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Exploring Carcinogen Risk Analysis Through Benzene. Image from Matthew J. Dowd Department of Medicinal Chemistry Virginia Commonwealth University. Objective. Use benzene as a case for exploring Toxicology Epidemiology Uncertainty Regulatory Science. Toolbox Building.

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exploring carcinogen risk analysis through benzene
Exploring Carcinogen Risk Analysis Through Benzene

Image from Matthew J. Dowd

Department of Medicinal Chemistry

Virginia Commonwealth University

 2002

David M. Hassenzahl

objective
Objective
  • Use benzene as a case for exploring
  • Toxicology
  • Epidemiology
  • Uncertainty
  • Regulatory Science

 2002

David M. Hassenzahl

toolbox building
Toolbox Building
  • Likelihood Maximization
  • Curve fitting
  • Bootstrapping
  • Z-Scores
  • Relative Risk
  • Dose-Response extrapolation

 2002

David M. Hassenzahl

overview of benzene
Overview of benzene
  • Fairly common hydrocarbon
    • Manufacturing
    • Petroleum products
  • Strongly suspected human carcinogen
    • Animal assays
    • Many epidemiological studies
    • Leukemia as important endpoint

 2002

David M. Hassenzahl

benzene structure
Benzene structure

Image from Matthew J. Dowd

Department of Medicinal Chemistry

Virginia Commonwealth University

 2002

David M. Hassenzahl

benzene data in should we risk it
Benzene Data in Should We Risk It?
  • Toxicological Data, p. 175 et seq.
  • Epidemiological Data p 211 – 216
  • But many other data sets
    • Other toxicological data (rare)
    • Chinese workers
    • Turkish workers

 2002

David M. Hassenzahl

toxicology data set
Toxicology Data Set

 2002

David M. Hassenzahl

Crump and Allen 1984

what are risks from benzene
What are risks from benzene?
  • Risk as potency times exposure
  • How do we determine potency?
    • Extrapolate from animal data?
    • Extrapolate from epidemiological data?
    • How wrong will we be?
  • What are “real” exposures?
    • What are effects at these levels?

 2002

David M. Hassenzahl

toxicology
Toxicology
  • Paracelsus “the dose makes the poison”
  • Regulatory assumptions!
  • This is not Dr. Gerstenberger’s Toxicology!

 2002

David M. Hassenzahl

reading
Reading
  • SWRI Chapter 5
  • US EPA Proposed guidelines (US EPA 1996)
  • Cox 1996

 2002

David M. Hassenzahl

general idea
General idea
  • Applied doses
    • Greater specificity about exposure than epidemiology
  • Observed effects
  • Artificial control of exposure

 2002

David M. Hassenzahl

physiologically based pharmacokinetics
Physiologically Based Pharmacokinetics
  • PBPK
  • Investigate flows of materials through bodies
  • System dynamics models
  • More on these in exposure lecture

 2002

David M. Hassenzahl

studies
Studies
  • Animals
    • Rarely humans
  • Parts
    • Cell
    • tissue

 2002

David M. Hassenzahl

effects
Effects
  • Chronic
    • cancer fatality
    • increasing interest in other issues
    • lead and intelligence in children.
  • Acute
    • Reversible
    • Irreversible

 2002

David M. Hassenzahl

crump and allen benzene data set
Crump and Allen Benzene data set
  • Animals at various concentrations
  • Four data points
  • “Designer” mice

 2002

David M. Hassenzahl

relevance to humans
Relevance to Humans
  • How to get from
  • high level, lifetime studies of animals

to

  • anticipated low dose effects in humans?

 2002

David M. Hassenzahl

questions about benzene
Questions about benzene
  • Is benzene a mouse carcinogen?
  • Is benzene a human carcinogen?
  • If so, how potent?

 2002

David M. Hassenzahl

benzene data set i
Benzene data set I

Crump and Allen data set (Crump and Allen 1984)

Note: the actual doses are not stated correctly here. See “notes for more information

 2002

David M. Hassenzahl

benzene data set ii
Benzene data set II

1.0

0.8

0.6

P(cancer)

0.4

0.2

0

0

25

50

75

100

Dose (mg/kg/day)

Crump and Allen data set.

 2002

David M. Hassenzahl

uncertainty pervades
Uncertainty Pervades
  • Often understated
  • Creates (or at least prolongs) conflict
  • Think as we go! (Part of Homework PS 2)

 2002

David M. Hassenzahl

animal test issues
Animal Test Issues
  • Interspecific comparison
  • Statistical uncertainty
  • Heterogeneity
  • Extrapolation
  • Dose Metric

 2002

David M. Hassenzahl

interspecific comparison
Interspecific comparison
  • Mouse-human
    • Metabolism as a function of body weight
    • Dosehuman = sf  Dosemouse
    • sf = (BWhuman/BWmouse)1-b
    • b is empirically derived as 0.75a

a. See SWRI page 177.

 2002

David M. Hassenzahl

interspecific comparison1
Interspecific comparison
  • Lifetime of human = lifetime mouse?
    • Mice age 30 days per human day
    • Total mouse lifetime is much shorter
  • Analogous organs or processes?
    • Do mice have cancer points we do not?
    • Do we have cancer points mice do not?

a. See SWRI page 177.

 2002

David M. Hassenzahl

interspecific comparison2
Interspecific comparison

1. Hallenbeck, 1993

2. Finley et al., 1994

 2002

David M. Hassenzahl

interspecific comparison3
Interspecific comparison

sf = (BWhuman/BWmouse)1-b

sf = (70/0.03)0.25 = 7.0

Dosehuman = 7.0  Dosemouse

 2002

David M. Hassenzahl

interspecific comparison4
Interspecific comparison

Crump and Allen data set, converted to humans

 2002

David M. Hassenzahl

animal test issues1
Animal Test Issues
  • Interspecies comparison
  • Statistical uncertainty
  • Heterogeneity
  • Extrapolation
  • Dose Metric

 2002

David M. Hassenzahl

binomial distribution
Binomial Distribution
  • 50 genetically “identical” mice…binomial distribution?
  • Can use this to generate “likelihood function” to compare the likelihood that any given probability is

 2002

David M. Hassenzahl

likelihood maximization
Likelihood Maximization
  • More appropriate than Least Squares when you know something about likelihoods
  • “Bootstrapping” method needed
  • We will work through likelihood maximization

 2002

David M. Hassenzahl

statistical uncertainty
Statistical Uncertainty

Can calculate standard deviation using the binomial

Recall that two standard deviations to either side represents a 95% confidence interval, and...

 2002

David M. Hassenzahl

statistical uncertainty1
Statistical Uncertainty

1.0

0.8

0.6

P(cancer)

0.4

0.2

0

0

175

350

525

700

Human Dose (mg/kg/day)

Crump and Allen data set, applied to humans

 2002

David M. Hassenzahl

animal test issues2
Animal Test Issues
  • Interspecies comparison
  • Statistical uncertainty
  • Heterogeneity
  • Extrapolation
  • Dose Metric

 2002

David M. Hassenzahl

heterogeneity
Heterogeneity
  • Epidemiology and toxicology
  • Genetically identical mice compared to diverse humans
  • Predictable versus unpredictable susceptibility
  • Male and female differences (observed cancer rates are different)

 2002

David M. Hassenzahl

heterogeneity1
Heterogeneity
  • Genetic diversity among humans
  • Early insights into cancer mechanism: subpopulation born with one of two “steps” competed
  • Variability as a function of age

 2002

David M. Hassenzahl

animal test issues3
Animal Test Issues
  • Interspecies comparison
  • Statistical uncertainty
  • Heterogeneity
  • Extrapolation
  • Dose Metric

 2002

David M. Hassenzahl

extrapolation
Extrapolation
  • Theoretical or “Mechanistic” models:
    • one-hit
    • two-hit
    • two-stage
  • Empirical
    • Cox “data-driven, model free curve fitting”
  • EPA Proposed Guidelines

 2002

David M. Hassenzahl

extrapolation concerns
Overestimation

Tautological effects

Thresholds

Hormesis, or “Vitamin” effect

Underestimation

Saturation

Synergistic effects

Susceptibility

Omission

Extrapolation Concerns

 2002

David M. Hassenzahl

slide38
 2002

David M. Hassenzahl

slide39

After EPA (1996)

 2002

David M. Hassenzahl

statistical uncertainty2
Statistical Uncertainty

1.0

0.8

0.6

P(cancer)

0.4

0.2

0

0

175

350

525

700

Human Dose (mg/kg/day)

Crump and Allen data set, applied to humans

 2002

David M. Hassenzahl

slide41

1.0

LED(10) =

100 mgb/kg/day

0.8

0.6

P(cancer)

0.4

0.2

0

0

175

350

525

700

Human Dose (mg/kg/day)

 2002

David M. Hassenzahl

extrapolation1
Extrapolation

If LED(10) = 100 mg/kg/day, then

LED(10-6) = 100  10-6 / 0.1

= 1  10-4 mg/kg/day

 2002

David M. Hassenzahl

animal test issues4
Animal Test Issues
  • Interspecies comparison
  • Statistical uncertainty
  • Heterogeneity
  • Extrapolation
  • Dose Metric

 2002

David M. Hassenzahl

dose metric
Dose Metric
  • Assumption: exposure is irrelevant to effect
  • Area under the curve/expected value.
  • Lifetime dose leads to average daily dose.
  • Particularly problematic if there are threshold effects or extreme effects

 2002

David M. Hassenzahl

risk to humans
Risk to Humans?
  • Lifetime cancer risk
  • 40 hours per week
  • 50 weeks per year
  • 30 years
  • Average 10 ppm(v) exposure?

 2002

David M. Hassenzahl

calculate risk
Calculate Risk
  • 10ml benzene/liter air
  • 0.313 ml/mg
  • 20m3 air / day
  • 1000 liters/ m3
  • 70kg person

 2002

David M. Hassenzahl

cancer risk
Cancer Risk
  • Lifetime Cancer Probability is a function of Dose and Potency
  • Assume cumulative dose
    • Use Daily Dose per kg body weight, averaged over lifetime
  • Potency usually given as q*
    • Additional risk per unit dose

 2002

David M. Hassenzahl

cancer risk exposure term
Cancer Risk: Exposure Term

 2002

David M. Hassenzahl

computed exposure terms
Computed Exposure Terms

 2002

David M. Hassenzahl

computed exposure terms1
Computed Exposure Terms

 2002

David M. Hassenzahl

cancer risk1
Cancer Risk

 2002

David M. Hassenzahl

regulatory science issues
“Regulatory Science” Issues
  • Neither a simple question nor a mindless approach
    • (although often stated this way) 
  • “Human health conservative” versus
  • “Heavy hand of conservative assumptions?”
    • May be overestimates
    • May be underestimates

 2002

David M. Hassenzahl

regulatory toxicology
Regulatory Toxicology
  • “Real risk” is a reified risk
  • ALL estimates, including central tendencies, are probably wrong
  • More science does not guarantee
    • “less risk”
    • “less uncertainty”

 2002

David M. Hassenzahl

likelihood maximization1

Likelihood Maximization

A curve fitting technique

 2002

David M. Hassenzahl

binomial distribution1
Binomial Distribution
  • 50 genetically “identical” mice…binomial distribution?
  • Can use this to generate “likelihood function” for a predicted outcome given an observed outcome

 2002

David M. Hassenzahl

likelihood maximization2
Likelihood Maximization
  • More appropriate than Least Squares when you know something about likelihoods
  • “Bootstrapping” method needed

 2002

David M. Hassenzahl

statistical uncertainty3
Statistical Uncertainty

Can calculate standard deviation using the binomial

Recall that two standard deviations to either side represents a 95% confidence interval, and...

 2002

David M. Hassenzahl

statistical uncertainty4
Statistical Uncertainty

1.0

0.8

0.6

P(cancer)

0.4

0.2

0

0

100

200

300

400

Human Dose (mg/kg/day)

Crump and Allen data set, applied to humans

 2002

David M. Hassenzahl

counting rules
Counting Rules
  • What is the likelihood of getting 13 heads on 50 flips of a fair coin?
  • We know the EXPECTED value
    • Expected value is 25 heads

 2002

David M. Hassenzahl

binomial developed
P(13|50) =

0.000315

P(25|50) = 0.112

P(37|50) = 0.000315

P(24|50) = 0.108

P(50|50) = 8.88 E-16

P(20|50) = 0.0412

Can use function in excel

Binomial Developed

 2002

David M. Hassenzahl

slide61
 2002

David M. Hassenzahl

likelihood
Likelihood
  • Given
    • We’ve tested 50 mice at a dose Di
    • We found a cancer rate P(Di)
  • We expect that if we do it again, we will get the same rate
  • We acknowledge that there’s some randomness

 2002

David M. Hassenzahl

fitting a model
Fitting a model
  • We know that our model can’t fit ALL the data points exactly
  • P(100mg/kg/day) = 0.08, etc
  • Let’s get as close to this as we can!
  • Let’s “maximize the likelihood”

 2002

David M. Hassenzahl

likelihood function
Likelihood Function
  • From the binomial, we can derive the likelihood function
  • Likelihood {P*(Di)|P(Di) is
  • We don’t care the exact likelihood…we just want it as big as possible

 2002

David M. Hassenzahl

multiple likelihoods
Multiple Likelihoods
  • Multiple data points
    • maximize the multiplied probabilities
    • gives each equal weight
  • Or, take log
    • If y = xi
    • Then ln(y) = ln(xi)
    • Maximize sum of logs

 2002

David M. Hassenzahl

simple model
Simple Model
  • P*(D) = kD + D0
  • Hypothetical data set

 2002

David M. Hassenzahl

bootstrap
Bootstrap
  • Simple method to fit a model to data
  • Akin to the game “hotter-colder”
  • Optimizes a function
    • Least squares
    • Maximum likelihood
  • Varies model parameters
    • hotter or colder

 2002

David M. Hassenzahl

bootstrap for benzene data set
Bootstrap for benzene data set
  • Create equation where
  • Give known
    • P(Di), Di
  • P*(D) = k*D + P*0
  • Allow bootstrap to vary k*, P*0
  • Maximize sum of log-likelihoods

 2002

David M. Hassenzahl

epidemiology for risk analysis

Epidemiology for Risk Analysis

An Introduction

 2002

David M. Hassenzahl

objective1
Objective
  • Explore types of epidemiology methods
  • Understand the value and limitations of epidemiology
    • Bradford-Hill criteria
  • Learn essential epidemiology calculations
  • Address benzene risk using epidemiological data

 2002

David M. Hassenzahl

overview of epidemiology
Overview of epidemiology
  • Exposed human populations
  • Hard to control
  • Rarely addresses causality
  • Common measures
    • Relative Risk
    • Z-scores

 2002

David M. Hassenzahl

pliofilm cohort data swri page 215
Pliofilm Cohort Data(SWRI Page 215)

 2002

David M. Hassenzahl

two major classes
Descriptive

Population Studies

Case Reports

Case Series

Cross-Sectional Analyses

Analytical

Intervention Studies

Cohort Studies

Case-Control studies

Toxicology?

Two Major Classes

 2002

David M. Hassenzahl

uncertainty issues
Uncertainty Issues
  • Many toxicology uncertainties apply!
  • Statistical uncertainty
  • Heterogeneity
  • Extrapolation
  • Dose Metric

 2002

David M. Hassenzahl

population
Population
  • Also called “Correlational”
  • Most of what we call “environmental epidemiology
  • Not controlled
  • No causation
  • Can point us in the right direction

Note: this and subsequent slides draw heavily on

Gots (1993)

 2002

David M. Hassenzahl

populations pros and cons
Populations: pros and cons
  • Large samples
  • Can address
    • major effects
    • potential causes
  • Low relative risk ratios
  • Study design challenges 

 2002

David M. Hassenzahl

case studies
Case studies
  • Observed correlation
  • Event and outcome
  • Examples
    • mobile phones and brain tumors
    • “Cancer clusters”
  • No control group! 
  • A starting point only

 2002

David M. Hassenzahl

cross sectional analysis
Cross-sectional analysis
  • One time deal
  • Bunch of questions or data points

 2002

David M. Hassenzahl

intervention studies
Intervention studies
  • Common in medicine
  • Double-blind
  • Placebo
  • Treatment
  • Some ethical issues

 2002

David M. Hassenzahl

case control
Case-control
  • Retrospective method
  • One group with effect
  • Comparable group without effect
  • Observed differences in possible causes  

 2002

David M. Hassenzahl

cohort studies
Cohort studies
  • Retrospective or prospective
  • Look at exposure groups
  • Compare rates of effects

 2002

David M. Hassenzahl

case control1
Pros

Rare / long latency outcomes

Efficient / small samples

Existing data

Range of causes / exposures

Cons

Reconstructed exposure

Data hard to validate

Confounders

Selection of control

Can’t calculate rates

Causation unknown

Case-control

 2002

David M. Hassenzahl

cohort studies1
Pros

Compares Exposures

Multiple outcomes

Complete data

Cases

Stages

Some data quality control

Cons

Large samples

Long-term commitment

Funding and researchers

Subjects

Extraneous factors

Expensive

Causation rare

Cohort Studies

 2002

David M. Hassenzahl

bradford hill criteria determining causation
Bradford-Hill Criteria (determining causation)
  • Temporality (Chronological relationship)
  • Strength of Association
  • Intensity or duration of exposure
  • Specificity of Association
  • Consistency
  • Coherence and biological plausibility 
  • Reversibility 

 2002

David M. Hassenzahl

temporality
Temporality
  • Chronological relationship
  • Does the presumed cause precede the effect?
  • A cause must precede its effect
  • This does not imply the reciprocal

 2002

David M. Hassenzahl

strength of association
Strength of Association
  • High relative risk of acquiring the disease
  • Strong p-value (low statistical uncertainty)

 2002

David M. Hassenzahl

intensity
Intensity
  • Also duration of exposure
  • As exposure increases
  • Does proposed effect increase?

 2002

David M. Hassenzahl

specificity of association
Specificity of Association.
  • Highly specific case
  • Highly specific exposure
  • Example:
    • “leukemia from benzene”

versus

    • “cancer from hydrocarbons”  

 2002

David M. Hassenzahl

consistency
Consistency
  • If multiple findings
  • Do all point the same way?
  • “Meta-analysis” is common (SWRI page 373 - 377

 2002

David M. Hassenzahl

coherence and biological plausibility
Coherence and biological plausibility
  • Postulate a mechanism
  • Consistent with our understanding of biological processes
  • Better if supporting toxicological data  

 2002

David M. Hassenzahl

reversibility
Reversibility
  • Does removal of a presumed cause lead to a reduction in the risk of ill-health?
    • MAY strengthen cause-effect relationship
  • May suffer from similar fallacies as temporality

 2002

David M. Hassenzahl

some correlation issues
Some Correlation Issues
  • Uncertain dosimetry
    • very difficult to estimate exposure
  • Latency of effects, especially cancer
  • Confounding factors
  • Bias
  • Representativeness of control group
  • Small numbers

 2002

David M. Hassenzahl

risk in the time of cholera
Risk in the Time of Cholera
  • Famous case
  • SWRI 207 to 211
  • See Gots (1993) and Aldrich and Griffith (1993)
  • …and almost any other epidemiology or statistics text!

 2002

David M. Hassenzahl

cholera in london mid1800 s
Cholera in London, mid1800’s
  • John Snow
  • Drinking water from the Thames
  • High rates of cholera
  • Unknown cause of cholera
    • Ill humours?
    • Vapours?

 2002

David M. Hassenzahl

cholera in london mid 1800 s
Cholera in London mid 1800’s
  • Many water companies
    • Southwark and Vauxhall, downstream
    • Lambeth, upstream
    • Several others

 2002

David M. Hassenzahl

london cholera data 1853 4
London Cholera Data 1853-4

 2002

David M. Hassenzahl

assumptions
Assumptions
  • No confounders, selection problems
    • Snow did a good job of this, we think
  • Number of people per household
    • SWRI used 1 per household
    • Could use other (see whether it makes a difference!)

 2002

David M. Hassenzahl

relative risk
Relative Risk
  • Risk (or lack thereof)
    • to exposed group
    • compared to unexposed group
  • RR = 1 if no effect
  • RR  1 means benefit
  • RR  1 means injury

 2002

David M. Hassenzahl

relative risk caveats
Relative Risk Caveats
  • Beware when 1  RR  x
    • x = 1.1? 2? 10?
  • Depends on how good the data are
    • Sample size
    • Confounders
    • Other uncertainties

 2002

David M. Hassenzahl

back to london
Back to London
  • RR Southwark and Vauxhall versus the rest of London
  • RR = 1263/40,046 / 1520/282,530
  • RR = 5.86
  • Expected rate is S and V is the same as the rest of London
    • p = 1520 / 282,530 = 0.00538

 2002

David M. Hassenzahl

statistical test
Statistical Test

 2002

David M. Hassenzahl

risk of cholera
Risk of Cholera?
  • RR Lambeth versus rest of London is less than one
  • IF Snow found a suitably unbiased, accurate, precise, etc estimator
  • THEN Cholera is probably water-borne!

 2002

David M. Hassenzahl

benzene and cancer
Benzene and Cancer
  • Given Pliofilm data
  • Is benzene a human carcinogen?
  • Is benzene a human carcinogen at low concentrations?
  • How potent is it?
    • RR is basically a linear estimator

 2002

David M. Hassenzahl

pliofilm data swri page 215
Pliofilm Data (SWRI Page 215)

 2002

David M. Hassenzahl

pliofilm
Pliofilm
  • Rubber manufacturer
  • Retrospective cohort study
  • Recreated exposure
  • Many effects
  • Think about potential uncertainties!

 2002

David M. Hassenzahl

pliofilm relative risk
Pliofilm Relative Risk
  • Overall RR = 21 / 12.1 = 1.74
  • Z = 2.56
  • p = 99.5

 2002

David M. Hassenzahl

meaning of rr
Meaning of RR?
  • Is there a threshold?
    • RR a bit less than one for lowest group
    • Calculate Z-score (not significant)
  • What is RR excluding lowest group?
  • Is there a non-linear effect?

 2002

David M. Hassenzahl

slide108
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David M. Hassenzahl

slide109
 2002

David M. Hassenzahl

slide110
 2002

David M. Hassenzahl

slide111
 2002

David M. Hassenzahl

what about benzene
What about benzene?
  • Probably a cause of leukemia and other cancers in humans
  • Data suggest a threshold
    • But maybe not
    • Or is benzene hormetic?
  • Lots of uncertainty

 2002

David M. Hassenzahl

conclusions
Conclusions
  • Epidemiology and Toxicology are useful tools
  • We HAVE to make assumptions
  • We don’t know what “X” does
    • X = benzene, ionizing radiation, Alar…
  • We have to decide what to do about X
    • Even if that means do nothing

 2002

David M. Hassenzahl

lessons learned
Lessons Learned
  • Managing types and sources of uncertainty
  • Adding toolbox items
    • Bootstrapping, likelihood maximization, spreadsheet skills, extrapolation
  • If you are better informed but less certain now than several weeks ago, I’ve done my job

 2002

David M. Hassenzahl

references
References

Aldrich, T and Griffith, J., Eds. (1993). Environmental Epidemiology and Risk Assessment, Van Nostrand Reinholt, NY NY.

Cox, L.A. (1995). “Reassessing benzene risks using internal doses and Monte-Carlo Uncertainty analysis.” Environmental Health Perspectives 104(Suppl.6):1413-29.

Gots, Ronald (1993). Toxic risks : science, regulation, and perception, Boca Raton, Lewis Publishers.

Kammen, D.M. and Hassenzahl, D.M. (1999). Should We Risk It? Exploring Environmental, Health and Technological Problem Solving Princeton University Press, Princeton NJ

Krump, K.S. and Allen, B.C. (1984). Quantitative Estimates of the Risk of Leukemia from Occupational Exposures to Benzene. Final Report to the OSHA. Ruston, LA: Science Research Systems

US EPA (1997) “Proposed Guidelines for Carcinogen Risk Assessment.” Federal Register 61(79) (April 23) 17960-18011.

 2002

David M. Hassenzahl

slide116
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slide117
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slide118
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