2002

David M. Hassenzahl

Exploring Carcinogen Risk Analysis Through Benzene

Image from Matthew J. DowdDepartment of Medicinal ChemistryVirginia Commonwealth University

2002

David M. Hassenzahl

Objective

• Use benzene as a case for exploring

• Toxicology

• Epidemiology

• Uncertainty

• Regulatory Science

2002

David M. Hassenzahl

Toolbox Building

• 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

2002

David M. Hassenzahl

Benzene structure

Image from Matthew J. DowdDepartment of Medicinal ChemistryVirginia 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

2002

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

2002

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?

2002

David M. Hassenzahl

Toxicology

• Paracelsus “the dose makes the poison”

• Regulatory assumptions!

• This is not Dr. Gerstenberger’s Toxicology!

2002

David M. Hassenzahl

Reading

• SWRI Chapter 5

• US EPA Proposed guidelines (US EPA 1996)

• Cox 1996

2002

David M. Hassenzahl

General idea

• Applied doses– Greater specificity about exposure than

epidemiology

• Observed effects

• Artificial control of exposure

2002

David M. Hassenzahl

Physiologically Based Pharmacokinetics

• PBPK

• Investigate flows of materials through bodies

• System dynamics models

• More on these in exposure lecture

2002

David M. Hassenzahl

Studies

• Animals– Rarely humans

• Parts– Cell– tissue

2002

David M. Hassenzahl

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

• Animals at various concentrations

• Four data points

• “Designer” mice

2002

David M. Hassenzahl

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

• Is benzene a mouse carcinogen?

• Is benzene a human carcinogen?

• If so, how potent?

2002

David M. Hassenzahl

Crump and Allen data set (Crump and Allen 1984)Note: the actual doses are not stated correctly here. See “notes for more information

Benzene data set INumber of Test mice

Number of Mice with tumors

Mouse Test Dose (mg/kg/d) (Oral gavage)

50 0 0 50 4 25 50 20 50 50 37 100

2002

David M. Hassenzahl

Crump and Allen data set.

Benzene data set II

P(c

ance

r)

0

0.2

0.4

Dose (mg/kg/day)

0 25 50 75 100

1.0

0.8

0.6

2002

David M. Hassenzahl

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

• Interspecific comparison

• Statistical uncertainty

• Heterogeneity

• Extrapolation

• Dose Metric

2002

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.

2002

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.

2002

David M. Hassenzahl

Species Sex Std. Adult BW (kg1,2)

Human Male 78.7 Female 65.4 Both 71.0 Rat Male 0.5 Female 0.35 Mouse Male 0.03 Female 0.025

1. Hallenbeck, 19932. Finley et al.,

1994

Interspecific comparison

2002

David M. Hassenzahl

sf = (BWhuman/BWmouse)1-b

sf = (70/0.03)0.25 = 7.0Dosehuman = 7.0 Dosemouse

Number of Test mice

Number of Mice with tumors

Mouse Test Dose (mg/kg/day) (Oral gavage)

Equivalent human dose (mg/kg/day)

50 0 0 50 4 25 50 20 50 50 37 100

Interspecific comparison

2002

David M. Hassenzahl

Crump and Allen data set, converted to humans

Number of Test mice

Number of Mice with tumors

Mouse Test Dose (mg/kg/day) (Oral gavage)

Equivalent human dose (mg/kg/day)

50 0 0 0 50 4 25 175 50 20 50 350 50 37 100 700

Interspecific comparison

2002

David M. Hassenzahl

Animal Test Issues

• Interspecies comparison

• Statistical uncertainty

• Heterogeneity

• Extrapolation

• Dose Metric

2002

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

2002

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

2002

David M. Hassenzahl

Can calculate standard deviation using the binomial

npps 1

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

Statistical Uncertainty

2002

David M. Hassenzahl

Crump and Allen data set, applied to humans

P(c

ance

r)

0

0.2

0.4

Human Dose (mg/kg/day)

0 175 350 525 700

1.0

0.8

0.6

Statistical Uncertainty

2002

David M. Hassenzahl

Animal Test Issues

• Interspecies comparison

• Statistical uncertainty

• Heterogeneity

• Extrapolation

• Dose Metric

2002

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)

2002

David M. Hassenzahl

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 Issues

• Interspecies comparison

• Statistical uncertainty

• Heterogeneity

• Extrapolation

• Dose Metric

2002

David M. Hassenzahl

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

2002

David M. Hassenzahl

Res

pons

e

Dose orexposure

Res

pons

e

Dose orexposure

Res

pons

e

Dose orexposure

Res

pons

e

Dose orexposure

2002

David M. Hassenzahl

Extrapolation Range Observed RangeR

espo

nse

10%

0%

HumanExposureof Interest

LED 10 ED 10

Dose

Projected Linear

(Con

fiden

ce Li

mit on D

ose)

(Cen

tral E

stim

ate)

After EPA (1996)

2002

David M. Hassenzahl

Crump and Allen data set, applied to humans

P(c

ance

r)

0

0.2

0.4

Human Dose (mg/kg/day)

0 175 350 525 700

1.0

0.8

0.6

Statistical Uncertainty

2002

David M. Hassenzahl

P(ca

ncer

)

0

0.2

0.4

Human Dose (mg/kg/day)

0 175 350 525 700

1.0

0.8

0.6

LED(10) =100 mgb/kg/day

2002

David M. Hassenzahl

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

LED(10-6) = 100 10-6 / 0.1 = 1 10-4 mg/kg/day

Extrapolation

2002

David M. Hassenzahl

Animal Test Issues

• Interspecies comparison

• Statistical uncertainty

• Heterogeneity

• Extrapolation

• Dose Metric

2002

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

2002

David M. Hassenzahl

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

• 10ml benzene/liter air

• 0.313 ml/mg

• 20m3 air / day

• 1000 liters/ m3

• 70kg person

2002

David M. Hassenzahl

• 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

Cancer Risk

lifetime*b ADDqLCP(D)

2002

David M. Hassenzahl

exposedexposurelifetime fADDADD

LHpWWpYYpLf exposed

factors conversionBWIRCADD -1airb,exposure

Cancer Risk: Exposure Term

2002

David M. Hassenzahl

Computed Exposure Terms

b

b

b

b3air

3air

bexposure mmole

78mg

ml

e0.0446mmol

70kg

1

day

20m

m

10mlADD

daykg

69.6mgADD b

exposure

8760HpY70YpL

40HpW50WpY30YpLf exposed

098.0f exposed

2002

David M. Hassenzahl

Computed Exposure Terms

daykg

69.6mgADD b

exposure

098.0f exposed

exposedexposurelifetime fADDADD

daykg

6.8mg098.0

daykg

69.6mgbADD b

lifetime

2002

David M. Hassenzahl

Cancer Risk

lifetime*b ADDqLCP(D)

daykg

mg8.6ADD b

lifetime

001.0100mg

daykg1.0q

b

*b

007.0daykg

6.8mg

mg

daykg001.0LCP(D) b

b

2002

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”

2002

David M. Hassenzahl

Likelihood Maximization

A curve fitting technique

2002

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

Can calculate standard deviation using the binomial

npps 1

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

Statistical Uncertainty

2002

David M. Hassenzahl

Crump and Allen data set, applied to humans

P(c

ance

r)

0

0.2

0.4

Human Dose (mg/kg/day)

0 100 200 300 400

1.0

0.8

0.6

Statistical Uncertainty

2002

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

XNXqp

!XNX!

N!P(X)

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

1350130.50.5

!135013!

50!P(13)

2002

David M. Hassenzahl

Binomial, n = 50, p = 0.5

0

0.02

0.04

0.06

0.08

0.1

0.12

0 10 20 30 40 50 60

2002

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

2002

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”

2002

David M. Hassenzahl

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

iiDP1n

i*nDP

i* DP1DP

2002

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

2002

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

2002

David M. Hassenzahl

Epidemiology for Risk Analysis

An Introduction

2002

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

2002

David M. Hassenzahl

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)

Cumulative Exposure

ppm-years

Leukemia

Range Mean Person years

Observe deaths

Expected 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

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?

2002

David M. Hassenzahl

Uncertainty Issues

• Many toxicology uncertainties apply!

• Statistical uncertainty

• Heterogeneity

• Extrapolation

• Dose Metric

2002

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)

2002

David M. Hassenzahl

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

• 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

• One time deal

• Bunch of questions or data points

2002

David M. Hassenzahl

Intervention studies

• Common in medicine

• Double-blind

• Placebo

• Treatment

• Some ethical issues

2002

David M. Hassenzahl

Case-control

• 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

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

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)

• 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

2002

David M. Hassenzahl

Strength of Association

• High relative risk of acquiring the disease

• Strong p-value (low statistical uncertainty)

2002

David M. Hassenzahl

Intensity

• Also duration of exposure

• As exposure increases

• Does proposed effect increase?

2002

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

2002

David M. Hassenzahl

Coherence and biological plausibility

• Postulate a mechanism

• Consistent with our understanding of biological processes

• Better if supporting toxicological data  

2002

David M. Hassenzahl

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

• 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!

2002

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?

2002

David M. Hassenzahl

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

Water Company

Number of Houses

Cholera Deaths

Southwark and Vauxhall

40,046 1,263

Lambeth 26,107 98

Rest of London

256,423 1,422

2002

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!)

2002

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

0.0053810.0053840046

.00538040046 1263Z

p1pn

np x̂Z

table) the(off 6.72Z

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

ppm-years

Leuke-mia

Range Mean Person years

Observe deaths

Expected 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

2002

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 = 2.56

• p = 99.5

0.00023010.00023052584

1.12 21Z

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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 500 1000 1500 2000

Mean exposure (ppm-years)

P *

100

2002

David M. Hassenzahl

P(leukemia|exposure)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 500 1000 1500 2000

Low exposure (ppm-years)

P *

100

2002

David M. Hassenzahl

P(leukemia|exposure)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 500 1000 1500 2000

High exposure (ppm-years)

P *

100

2002

David M. Hassenzahl

P(leukemia|cumulative exposure)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 500 1000 1500 2000

Cumulative exposure (ppm-years)

P *

100

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.

2002

David M. Hassenzahl

2002

David M. Hassenzahl

2002

David M. Hassenzahl