Modeling Dose Response for Risk Assessment, George Gray

Center for Risk Science and Public Health
Modeling Dose Response for
Risk Assessment
George Gray
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
%RESPONDING
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)
ProportionResponding
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
%RESPONDING
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
%RESPONDING
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!
ProportionResponding
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*)
AttributableRisk,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
Response(ratiow/cancer)
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
CancerRisk
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

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Modeling Dose Response for Risk Assessment, George Gray