Transcript Exploring Carcinogen Risk Analysis Through Benzene Image from Matthew J. Dowd

Exploring Carcinogen Risk
Analysis Through Benzene
Image from Matthew J. Dowd
Department of Medicinal Chemistry
Virginia Commonwealth University
 2002
David M. Hassenzahl
Objective
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Use benzene as a case for exploring
Toxicology
Epidemiology
Uncertainty
Regulatory Science
 2002
David M. Hassenzahl
Toolbox Building
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Likelihood Maximization
Curve fitting
Bootstrapping
Z-Scores
Relative Risk
Dose-Response extrapolation
 2002
David M. Hassenzahl
Overview of benzene
• Fairly common hydrocarbon
– Manufacturing
– Petroleum products
• Strongly suspected human carcinogen
– Animal assays
– Many epidemiological studies
– Leukemia as important endpoint
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David M. Hassenzahl
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?
• Toxicological Data, p. 175 et seq.
• Epidemiological Data p 211 – 216
• But many other data sets
– Other toxicological data (rare)
– Chinese workers
– Turkish workers
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David M. Hassenzahl
Toxicology Data Set
Number of
mice
Mice with
tumors
Mouse dose
50
0
0
50
4
14
50
20
27
50
37
59
Crump and Allen 1984
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David M. Hassenzahl
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?
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Toxicology
• Paracelsus “the dose makes the poison”
• Regulatory assumptions!
• This is not Dr. Gerstenberger’s
Toxicology!
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Reading
• SWRI Chapter 5
• US EPA Proposed guidelines (US EPA
1996)
• Cox 1996
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General idea
• Applied doses
– Greater specificity about exposure than
epidemiology
• Observed effects
• Artificial control of exposure
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Physiologically Based
Pharmacokinetics
• PBPK
• Investigate flows of materials through
bodies
• System dynamics models
• More on these in exposure lecture
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Studies
• Animals
– Rarely humans
• Parts
– Cell
– tissue
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David M. Hassenzahl
Effects
• Chronic
– cancer fatality
– increasing interest in other issues
– lead and intelligence in children.
• Acute
– Reversible
– Irreversible
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Crump and Allen Benzene
data set
• Animals at various concentrations
• Four data points
• “Designer” mice
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Relevance to Humans
• How to get from
• high level, lifetime studies of animals
to
• anticipated low dose effects in humans?
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Questions about benzene
• Is benzene a mouse carcinogen?
• Is benzene a human carcinogen?
• If so, how potent?
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Benzene data set I
Number of Test Number of Mice Mouse
Test
mice
with tumors
Dose (mg/kg/d)
(Oral gavage)
50
0
0
50
4
25
50
20
50
50
37
100
Crump and Allen data set
(Crump and Allen 1984)
Note: the actual doses are not stated correctly here.
See “notes for more information
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David M. Hassenzahl
Benzene data set II
1.0
P(cancer)
0.8
0.6
0.4
0.2
0
0
25
50
75
100
Dose (mg/kg/day)
Crump and Allen data set.
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Uncertainty Pervades
• Often understated
• Creates (or at least prolongs) conflict
• Think as we go! (Part of Homework PS
2)
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Animal Test Issues
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Interspecific comparison
Statistical uncertainty
Heterogeneity
Extrapolation
Dose Metric
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David M. Hassenzahl
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.
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David M. Hassenzahl
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.
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David M. Hassenzahl
Interspecific comparison
Species
Sex
Human
Male
Female
Both
Male
Female
Male
Female
Rat
Mouse
1. Hallenbeck, 1993
2. Finley et al., 1994
Std. Adult
BW (kg1,2)
78.7
65.4
71.0
0.5
0.35
0.03
0.025
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David M. Hassenzahl
Interspecific comparison
sf = (BWhuman/BWmouse)1-b
sf = (70/0.03)0.25 = 7.0
Dosehuman = 7.0  Dosemouse
Number of Test Number
mice
Mice
tumors
50
50
50
50
0
4
20
37
of Mouse
Test Equivalent
with Dose
human dose
(mg/kg/day)
(mg/kg/day)
(Oral gavage)
0
25
50
100
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David M. Hassenzahl
Interspecific comparison
Crump and Allen data set, converted to humans
Number of Test Number
mice
Mice
tumors
50
50
50
50
0
4
20
37
of Mouse
Test
with Dose
(mg/kg/day)
(Oral gavage)
0
25
50
100
Equivalent
human dose
(mg/kg/day)
0
175
350
700
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Animal Test Issues
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Interspecies comparison
Statistical uncertainty
Heterogeneity
Extrapolation
Dose Metric
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David M. Hassenzahl
Binomial Distribution
• 50 genetically “identical” mice…binomial
distribution?
• Can use this to generate “likelihood
function” to compare the likelihood that
any given probability is
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David M. Hassenzahl
Likelihood Maximization
• More appropriate than Least Squares
when you know something about
likelihoods
• “Bootstrapping” method needed
• We will work through likelihood
maximization
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David M. Hassenzahl
Statistical Uncertainty
Can calculate standard deviation using the
binomial
s
p1  p 
n
Recall that two standard deviations to
either side represents a 95% confidence
interval, and...
 2002
David M. Hassenzahl
Statistical Uncertainty
1.0
P(cancer)
0.8
0.6
0.4
0.2
0
0
175
350
525
700
Human Dose (mg/kg/day)
Crump and Allen data set, applied to humans
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David M. Hassenzahl
Animal Test Issues
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•
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Interspecies comparison
Statistical uncertainty
Heterogeneity
Extrapolation
Dose Metric
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David M. Hassenzahl
Heterogeneity
• Epidemiology and toxicology
• Genetically identical mice compared to
diverse humans
• Predictable versus unpredictable
susceptibility
• Male and female differences (observed
cancer rates are different)
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Heterogeneity
• Genetic diversity among humans
• Early insights into cancer mechanism:
subpopulation born with one of two
“steps” competed
• Variability as a function of age
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Animal Test Issues
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Interspecies comparison
Statistical uncertainty
Heterogeneity
Extrapolation
Dose Metric
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Extrapolation
• Theoretical or “Mechanistic” models:
– one-hit
– two-hit
– two-stage
• Empirical
– Cox “data-driven, model free curve fitting”
• EPA Proposed Guidelines
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Extrapolation Concerns
Overestimation
• Tautological
effects
• Thresholds
• Hormesis, or
“Vitamin” effect
Underestimation
• Saturation
• Synergistic effects
• Susceptibility
• Omission
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David M. Hassenzahl
Response
Response
Dose or
exposure
Response
Response
Dose or
exposure
Dose or
exposure
Dose or
exposure
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os
e)
Es
tim
ate
)
Observed Range
al
en
tr
(C
(C
en
ce
Li
m
it
on
D
Human
Exposure
of Interest
on
fid
Response
Extrapolation Range
10%
r
inea
L
d
ecte
Proj
0%
LED10
ED10
Dose
After EPA (1996)
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David M. Hassenzahl
Statistical Uncertainty
1.0
P(cancer)
0.8
0.6
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
1.0
LED(10) =
100 mgb/kg/day
0.8
P(cancer)
0.6
0.4
0.2
0
0
175
350
Human Dose (mg/kg/day)
525
700
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David M. Hassenzahl
Extrapolation
If LED(10)
= 100 mg/kg/day, then
LED(10-6)
= 100  10-6 / 0.1
= 1  10-4 mg/kg/day
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David M. Hassenzahl
Animal Test Issues
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Interspecies comparison
Statistical uncertainty
Heterogeneity
Extrapolation
Dose Metric
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David M. Hassenzahl
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
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David M. Hassenzahl
Risk to Humans?
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Lifetime cancer risk
40 hours per week
50 weeks per year
30 years
Average 10 ppm(v) exposure?
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David M. Hassenzahl
Calculate Risk
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10ml benzene/liter air
0.313 ml/mg
20m3 air / day
1000 liters/ m3
70kg person
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David M. Hassenzahl
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
LCP(D)  q  ADD lifetime
*
b
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David M. Hassenzahl
Cancer Risk: Exposure Term
ADD lifetime  ADD exposure  f exposed
f exposed  YpL  WpY  HpW L
ADD exposure  C b,air  IR  BW -1  conversion factors 
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David M. Hassenzahl
Computed Exposure Terms
ADD exposure
10ml b 20m 3air
0.0446mmol e b 78mg b
1





3
day
70kg
ml b
mmole b
m air
ADD exposure
69.6mg b

kg  day
f exposed
30YpL  50WpY  40HpW

70YpL  8760HpY
f exposed  0.098
 2002
David M. Hassenzahl
Computed Exposure Terms
ADD lifetime  ADD exposure  f exposed
ADD exposure
69.6mg b

kg  day
f exposed  0.098
ADD lifetime
6.8mg b
69.6mgb

 0.098 
kg  day
kg  day
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David M. Hassenzahl
Cancer Risk
LCP(D)  q  ADD lifetime
*
b
ADD lifetime
6.8mg b

kg  day
kg  day
q  0.1 
 0.001
100mg b
*
b
0.001kg  day 6.8mg b
LCP(D) 

 0.007
mg b
kg  day
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David M. Hassenzahl
“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
• “Real risk” is a reified risk
• ALL estimates, including central
tendencies, are probably wrong
• More science does not guarantee
– “less risk”
– “less uncertainty”
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David M. Hassenzahl
Likelihood Maximization
A curve fitting technique
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David M. Hassenzahl
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 Maximization
• More appropriate than Least Squares
when you know something about
likelihoods
• “Bootstrapping” method needed
 2002
David M. Hassenzahl
Statistical Uncertainty
Can calculate standard deviation using the
binomial
s
p1  p 
n
Recall that two standard deviations to
either side represents a 95% confidence
interval, and...
 2002
David M. Hassenzahl
Statistical Uncertainty
1.0
P(cancer)
0.8
0.6
0.4
0.2
0
0
100
200
300
400
Human Dose (mg/kg/day)
Crump and Allen data set, applied to humans
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David M. Hassenzahl
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

 X  NX 
N!
p q
P(X)  
 X! N  X ! 
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David M. Hassenzahl
Binomial Developed
P(13|50) =

 13 5013
50!
0.5 0.5
P(13)  
 13!50  13! 
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
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David M. Hassenzahl
Binomial, n = 50, p = 0.5
0.12
0.1
0.08
0.06
0.04
0.02
0
0
10
20
30
40
50
60
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David M. Hassenzahl
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
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David M. Hassenzahl
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”
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David M. Hassenzahl
Likelihood Function
• From the binomial, we can derive the
likelihood function
• Likelihood {P*(Di)|P(Di) is
P D 
P  Di n
*
i
 1  P D 
n1 P  Di 
*
i
• We don’t care the exact likelihood…we
just want it as big as possible
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David M. Hassenzahl
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
• P*(D) = kD + D0
• Hypothetical data set
n
Dose
P(Cancer|Dose)
50
0
0.02
50
500
0.04
50
1000
0.10
50
2000
0.18
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David M. Hassenzahl
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
• 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
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David M. Hassenzahl
Epidemiology for Risk
Analysis
An Introduction
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David M. Hassenzahl
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
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Overview of epidemiology
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Exposed human populations
Hard to control
Rarely addresses causality
Common measures
– Relative Risk
– Z-scores
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David M. Hassenzahl
Pliofilm Cohort Data
(SWRI Page 215)
Cumulative Exposure
ppm-years
Leukemia
Range
Mean
Person
years
Observe Expected
deaths
per pers-yr
0-45
11
30482
6
2.02E-4
45-400
151
16320
6
2.35E-4
400-1000 602
4667
3
3.39E-4
>1000
1341
915
6
4.81E-4
Total
132
52584
21
2.30E-4
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David M. Hassenzahl
Two Major Classes
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Descriptive
Population Studies
Case Reports
Case Series
Cross-Sectional
Analyses
Analytical
• Intervention Studies
• Cohort Studies
• Case-Control
studies
– Toxicology?
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David M. Hassenzahl
Uncertainty Issues
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Many toxicology uncertainties apply!
Statistical uncertainty
Heterogeneity
Extrapolation
Dose Metric
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David M. Hassenzahl
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)
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David M. Hassenzahl
Populations: pros and cons
• Large samples
• Can address
– major effects
– potential causes
• Low relative risk ratios
• Study design challenges
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David M. Hassenzahl
Case studies
• Observed correlation
• Event and outcome
• Examples
– mobile phones and brain tumors
– “Cancer clusters”
• No control group!
• A starting point only
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David M. Hassenzahl
Cross-sectional analysis
• One time deal
• Bunch of questions or data points
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David M. Hassenzahl
Intervention studies
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Common in medicine
Double-blind
Placebo
Treatment
Some ethical issues
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Case-control
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Retrospective method
One group with effect
Comparable group without effect
Observed differences in possible
causes
 2002
David M. Hassenzahl
Cohort studies
• Retrospective or prospective
• Look at exposure groups
• Compare rates of effects
 2002
David M. Hassenzahl
Case-control
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•
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•
Pros
Rare / long latency
outcomes
Efficient / small
samples
Existing data
Range of causes /
exposures
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•
•
•
•
•
Cons
Reconstructed
exposure
Data hard to
validate
Confounders
Selection of control
Can’t calculate rates
Causation unknown
 2002
David M. Hassenzahl
Cohort Studies
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
 2002
David M. Hassenzahl
Bradford-Hill Criteria
(determining causation)
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•
•
•
•
•
•
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
• Chronological relationship
• Does the presumed cause precede the
effect?
• A cause must precede its effect
• This does not imply the reciprocal
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David M. Hassenzahl
Strength of Association
• High relative risk of acquiring the
disease
• Strong p-value (low statistical
uncertainty)
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David M. Hassenzahl
Intensity
• Also duration of exposure
• As exposure increases
• Does proposed effect increase?
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David M. Hassenzahl
Specificity of Association.
• Highly specific case
• Highly specific exposure
• Example:
– “leukemia from benzene”
versus
– “cancer from hydrocarbons”
 2002
David M. Hassenzahl
Consistency
• If multiple findings
• Do all point the same way?
• “Meta-analysis” is common (SWRI page
373 - 377
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Coherence and biological
plausibility
• Postulate a mechanism
• Consistent with our understanding of
biological processes
• Better if supporting toxicological data
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David M. Hassenzahl
Reversibility
• Does removal of a presumed cause
lead to a reduction in the risk of illhealth?
– MAY strengthen cause-effect relationship
• May suffer from similar fallacies as
temporality
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David M. Hassenzahl
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
• Famous case
• SWRI 207 to 211
• See Gots (1993) and Aldrich and Griffith
(1993)
• …and almost any other epidemiology or
statistics text!
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David M. Hassenzahl
Cholera in London, mid1800’s
•
•
•
•
John Snow
Drinking water from the Thames
High rates of cholera
Unknown cause of cholera
– Ill humours?
– Vapours?
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David M. Hassenzahl
Cholera in London mid 1800’s
• Many water companies
– Southwark and Vauxhall, downstream
– Lambeth, upstream
– Several others
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David M. Hassenzahl
London Cholera Data 1853-4
Water
Company
Number of
Houses
Cholera
Deaths
Southwark and 40,046
Vauxhall
1,263
Lambeth
26,107
98
Rest of
London
256,423
1,422
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David M. Hassenzahl
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!)
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David M. Hassenzahl
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
• 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
• 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
Z
Z
x̂  np
n  p  1  p 
1263  40046  0.00538
40046  0.00538  1  0.00538
Z  72.6 (off the table)
 2002
David M. Hassenzahl
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
• 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)
Cum.
Expose
ppmyears
Leukemia
Range
Mean
Person
years
Observe Expected
deaths
per yr
0-45
11
30482
6
6.16
45-400
151
16320
6
3.84
400-1000 602
4667
3
1.58
>1000
1341
915
6
0.440
Total
132
52584
21
12.1
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David M. Hassenzahl
Pliofilm
•
•
•
•
•
Rubber manufacturer
Retrospective cohort study
Recreated exposure
Many effects
Think about potential uncertainties!
 2002
David M. Hassenzahl
Pliofilm Relative Risk
• Overall RR = 21 / 12.1 = 1.74
Z
21  12.1
52584  0.000230  1  0.000230
• Z = 2.56
• p = 99.5
 2002
David M. Hassenzahl
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
P(leukemia|exposure)
0.7
0.6
P * 100
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
2000
Mean exposure (ppm-years)
 2002
David M. Hassenzahl
P(leukemia|exposure)
0.7
0.6
P * 100
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
2000
Low exposure (ppm-years)
 2002
David M. Hassenzahl
P(leukemia|exposure)
0.7
0.6
P * 100
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
2000
High exposure (ppm-years)
 2002
David M. Hassenzahl
P(leukemia|cumulative exposure)
0.7
0.6
P * 100
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
2000
Cumulative exposure (ppm-years)
 2002
David M. Hassenzahl
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
• 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
• 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
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.
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David M. Hassenzahl
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David M. Hassenzahl
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David M. Hassenzahl
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David M. Hassenzahl