Modeling Dose Response for Risk Assessment, George Gray

Center for Risk Science and Public Health

Modeling Dose Response for Risk Assessment

George Gray

Center for Risk Science and Public Health Department of Environmental and Occupational Health

Milken Institute School of Public Health


The Dose-Response Relationship

Toxicity is quantified through the dose-response relationship

• Individual - change in severity of effect with dose

• Population - change in likelihood of response with dose • different relationships for different effects • shape of curve gives information about population

variability and toxicity of the compound


Individual Dose-Response Function (Dose-Effect)

Example - Aspirin in humans!

Dose (mg/kg)

0! 100! 200! 300! 400! 500! 600!

death!hemorrhage!encephalophathy!

acidosis!

hyperventilation!

nausea!

therapeutic!

Severity

2004 US Data •  21,000 reports to poison control centers •  43 deaths


Population Dose-Response Function

• Made up of many individual dose-response functions

• At each dose level, individual members of the population either do, or don't, respond

• Measure proportion of population responding at each dose level


Tolerance Distribution

Population of Varying Reserve Capacity

There is a dose-response because higher doses exceed the ability to tolerate the challenge in an increasing fraction of the population.

0 10 20 30 DOSE

% R

ESPO

ND

ING

40 0 %

100 %


The Population Dose-Response Relationship

•  For non-stochastic effects a dose response relationship is the distribution of individual response thresholds in a population

•  The distribution of thresholds reflects variability in sensitivity to the agent in the test population

•  Variability is likely to differ by species/sex/strain

•  Different modes of action or target sites may lead to different dose-response relationships for different adverse effects caused by the same agent in the same species/sex/strain


Population Dose-Response Function

Dose (mg/kg/day)

Pro

porti

on R

espo

ndin

g

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

0 10 100

Liver Effects

CNS Effects Lethality

Example - Aldrin in Rats!


Some Definitions

•  NOAEL - No Observed Adverse Effect Level the highest dose administered that does not produce

a statistically significant increase in an adverse effect

•  LOAEL - Lowest Observed Adverse Effect Level the lowest dose tested which produces a

statistically significant increase in an adverse effect

•  Threshold the dose level below which no adverse effects will

occur


NOAELs and LOAELs

Dose (mg/kg/day)!

0!

0.1!

0.2!

0.3!

0.4!

0.5!

0.6!

0.7!

0.8!

0.9!

1!

0! 1! 3! 10! 30! 100! 300! 1000!

NOAEL!LOAEL!

Proportion Responding

Threshold!


What to Do?

•  We have data from experiments with animals •  Often high doses •  Usually minimized interindividual variation •  Well controlled

•  Want to say something about what might happen to exposed humans •  Usually lower doses •  Presumably more – but unknown – variability


Dose-Response Assessment in Risk Assessment

Two Primary Approaches

•  Assume threshold for adverse effects

•  Assume no threshold and proportional (linear) relationship between dose and response


Two Approaches

•  Long latency •  Irreversible, lesions become

independent of dose •  Caused by small, rare

events in a single cell •  Auto-amplifying, “all-or-

none” •  Generally treated as a non-

threshold process

•  Often short latency •  Often reversible, lesions

may remain dependent on dose

•  Caused by collective effects on many cells

•  Severity depends on dose •  Generally treated as a

threshold process

Non-threshold Threshold


Tolerance Distribution

Population of Varying Reserve Capacity

There is a dose-response because higher doses exceed the ability to tolerate the challenge in an increasing fraction of the population.

0 10 20 30 DOSE

% R

ESPO

ND

ING

40 0 %

100 %


Stochastic Events

There is a dose-response because, for all individuals, higher doses cause a higher random chance of being “hit” (but only some actually are).

Population of Uniform Susceptibility

0 10 20 30 DOSE

% R

ESPO

ND

ING

40 0 %

100 %

Random Events Increase with Dose


The Goal of Noncancer Risk Assessment

•  The goal is identification of exposure levels that will be below the population threshold - theoretically the threshold of the most sensitive individual in a population

•  Two Approaches •  Calculate risk value by adjusting data from animal

tests (or epidemiological studies) with uncertainty factors

•  Calculate margin of exposure (MOE)


Noncancer Risk Values

Sample definition - U.S. EPA Reference Dose (RfD) An estimate (with uncertainty spanning perhaps an

order of magnitude) of a daily exposure to the human population (including sensitive groups) that is likely to be without appreciable risk of deleterious effects during a lifetime

•  Similar to WHO or CPSC Acceptable Daily Intake (ADI), IPCS and JMPR Tolerable Intakes (TIs), etc.


Margin of Exposure

•  Sample definition – Australian Department of Health and Ageing “The MOE provides a measure of the likelihood that a

particular adverse health effect will occur under the conditions of exposure. As the MOE increases, the risk of potential adverse effects decreases. In deciding whether the MOE is of sufficient magnitude, expert judgment is required. Such judgments are usually made on a case-by-case basis and should take into account uncertainties arising in the risk assessment process, such as the completeness and quality of the database, the nature and severity of effect(s) and intra/interspecies variability”


Key Steps

•  Identify available data

•  Evaluate endpoints and dose-response relationships

•  Choose “critical effect” in “critical study”

•  Identify “point of departure” for critical effect


Effect or Adverse Effect?

•  Matter of toxicological judgment - often depends on how thoroughly a substance has been studied

examples changes in body weight gain increased liver enzyme levels diarrhea or reduced stool size fewer offspring increased rates of malformed offspring

•  Try to identify the “critical effect” in the “critical study”

•  Identify NOAEL and LOAEL in critical study


Critical Study, Critical Effect?

Standard method is to choose the most sensitive sex of the the most sensitive species for the most sensitive endpoint

Neurotoxicity

Hepatotoxicity

Mice

Rats

M F M F

Mice

Rats

M F M F

Dose (mg/kg)

NOAEL


Point of Departure

•  Non-cancer risk estimates build from a “point of departure” (POD) on the dose response curve of the critical effect in the critical study

•  Two primary approaches to setting POD •  NOAEL •  Benchmark dose


NOAEL as POD

Dose (mg/kg/day)!

0!0.1!0.2!0.3!0.4!0.5!0.6!0.7!0.8!0.9!

1!

0! 2! 4! 8!

Pro

porti

on R

espo

ndin

g

10!6!

NOAEL

LOAEL


Benchmark Dose Approach

•  Begins with dose at “benchmark” level of response instead of NOAEL

•  Process: •  Identify critical effect and critical study •  Fit simple dose-response model with confidence

limits •  Identify dose at “benchmark” response (often

upper confidence limit on ED10) •  Apply appropriate uncertainty factors to

benchmark dose


Description of BMD

Dose!

Response

0.05

0.10

0.20

0.15

Dose-Response Fit to Experimental Data

95% Confidence Limit on Dose-Response

ED10 (BMD) BMDL10


Advantages of the BMD Approach

•  Provides consistent basis for calculating RfD or ADI

•  Rewards bigger and better studies

•  Includes information about shape of dose-response relationship

•  Provides information about risk at exposure near benchmark dose


Concerns About BMD Approach

•  More laborious than NOAEL approach •  Some data sets may be difficult to model •  Choice of model may have strong influence on

BMD but no scientific criteria for choosing among models

•  Critical effect will still vary between chemicals •  BMD approach is more conservative than NOAELs

•  NOAEL/BMD (1%,95%) ~ 30 •  NOAEL/BMD (5%,95%) ~ 6 •  NOAEL/BMD (10%,95%) ~ 3


Calculating Risk Values

•  Point of Departure is adjusted by uncertainty factors

•  Account for uncertainties and data amount/quality

•  Uncertainty factors evolved as part of regulation and have little empirical basis

•  Factors differ depending on characteristics of the critical study


Safety (Uncertainty) Factors

Extrapolation !Uncertainty Factor!Animal to Human (H) ! !10!Average to Sensitive Human (S) ! !10!LOAEL to NOAEL (L) ! !10!Less than Chronic to Chronic (C) ! !10!Data Quality (MF) ! !1-10!

U.S. EPA Guidelines for Development of RfD*

*Barnes, D.G., and Dourson, M.L. (1988) Reference Dose (RfD): Description and Use in Health Risk Assessments, Regulatory

Toxicology and Pharmacology 8:471-486


Animal to Human (10H) •  Adjustment for interspecies differences in sensitivity to

toxic agents •  Current justification based on observation that

animal’s metabolic rates scale approximately as surface area (~BW2/3)

•  This means that animals of higher body weight appear more sensitive per mg/kg than smaller animals

•  By this calculation a human is about 6 times more sensitive than a rat, 4 times more sensitive than a guinea pig, and 12 times more sensitive than a mouse

•  Therefore factor of 10 is overestimate for some species, underestimate of sensitivity differences for others


Average to Sensitive Human (10S)

•  Adjustment to account for variability in response in the human population

•  Essentially says that most sensitive human may be 10 times more sensitive than average human (and experimental animal)

•  Empirical studies* of differences in sensitivity for acute lethality in rats indicate that 92% of the time range between most and least sensitive was less than 10-fold (average difference was 2.4 fold)

* Dourson, M.L., and Stara, J.F. (1983) Regulatory History and Experimental Support of Uncertainty (Safety) Factors, Regulatory Toxicology and Pharmacology 3:224-238


Less Than Chronic to Chronic (10C)

•  Since “safe exposures” like ADI or RfD are for lifetime exposure it is preferred that NOAEL come from chronic study

•  If critical study and critical effect are determined to be from less than lifetime exposure this factor is used

•  Empirical analysis of subchronic and chronic studies in rats and dogs indicates that 96% of the time the ratio chronic/subchronic NOAEL (or LOAEL) is less than 10 with an average ratio of 2


LOAEL to NOAEL (10L)

•  Sometimes the critical study finds an adverse response at even the lowest dose tested meaning that there is not a NOAEL, only a LOAEL

•  When using LOAEL this factor of 10 is used

•  An empirical analysis found all ratios of LOAEL to NOAEL were less than 10 and 96% were less than 5

•  Sometimes an adjustable factor between 1 and 10 is used


Data Quality (MF 1-10)

•  An additional factor used by the U.S. EPA to account for data quality and quantity

•  “The magnitude of the MF depends upon the professional assessment of scientific uncertainties in the study not explicitly treated [by other uncertainty factors] e.g., the completeness of the overall database and the number of species tested. The default value for the MF is 1”


Calculate Risk Values

•  Simply divide NOAEL (or LOAEL) of critical effect from critical study by appropriate uncertainty factors

NOAEL!UFH x UFS x UFL x UFC x MF! = RfD (or ADI, TI etc.)!


Example

Example: Bromate!

Critical Effect – kidney hyperplasia!Critical Study – male mice exposed for 100 weeks!

NOAEL – 1.1 mg/kg/day!LOAEL – 6.1 mg/kg/day!

!RfD = 1.1 mg/kg/day!! 10(H) x 10(S) x MF!


Example

Bromate (continued)

NOAEL – 1.1 mg/kg/day

RfD = 1.1 mg/kg/day 10(H) x 10(S) x 3 (MF)

RfD = 0.004 mg/kg/day (0.000367 rounded off)


Different Choices

Non-Cancer Evaluation of PCBs (circa 2000)

Standard Level Critical Effect NOAEL Exposure Uncertainty (Agency) (mg/kg/day) (mg/kg/day) Regimen Factors

RfD 0.00007 reduced 0.007 monkey 3H (EPA) (70 ng/kg/day) birth weight exposed in diet 3S

for 22 months 3C 3 M

MRL 0.000005 decreased none monkey exposed 10H (ATSDR) (5 ng/kg/day) immunoglobulin (LOAEL of by oil gavage 10S

levels after 0.005 7 days/wk for 10L challenge mg/kg/day) 27 months


Using the Benchmark Dose

BMD!UFH x UFS x UFC x MF! = RfD (or ADI, TI etc.)!


The Margin of Exposure (MOE)

_____RfV_____ Exposure

•  Reference Value (RfV) is a point of departure (POD) from toxicologic or epidemiologic data •  No Observed Adverse Effect Level •  Benchmark Dose (or bound)

•  Exposure can be measured or modeled – reflect variability

= MOE


Using MOE

MOE = PoD Exposure

•  Sufficiency of MOE is “matter of expert judgment”

•  Usually MOE > 100 considered of minimal concern

•  POD can be NOAEL or BMD - Organizations that use MOE (Australia, EU, etc. rarely use BMD approach)


Advantages of RfV/MOE Approach

•  Faster – more chemical coverage

•  More transparent – science policy choices made in risk management phase

•  Readily applied to different settings/uses (i.e., fit for purpose (NAS and EPA))


Concerns About RfV/MOE Approach

•  How to calculate RfV?

•  Which endpoints? •  sex/species/strain •  Concordance?

•  How to judge adequacy of MOE (>100? >1000? >233?) – are we putting science judgments in the wrong hands?

•  Does use imply linearity (e.g., MOE of 500 is 5X better than 100?

•  Can it be used in benefit/cost analysis and other important uses of risk assessment?


Non-Cancer Summary

•  Noncancer risk assessment is predicated on the idea of individual and population thresholds for adverse effects

•  The goal of non-cancer risk assessment is to determine “safe” level of exposure for a population

•  Current practice involves adjustment of NOAEL or Benchmark Dose with uncertainty factors or calculation of a margin of exposure (MOE)


Cancer Risk Assessment

•  Sources of Data

•  The extrapolation issue

•  Current practice


Rodent Carcinogenesis Bioassays

•  Rats and mice •  Male and female •  3 dose groups

•  Control •  Maximum tolerated dose (MTD) •  MTD/2

•  Exposure in feed, water, or by gavage •  2 years


Low Dose Extrapolation

•  Because the bioassay cannot directly detect the levels of risk of interest, it is necessary to extrapolate.

•  Many mathematical models have been proposed for low dose extrapolation -- including the one-hit, the multistage, the multi-hit and the Weibull.

•  Although these models may give similar fits to the data in the experimental region, they often give quite divergent estimates of low dose risk.

•  Some organizations choose not to model some carcinogens and calculate MOE instead


Example – Saccharin

10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 10 10-8

10-7

10-6

10-5

10-4

10-3

10-2

One Hit Armitage-Doll

Weibull

Gamma Multi - Hit

Dose, d (ppm*)

Attr

ibut

able

Ris

k, P

(d) –

P(0

)

Source: Taylor et al. Toxic Applied Pharmicol, 29, 154 Abstr. 200, 1974


Cancer Data Extrapolation Assume “no threshold” and “linear”

Animal Toxicity Data

Res

pons

e (r

atio

w/ c

ance

r)

Dose mg/kg/day

10 20 30

0.1

0.4

1.0 0.9 0.8 0.7 0.6 0.5

0.3 0.2

0 40 50 60

10-7

10-8

0 0 10-6 10-5

Dose mg/kg/day

Can

cer R

isk

slope factor or cancer slope factor


Current EPA Approach

•  Model data in observed range (essentially BMD)

•  Assume low-dose linear below observed

•  Estimate Cancer Slope Factor (CSF) from Point of Departure (POD)

•  CSF = 0.10/LED10


Differences in Potency

Pesticide Cancer Slope Factor !(mg/kg/day)!

Linuron !1.5 x 10 !Captan !4.7 x 10!Acephate !3.7 x 10!Cypermethrin !3.7 x 10!Glyphosphate !2.7 x 10!Fosetyl Al !3.3 x 10!Azinphos-methyl !1.7 x 10!

-3!

-6!-5!

-7!-8!-9!

-4!

-1!


Take Home Messages

•  Risk assessment is the way toxicologic information is processed to inform public health decisions

•  For risk assessment, dose response relationships are assumed to either have a threshold (primarily non-cancer effects) or to be linear at low doses (primarily carcinogens

•  The goal of non-cancer risk assessment is to determine “safe” level of exposure for a population - current practice involves adjustment of NOAEL or Benchmark Dose with uncertainty factors

•  Cancer risk assessment develops Cancer Slope Factors to allow estimation of cancer risk associated with a specific exposure – based on linear extrapolation of rodent bioassay data

Modeling Dose Response for Risk Assessment, George Gray

Government & Nonprofit

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