• Computer
• Sink in classroom
• Viruses isolated
• Influenza
• Norovirus
• Parainfluenza

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Time Coliform Bacteria Detected (public
restrooms)

• Top of the toilet seat 20
• Flush handle 6
• Wall behind toilet 9
• Floor in front of toilet 64
• Sink 61
• Tap 15
• Urinal inside 30
• Urinal flush handle 0
• Sanitary napkin disposal outside 57
• Door knob 4

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MRSA Occurrence not Related to Total Bacterial
Numbers in Cars
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Staph. aureus in Autos
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The Forgotten Fomites Critical Control Points?

• Phone (cell phone)
• TV remote
• Computer keyboard
• Computer mouse
• Sink taps/handles
• Sponges/cleaning clothes
• Laundry

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Risk of Rotavirus Infection from Laundering
Concentration of Virus
Assumption
The amount in 0.001 gr of feces
2 x 107
2 x 105
After washing 99 reduction cm2 clothing
2 x 104
After 28 min. drying
200
1 transferred to hands
2
10 transferred to mouth
Risk of infection 110
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Bio aerosols
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Types of Bioaerosols

• Sneezing
• Showers
• Cooling towers
• Waste handling
• Sewage treatment
• Land application of biosolids and sewage
• Compost facilities

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Factors Affecting the Survival of Microorganisms
in Aerosols

• Relative humidity
• Depends upon the microorganism optimal may be
  at either high, low, or medium relative humidity
• Sunlight (UV light)
• Longer survival at night
• Suspending media
• Lower survival in the presence of organic matter
• Temperature
• Greater survival at lower temperatures

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Basic Microbial Dose Response

• Charles N. Haas, Ph.D. Drexel University

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The Risk Analysis Process
Risk Assessment
NAS, 1983
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Why do we need a DR model?

• We can (never) do a direct study (even with
  animals) to assess dose corresponding to an
  acceptably low risk
• We use a model to (extrap)(interp)olate to low
  dose

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The Dose

• Average administered to a population
• Actual number an individual experiences
• Retention
• In vivo body burden after multiplication

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Plausibility of Models

• Should consider discrete (particulate) nature of
  organisms (high variability at low dose)
• Based on concept of infection from one or more
  survivors of initial dose (birth-death models)

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Derivation of Exponential DR Model

• Poisson distribution of organisms among replicate
  doses (mean in dosed).
• One organism is capable of producing an infection
  if it arrives at an appropriate site.
• Organisms have independent and identical
  probability of surviving to reach and infect at
  an appropriate site (k).

If k1, what does that tell us?
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Derivation of Beta-Poisson Model (assumptions)

• Same as the exponential model except nonconstant
  survival and infection probabilities
• Survival probabilities (k) are given by the beta
  distribution
• Slope of dose response curve more shallow than
  exponential

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Comparison of Exponential and Beta-Poisson (I)
Beta-Poisson Model
Original Form
Revised Parameterization
N50 organisms for 50 infectivity
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Comparison of Exponential and Beta-Poisson (II) -
low dose extrapolation
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A Generalized Framework
Organisms ingested --gtorganisms survive to
colonize--gtsufficient colonies to cause effect

• P(kmin) fraction of subjects that require kmin
  original organisms to survive in order to become
  infected (point truncated Poisson, etc.)
• P1(jd) fraction of subjects ingesting from an
  average dose d who actually ingest j organisms
  (Poisson...)
• P2(kj) fraction of subjects ingesting j
  organisms in which k organisms survive (binomial
  beta-binomial)

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Threshold (gt1) Models
Median dose fixed at 5

• threshold models (kmingt1) yield steeper slopes
  and non-linear low dose models
• no human data sets yet examined justify these
  models

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Empirical Models

• obviously others as well
• but these do not take into account the particle
  nature of organisms
• give nonlinear low-dose behavior

• Log probit
• Log logistic
• Weibull

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PBDRMs

• Requires insight into biological/physical
  mechanisms leading to infection/disease
• May be more complex than extant data justify

Thran, personal comm.
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Experimental Protocol

• Animals/subjects divided (randomly) into k groups
• In group i (i1..k)
• All subjects exposed to (poisson average) dose di
• Of the Ti total subjects, Pi are positive
• Quantal
• Poisson average dose
• Binomial variability

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Mechanics of Fitting (I)

• each dose of our bioassay is a sample from a
  binomial distribution (with Ti) total organisms
  and an unknown positive probability (of adverse
  outcome) of p. so from binomial relationship, we
  would have

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Mechanics of Fitting (II)

• but we have multiple doses (igt1, including
  control), and so if we use the likelihood
  criteria
• we would have
• the best possible fit (maximum value of ln L) we
  could have is when our dose response predictor
  precisely goes through the observed data, i.e.,

Any dose-response model must give a fit no
better, i.e., ln L would be smaller --- more
negative.
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Mechanics of Fitting (III)

• it is convenient to look at the fit of some model
  versus the best possible, and also to multiply by
  -2 (to transform to minimization of a positive
  value, and recall c2 confidence limit behavior
  for likelihoods)
• obtain best fit parameters by finding
  (parameter vector) that minimizes Y

fit is acceptable if Y is less than the upper 5
(or 1...) of the c2 distribution with degrees
of freedom number of doses minus number of dose
response parameters
With pi from dose-response function (function of
Q)
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Data Fitting Methodology

• Y provides an index of goodness of fit
• test vs chi square doses-( params)
• Unconstrained nonlinear optimization
• Excel
• R
• (Matlab, Mathematica )

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Example of Point Estimation
Ward, human rotavirus

• rotavirus (human)
• BP fits better than others, and is accepted as
  adequate

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Characterizing Uncertainty-Confidence Limits

• Confidence regions determined from Likelihood
  Ratio approach
• all ??in confidence region if
• need to determine n-dimensional region, which may
  or may not be closed
• can be done in Excel (but tedious and slow)

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Example Uncertainty Rotavirus
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Reasons for Lack of Fit

• Outlier
• Overdispersion
• Systematic deviations

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Dealing with Outliers

• Identification by likelihood (fit by removal of
  outliers and compute likelihood ratio)
• significance levels confirmed by Monte Carlo
• Problems with multiple outliers (masking,
  swamping)
• Not yet a well treated problem in statistics
  (non-normal, non-linear models)
• Outlier identification is typically with respect
  to a model -- hence we must place trust in a
  model to identify outliers

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Dealing with Overdispersion

• Replace a binomial likelihood with a
  beta-binomial
• This introduces an extra parameter
• Most dose-response studies do not have sufficient
  dose levels or replicates to truly validate this
  approach

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Dealing with Systematic LOF

• Systematic trends in deviance residuals are
  suggestive of need to use a different
  dose-response model
• Perhaps one with additional parameters

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CAMRA Project III Workflow
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Risk Characterization

• Patrick L. Gurian, Ph.D.
• Drexel University

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The Risk Assessment Framework
specific exposures in the scenario of concern
Exposure Assessment
Risk Characterization
Plug exposure into the dose-response function
Hazard Identification
Dose Response
literature dose-response function
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Point Estimate

• Single numeric value of risk
• May correspond to best estimate of risk
• May be maximum reasonable exposure
• Use parameter values of exposure and dose
  response parameters corresponding to point
  estimate of interest

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Example Anthrax

• What is the risk of Anthrax attack?
• Best fit dose-response is Beta-Poisson model
• Alpha 0.974 and N50 62817 (Haas unpublished)
• Risk 1-(1(dose/62817)(2(1/0.974)-1))-0.974
  
• If 1 spore of B. antracis is inhaled
• Risk 1-(1(dose/62817)(2(1/0.974)-1))-0.97
• Risk 1.6 x 10-5
• Note this is the fatality risk

144
Example Cryptosporidium Risk

• Cryptosporidium is present in a surface water
• What is risk of swimming in this water?
• Lets calculate a point estimate for our best
  estimate of risk
• Use most likely exposure and dose response
  parameter values

145
Exposure Analysis

• Assume 10 infective oocysts/liter
• 0.13 liters consumed per swim, 7 swims per year
  (Lodge et al. 2002)
• Dose contact rate x concentration
• Dose 0.13 liters/swim x 10 oocyst/liter
• Dose 1.3 oocysts/swim

146
Dose-Response

• Exponential with r 0.004191
• Table 14.13 Gerba
• Risk 1-exp(-dose x 0.004191)

147
Risk Characterization

• Risk 1-exp(-dose x 0.004191)
• Dose 1.3 oocysts/swim
• Risk 1-exp(-1.3 x 0.004191)
• Risk 1-exp(-.0054483)
• Risk 1-0.9946
• Risk0.0054
• Note this is risk of infection per swim

148
Morbidity and Mortality

• Often view risk of illness and death as
  independent of dose given that infection has
  occurred
• Based on Haas et al. 1999
• Probillnessinfection0.39
• Probdeathillness0.001

149
Risk of Illness and Death

• Risk of illness
• Probillnessinfection x Probinfection
• 0.39 x 0.0054 0.0021
• Risk of death
• Probdeathillness x Probillness
• 0.001 x 0.0021 2.1x10-6

150
Annual Risk

• Treat swims as discrete trials with discrete
  outcomes infected vs. not infected, ill vs.
  healthy, dead vs. alive
• Binomial distribution
• Risk occurs when infections occurs on 1 or more
  trials
• No risk occurs when all trials have non-infection
  outcomes
• Easier to calculate

151
Mathematics of Converting Daily to Annual Risk

• AnnualRisk 1probno infection in N trials
• Probno infect. in N trials prob no infectN
• Probno inf. in N trialsprob1-DailyRiskN
• AnnualRisk 1-prob1-DailyRiskN

152
Annual Risk of Infection

• AnnualRisk 1-prob1-DailyRiskN
• AnnualRisk 1-prob1-0.00547
• AnnualRisk 1-prob0.99467
• 1-0.9630.037

153
Annual Risk of Illness

• AnnualRisk 1-prob1-DailyRiskN
• AnnualRisk 1-prob1- 0.00217
• AnnualRisk 1-prob0.99797
• 1-0.9850.015

154
Probabilistic Uncertainty Analysis

• Risk assessments are often subject to large
  uncertainties
• We often model these uncertainties
  probabilistically (as if uncertain quantity were
  subject to random variability)
• Propagate these uncertainties through our model

155
Smearing out parameter estimates
Now it is our most likely value, but not the only
possible value
This was our point estimate
156
What are the Goals of Uncertainty Analysis?

• Find range of possible outcomes
• Determine if the uncertainty matters
• Determine which inputs contribute the most to
  output uncertainty
• Compare range of outcomes under different
  decisions, policies
• Inform risk management

157
Propagating Uncertainty

• Usually use the same formulae as your point
  estimate
• Parameters are not single values but probability
  distributions

158
Uncertainty Propagation (a little more formally)

• Model F(x) where x is a vector of model inputs
  (parameters)
• Given probability distributions for x, what is
  distribution of F(x)?
• Propagation of uncertainty through model
• From inputs to outputs

159
Monte Carlo Uncertainty Analysis

• The work horse of probabilistic risk assessment
  (PRA)
• Algorithms exist to generate random numbers
• Generate or sample X1 and X2
• Calculate corresponding Y F(X1, X2)
• Repeat N times, each Y value equally plausible
  prob Yi 1/N

160
Monte Carlo Results

• Have a discrete distribution of Y that
  approximates true distribution of Y
• EY SYi/N
• VarY SYi EY2 /(N-1)
• True percentiles of Y percentile of Yi values
• Typically summarize by mean, median, upper bound,
  and lower bound

161
Monte Carlo Sensitivity Analysis

• Calculate Correlation of (Y, X1) and (Y, X2) in
  samples
• Larger (absolute value of) correlation indicates
  more important influence on Y
• May wish to do this based on rank order
  correlations (order all Y values from 1 to N, all
  X1 and X2, correlate ranks) to avoid influence of
  outliers, non-linearities
• Always good to look at scatter plots of Y vs. X

162
Implementing Monte Carlo Analysis

• Need large N
• How large? How many samples/iterations?
• Run until you get convergence
• Answer does not change much as you continue to do
  additional simulations
• As a rule of thumb 1000 is bare minimum
• 10,000 is recommended (see Kammen and Hassenzahl,
  Burmaster)

163
Monte Carlo implementation

• Add on software packages for Excel exist such as
  _at_risk and Crystal Ball
• Can be done in Excel without these packages
• Make each column a variable
• Each row a realization of your model with
  different inputs sampled by random number
  generator

164
Excel Random Number Generator

• Tools select Add ins
• Make sure Analysis Toolpak is checked
• Then select Data Analysis from the Tools menu
  and pick Random Number Generation.
• This will bring up a dialogue box and you can
  enter the appropriate distribution type and
  parameter values.

165
From Point Estimate to PRA

• Risk1-exp(-r x ingestion x concentration)
• Choose input distributions that reflect plausible
  spread in these values
• Ingestion 0.13 l/swim
• ConcentrationPoisson(10)
• Ln (r) N(-5.5, 0.352)
• generate LN (r) from normal generator
• r exp(generated number)

166
Heres What It Looks Like in Excel
167
Presenting Results

• Present both point estimates and distributions,
  as appropriate
• Give an estimate of central tendency
  (mean/median) or risk
• Generally want plausible upper bound for risk
• Not assume people drink nothing but wastewater
  for 70 years
• Reasonably maximally exposed individual
• Consider susceptible subpopulations
• Identify major contributors to output variance
• Are these uncertain? Variable? Both?

168
Specific Statistics to Present

• Mean, median, standard deviation
• 5th percentile, 95th percentile
• Histogram of output
• Correlations of inputs with output
• In Excel correl(input column, output column)
• Where input column is A1A1000 or similar
• Scatter plots of inputs with output

169
Histogram and Cumulative Histogram
Now we know that risk could plausibly be twice as
high.
Point estimate was at the median.
170
Scatterplot Risk vs. Dose (correl.64)
171
Scatterplot Risk vs. r (correl.74)
172
Risk Characterization

• After all the effort of a Monte Carlo analysis,
  in practice people want a number
• Tendency to collapse distribution to most likely
  number (or conservative, protective number)
• What do we really want to get out of our
  analysis?
• Not just a number but to inform multiple
  decisions
• Is risk acceptable? How bad could it be?
• Can the risk be reduced?
• What do we need to know to improve management of
  this risk?
• Are there subpopulations we should be concerned
  about?

173
Informing Risk Management

• What protective action is needed to reduce best
  estimate of risk to a target value? To reduce
  upper bound of risk to the target value?
• How much will different risk management actions
  cost and what risk reductions will they achieve?
  How certain are we?

174
Arsenic in Drinking Water ExampleDistribution
of Costs under 3 Policy Scenarios
This is the acceptable cost
Median costs are fine, here we look at upper bound
175
Contacts

• Faculty
• Dr. Joan B. Rose, rosejo_at_msu.edu
• Dr. Charles P. Gerba, gerba_at_ag.arizona.edu
• Dr. Charles N. Haas, haas_at_drexel.edu
• Dr. Patrick L. Gurian, pgurian_at_drexel.edu
• Conveners
• Dr. Tomoyuki Shibata, tshibata_at_msu.edu
• Dr. Yoshifumi Masago, ymasago_at_msu.edu
• Facilitator
• Miss. Rebecca L. Ives, ivesrebe_at_msu.edu