Exploring Carcinogen Risk Analysis Through Benzene

Slide 1:Exploring Carcinogen Risk Analysis Through Benzene

Image from Matthew J. Dowd Department of Medicinal Chemistry Virginia Commonwealth University Note to instructors: this is certainly a multi-session lecture. I do about two and a half hours on toxicology, one and a half hour on bootstrapping, and two and a half hours on epidemiology. That means a total of seven or eight hours. No, I didn’t do my math wrong…it takes about three full weeks (2.5 hours per week) to get through this. I assign one big monster problem set, “Integrated benzene problem set.” It is somewhat unorthodox, but makes the students make assumptions and defend them, bang their heads against some models, and apply the new methods. I expect them to submit the problem set about one week after I have completed the segment, so it’s in their hands for about 4 weeks. Note to instructors: this is certainly a multi-session lecture. I do about two and a half hours on toxicology, one and a half hour on bootstrapping, and two and a half hours on epidemiology. That means a total of seven or eight hours. No, I didn’t do my math wrong…it takes about three full weeks (2.5 hours per week) to get through this. I assign one big monster problem set, “Integrated benzene problem set.” It is somewhat unorthodox, but makes the students make assumptions and defend them, bang their heads against some models, and apply the new methods. I expect them to submit the problem set about one week after I have completed the segment, so it’s in their hands for about 4 weeks.

Slide 2:Objective

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

Slide 3:Toolbox Building

Likelihood Maximization Curve fitting Bootstrapping Z-Scores Relative Risk Dose-Response extrapolation

Slide 4:Overview of benzene

Fairly common hydrocarbon Manufacturing Petroleum products Strongly suspected human carcinogen Animal assays Many epidemiological studies Leukemia as important endpoint

Slide 5:Benzene structure

Image from Matthew J. Dowd Department of Medicinal Chemistry Virginia Commonwealth University

Slide 6: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

Slide 7:Toxicology Data Set

Crump and Allen 1984

Slide 8: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?

Slide 9:Toxicology

Paracelsus “the dose makes the poison” Regulatory assumptions! This is not Dr. Gerstenberger’s Toxicology! Note: We have a toxicology class that covers many non-Cancer endpoints, so I focus on cancer end-points in this class.Note: We have a toxicology class that covers many non-Cancer endpoints, so I focus on cancer end-points in this class.

Slide 10:Reading

SWRI Chapter 5 US EPA Proposed guidelines (US EPA 1996) Cox 1996

Slide 11:General idea

Applied doses Greater specificity about exposure than epidemiology Observed effects Artificial control of exposure

Slide 12:Physiologically Based Pharmacokinetics

PBPK Investigate flows of materials through bodies System dynamics models More on these in exposure lecture

Slide 13:Studies

Animals Rarely humans Parts Cell tissue

Slide 14:Effects

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

Slide 15:Crump and Allen Benzene data set

Animals at various concentrations Four data points “Designer” mice

Slide 16:Relevance to Humans

How to get from high level, lifetime studies of animals to anticipated low dose effects in humans?

Slide 17:Questions about benzene

Is benzene a mouse carcinogen? Is benzene a human carcinogen? If so, how potent?

Slide 18:Benzene data set I

Slide 19:Benzene data set II

Slide 20:Uncertainty Pervades

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

Slide 21:Animal Test Issues

Interspecific comparison Statistical uncertainty Heterogeneity Extrapolation Dose Metric

Slide 22: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.

Slide 23: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.

Slide 24:Interspecific comparison

Slide 25:Interspecific comparison

Slide 26:Interspecific comparison

These numbers differ from the values in SWRI. For an explanation of the difference, please see the page “Notes on teaching from Problem 5-2” at the Risk Analysis Teaching and Learning Site http://www.unlv.edu/faculty/dmh/ratl/ These numbers differ from the values in SWRI. For an explanation of the difference, please see the page “Notes on teaching from Problem 5-2” at the Risk Analysis Teaching and Learning Site http://www.unlv.edu/faculty/dmh/ratl/

Slide 27:Animal Test Issues

Interspecies comparison Statistical uncertainty Heterogeneity Extrapolation Dose Metric

Slide 28:Binomial Distribution

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

Slide 29:Likelihood Maximization

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

Slide 30:Statistical Uncertainty

Slide 31:Statistical Uncertainty

Slide 32:Animal Test Issues

Interspecies comparison Statistical uncertainty Heterogeneity Extrapolation Dose Metric

Slide 33:Heterogeneity

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

Slide 34:Heterogeneity

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

Slide 35:Animal Test Issues

Interspecies comparison Statistical uncertainty Heterogeneity Extrapolation Dose Metric

Slide 36:Extrapolation

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

Slide 37:Extrapolation Concerns

Overestimation Tautological effects Thresholds Hormesis, or “Vitamin” effect Underestimation Saturation Synergistic effects Susceptibility Omission

Slide 40:Statistical Uncertainty

Slide 42:Extrapolation

Slide 43:Animal Test Issues

Interspecies comparison Statistical uncertainty Heterogeneity Extrapolation Dose Metric

Slide 44: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

Slide 45:Risk to Humans?

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

Slide 46:Calculate Risk

10ml benzene/liter air 0.313 ml/mg 20m3 air / day 1000 liters/ m3 70kg person

Slide 47: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

Slide 48:Cancer Risk: Exposure Term

Slide 49:Computed Exposure Terms

Slide 50:Computed Exposure Terms

Slide 51:Cancer Risk

Slide 52:“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

Slide 53: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”

Slide 54:Likelihood Maximization

A curve fitting technique

Slide 55:Binomial Distribution

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

Slide 56:Likelihood Maximization

More appropriate than Least Squares when you know something about likelihoods “Bootstrapping” method needed

Slide 57:Statistical Uncertainty

Slide 58:Statistical Uncertainty

Slide 59: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

Slide 60: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

Slide 62: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

Slide 63: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”

Slide 64: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

Slide 65: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

Slide 66:Simple Model

P*(D) = kD + D0 Hypothetical data set

Slide 67: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 Following this lecture, I work through how to do bootstrapping using Solver in excel. There is a reference spreadsheet at the RATL websiteFollowing this lecture, I work through how to do bootstrapping using Solver in excel. There is a reference spreadsheet at the RATL website

Slide 68: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 Following this lecture, I work through how to do bootstrapping using Solver in excel. There is a reference spreadsheet at the RATL websiteFollowing this lecture, I work through how to do bootstrapping using Solver in excel. There is a reference spreadsheet at the RATL website

Slide 69:Epidemiology for Risk Analysis

An Introduction

Slide 70: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

Slide 71:Overview of epidemiology

Exposed human populations Hard to control Rarely addresses causality Common measures Relative Risk Z-scores

Slide 72:Pliofilm Cohort Data(SWRI Page 215)

Slide 73:Two Major Classes

Descriptive Population Studies Case Reports Case Series Cross-Sectional Analyses Analytical Intervention Studies Cohort Studies Case-Control studies ?Toxicology?

Slide 74:Uncertainty Issues

Many toxicology uncertainties apply! Statistical uncertainty Heterogeneity Extrapolation Dose Metric

Slide 75: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)

Slide 76:Populations: pros and cons

Large samples Can address major effects potential causes Low relative risk ratios Study design challenges 

Slide 77:Case studies

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

Slide 78:Cross-sectional analysis

One time deal Bunch of questions or data points

Slide 79:Intervention studies

Common in medicine Double-blind Placebo Treatment Some ethical issues

Slide 80:Case-control

Retrospective method One group with effect Comparable group without effect Observed differences in possible causes  

Slide 81:Cohort studies

Retrospective or prospective Look at exposure groups Compare rates of effects

Slide 82: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

Slide 83: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

Slide 84: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 

Slide 85:Temporality

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

Slide 86:Strength of Association

High relative risk of acquiring the disease Strong p-value (low statistical uncertainty)

Slide 87:Intensity

Also duration of exposure As exposure increases Does proposed effect increase?

Slide 88:Specificity of Association.

Highly specific case Highly specific exposure Example: “leukemia from benzene” versus “cancer from hydrocarbons”  

Slide 89:Consistency

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

Slide 90:Coherence and biological plausibility

Postulate a mechanism Consistent with our understanding of biological processes Better if supporting toxicological data  

Slide 91: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

Slide 92:Some Correlation Issues

Uncertain dosimetry very difficult to estimate exposure Latency of effects, especially cancer Confounding factors Bias Representativeness of control group Small numbers

Slide 93: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!

Slide 94:Cholera in London, mid1800’s

John Snow Drinking water from the Thames High rates of cholera Unknown cause of cholera Ill humours? Vapours?

Slide 95:Cholera in London mid 1800’s

Many water companies Southwark and Vauxhall, downstream Lambeth, upstream Several others

Slide 96:London Cholera Data 1853-4

Slide 97: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!)

Slide 98: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

Slide 99: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

Slide 100: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

Slide 101:Statistical Test

Slide 102: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!

Slide 103: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

Slide 104:Pliofilm Data (SWRI Page 215)

Slide 105:Pliofilm

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

Slide 106:Pliofilm Relative Risk

Overall RR = 21 / 12.1 = 1.74 Z = 2.56 p = 99.5

Slide 107: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?

Slide 112: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

Slide 113: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

Slide 114: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

Slide 115: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.