THE FORMULATION OF CARCINOGEN RISK STANDARDS ON THE BASIS OF THE
CREDIBILITY OF RISK ASSESSMENTS

Roy E. Albert, M.D. & Rakesh Shukla, Ph.D.
Department of Environmental Health
University of Cincinnati College of Medicine

7-27-1992

ABSTRACT

This paper describes an approach to the formulation of carcinogen
risk standards based on the level of credibility of the
carcinogen risk assessments. Credibility is characterized as the
product of the numeric ratings for the likelihoods that 1) a
given agent is a human carcinogen and 2) that the linear non-
threshold extrapolation model is valid for the given agent. The
approach assumes that one hundred percent credibility in the risk
assessment requires a hundred percent likelihood of a zero
carcinogen effect. Below one hundred percent, the level of
credibility is linearly related to the likelihood of a zero
carcinogen effect. The likelihood of a zero carcinogen effect is
then related to the fraction of the standard error of the
estimated national cancer rate, for all types of cancer, by means
of the Likelihood Ratio. The standard error of the cancer rate,
expressed as the lifetime probability of dying from all forms of
cancer, estimated either geographically (by states) or temporally
(year-to-year), is 4x10*. The fraction of the standard error of
the cancer rate associated with a given level of credibility in
the risk assessment yields the risk standard for the given agent.
Examples of risk standards for several carcinogens with varying
degrees of risk assessment credibility are presented; their
standards range from about 10% to about 6 x 10%.
INTRODUCTION

There is a difference between the legal and scientific mind-set.
The law generally operates on the basis of black and white
decisions. A person is guilty or not guilty. Medico-legal
causality is established when the likelihood of an agent being
the cause of a disease exceeds 50%. Science, by contrast, deals
in the weight of evidence. A great deal of evidence is generally
needed before a scientific hypothesis becomes accepted fact. In
the regulatory arena the legal and scientific views collided in
the early days of the US EPA, the mid-nineteen seventies. The
circumstances involved the regulatory actions being taken against
important pesticides, DDT, Heptachlor-Chlordane, Aldrin-Dieldrin,
and Mirex. In the course of the hearings on these pesticides, the
EPA sought to shorten the administrative hearing process by
introducing, a series of cancer principles as matters of
fact,i.e., which would not be arguable in court(1). These
principles were simple declarative statements about cancer that
raised the hackles of many scientists, e.g.," a carcinogen is any
agent which increases tumor induction in man or animals"(2).
Scientists were quick to point out that hormones and calories
modulate tumor formation, and was the EPA going to regulate these
modalities as carcinogens? The scientific community joined the
Agro-chemical industry in attacking the EPA as, for example, in
the Lancet editorial, entitled, " EPA’s seventeen principles
about cancer, or something"(3). After much internal debate, the
EPA countered by declaring that it was going to regulate on the
basis of weighing risks and benefits wherever it could, and in
order to do so, it was going to evaluate the scientific data for
putative carcinogens in a completely objective fashion,
independent of the regulatory considerations. To accomplish this
objective, it initiated Risk Assessment in a formalized way (4).
The guidelines, first published in 1976, took the approach of
setting up the format for an impartial display of the relevant
scientific evidence for and against carcinogenicity, and the
associated uncertainties(5). However, the uncertainties of the
risk assessments, which arise from the limitations of the
available evidence on given agents and the lack of understanding
of carcinogenic mechanisms, has been a source of discomfort to
the regulators. They naturally prefer to be told that a given
agent is or is not a carcinogen rather than a possible or
probable carcinogen. They prefer knowing how many people are
going to die of cancer by exposure to a carcinogen rather than
dealing with a plausible upper limit estimate of the incremental
cancer mortality which is how EPA describes its risk estimates
made with a low-dose linear non-threshold extrapolation model

(6).

The traditional approach to standard setting is to apply
arbitrary safety factors to the lowest observable toxic dose or
the highest non-toxic dose. The resulting standards are deemed

2
safe and provide straightforward guidance to regulatory action.
Risk Assessment, by introducing the scientific concepts of weight
of evidence and its uncertainties and emphasizing uncertainty,
has made regulatory decisions more complex.

No attempt has been made to utilize the uncertainty of risk
assessment as the basis for the formulation of risk- based
standards. The purpose of this paper is to explore a possible way
to accomplish this end. Our approach is restricted to
circumstances where there is no consideration of balancing risks
and benefits, as with the clean up of hazardous waste sites. We
also adopt the premise that in the absence of benefits, there is
no acceptable risk; this is expressed by the NIMBY view (not in
my back yard) about hazardous wastes. We use the credibility of
the risk assessment, as the determinant of the stringency of the
risk standard. The overall credibility of the risk assessment is
the product of the credibility of the hazard assessment and the
credibility of the linear low-dose extrapolation model. The
overall credibility is related, in a one-to-one fashion, to the
likelihood of a zero carcinogen effect. Given the variability of
the cancer rate for the USA, measured geographically or
temporally, the likelihood of a zero carcinogen effect determines
the risk-based standard.

CREDIBILITY OF THE CARCINOGEN RISK ASSESSMENT

Two issues with any risk are how likely is it to occur, and what
are the consequences if it does occur? Similarly, with carcinogen
risk assessment, there are two components, the Qualitative
aspect: how likely is the agent to be a human carcinogen? This
is also called Hazard Assessment. And the Quantitative aspect:
how much cancer would be produced by the agent for a given
exposure? This involves Dose Response Assessment, and an
Exposure Assessment.

In broad terms, the Qualitative aspect of carcinogen risk
assessment involves a weight-of- evidence judgement based on
molecular, cellular, and biochemical mechanisms, epidemiology,
animal bioassay, and short-term tests. There are grades for the
weight of evidence(7): A- a Definite human carcinogen on the
basis of persuasive human and animal evidence of carcinogenicity;
B- a Probable human carcinogen on the basis of at least two
positive animal studies, and C- a Possible human carcinogen based
on positive responses in a single animal species.

The Quantitative aspect of carcinogen assessment essentially
involves the selection of a low dose extrapolation model, which
determines the incremental risk in relation to the estimation of
exposure. The multistage model dominates current usage, the most
important aspect of which is its non-threshold low-dose linear
character.
The summing up of the carcinogen risk assessment for a given
agent, called Risk Characterization, involves the grading of the
evidence for human carcinogenicity and a statement of potency
which, in effect, is the low dose linear slope. For example, an
agent might be categorized as (B) 107 / wg/M’ for an airborne
carcinogen meaning that it is a probable human carcinogen with a
one percent lifetime incremental cancer risk for a lifetime
average exposure of one microgram per cubic meter. The guidelines
for risk assessment call for an explication of the uncertainties
in the assessment but there is no guidance on how to factor the
uncertainties into the risk assessment.

The approach proposed here formalizes uncertainty in terms of the
credibility of the risk assessment. Credibility is characterized
as the combination of the likelihood, from the qualitative
assessment, that the agent in question is a human carcinogen and
the likelihood, from the quantitative assessment, that the non-
threshold low-dose linear extrapolation model is valid for the
agent in question. Both factors have to be arrived at by the
judgement of knowledgeable scientists and expressed in numeric
form, e.g., from 0-1. The two factors are given equal weight and
the overall credibility is the product of the numeric factors for
both aspects of the risk assessment.

On the qualitative side, the weight of evidence for human
carcinogenicity represents a judgement of whether the agent in
question should be treated as a carcinogen or not. On the
quantitative side, essentially the same holds true from a
practical standpoint. The extrapolation models which are
plausibly alternative to low dose linearity, e.g., the probit or
dose square, produce negligible risk estimates compared to low
dose linearity(8). The alternative to low dose linearity is
virtual non-carcinogenicity due to negligible risks. Thus the
credibility of the carcinogen risk assessment is effectively a
judgement of how likely it is that the agent will behave as a
human carcinogen at low doses.

INSIGNIFICANCE OF THE RISK ESTIMATE

The Likelihood Ratio concept is customarily used to determine in
which population a data set is more likely to belong (9). Here,
we use the estimated incremental cancer risk as if it were the
observed data and use the Likelihood Ratio to obtain the odds
that the incremental cancer risk could be interpreted as a zero
carcinogen effect. This is illustrated in Figure 1. Let A
represent the non-exposed population with the mean background
cancer rate, m. Let B represent the exposed population with its
mean cancer rate, v, which is the mean background rate plus the
estimated incremental effect of the carcinogen; the incremental
effect is v-m. The likelihood that population B is the same as A
is given by the height of the intercept of v on the curve of
population A, namely, a/b. It can be seen that as the value of v-
m decreases, the Likelihood Ratio increases such that when v and
m coincide, the likelihood that population B is the same as
population A reaches 1.0; this is the certainty of a zero
carcinogen effect. The Likelihood Ratio can be expressed as a
fraction of the standard error of the mean for population A.
Based on an approximate Taylor series expansion, as described in
the Appendix, the standard error fraction (S.E.F.) of population
A = [2(1-(a/b))]'* (10). Examples of the relationship between the
Likelihood Ratio (zero carcinogen effect) and the standard error
fraction are shown in Table 1. The 0.99 likelihood that
population B is the same as population A occurs when the median
of population B is separated from the median of population A by
0.14 standard error, assuming normal distributions with the same
variability. It can be seen that the Likelihood Ratios, ranging
from 0.99 to 0.05, cover approximately one order of magnitude in
the standard error fraction: from 0.14 to 1.38.

Two approaches have been used to estimate the standard error in
the cancer mortality rate for the USA: the state-to-state
variability and the variability in the total number of cancer
deaths from year to year(11). The geographic variability
represents the average age-adjusted state cancer mortality rates
for all types of cancer in the. 20-year period from 1950 to
1969(12). These data were weighted according to the total number
of cancer cases in each state over the 20-year period. The
standard error, as a fraction of the mean for the combined sexes
is 2x10”.

The temporal variability of the average annual age-adjusted
mortality rates in the USA was determined for cancer of all types
during the same 20-year period(13). The mean annual cancer rate
was 1.8x10°. With the trend in the annual rates factored out by
linear regression,the standard error was 2.9x10°; the fractional
standard error (per unit mean) was 1.6x10°.

The fractional standard errors obtained by the two methods are
very similar at 2x10°% and 1.6x10° for an average 1.8x10°. The
cancer risk equivalent to one standard error of the average
cancer rate is the lifetime probability of dying of cancer (0.22)
times the fractional standard error 1.8x10%; this cancer risk is
4x10".

RELATION BETWEEN THE LIKELIHOOD OF A ZERO CARCINOGENIC EFFECT AND
THE CREDIBILITY OF THE RISK ASSESSMENT

The relationship between the credibility of the risk assessment
and the probability of a zero carcinogen effect, can be
visualized as a plot of the two functions with both axes ranging
from zero to one (Figure 2). At the upper end of the plot, the
credibility of the risk estimate and the likelihood of a zero
effect are both 1.0 and at the lower end both approach zero. The
question at issue is the shape of the relationship between the
upper and lower extremes. An upwardly and a downwardly curving
relationship would be more and less protective, respectively, as
in Figure 2. In the absence of guidance from any analogous
situations, we believe that the linear relationship is a
reasonable, middle-of-the-road position. Thus, if we think that
an agent has an equal likelihood of behaving like a carcinogen
and a non-carcinogen, i.e., a credibility of 0.5, the likelihood
of a zero carcinogen effect should be midway between a carcinogen
and a non-carcinogen. We have therefore chosen a linear
relationship between credibility and the likelihood of a zero
incremental cancer risk for the formulation of risk-based
standards.

ILLUSTRATIONS OF RISK-BASED CARCINOGEN STANDARDS

As an example of the process of formulating risk-based standards
for carcinogens, we might take the cases of external exposure to
gamma radiation, which is characteristic of whole body external
exposure to long-lived fission products. This form of radiation
involves high energy radiation with a linear energy transfer
(LET) in the range of 0.1-0.3 kev. On the basis of animal and
epidemiologic data the probability that such radiation is
carcinogenic for humans is 1.0. However, the credibility of the
linear low dose model is less sure. The results of an informal
canvassing of six experts in radiation biology indicated a wide
range of belief in the validity of the linear low-dose model,
ranging from 1.0 to 0.2 with an average of 0.6. The one
individual who was sure of the validity, based his argument on
only the physical considerations of a single hit model for
ionization damage of DNA. The others understood this, but
qualified their judgements on the basis of biological
considerations. Thus, the overall probability of the risk
estimate being valid is 1.0 x 0.6, or 0.6. The likelihood of a
zero risk, which is the ratio, a/b, is then 0.6. The S.E.F.
equal (2[1- -0.6])'? = 0.9. The risk-based standard equals the
S.E.F.x the risk per S.E., or 0.9 x 4 x 10% . The risk standard
is therefore, 3.6 x 10%.

A risk based standard for radon might well involve a probability
for human carcinogenicity of 1.0 and a probability of low dose
linearity equal to 0.9. The ample epidemiological and animal
evidence makes radon a certain human carcinogen. The high LET of
the radiation from radon and its decay products, gives ita high
rating for linearity. Thus, the certainty of the risk estimate
might be 0.9, and the risk standard would be 1.8x10*.

Perchlorethylene, which is a widely used chemical in the dry
cleaning industry, might have only a 0.25 probability of human
carcinogenicity, because it induces only relatively benign tumors
in the liver and kidney of rodents and there is no persuasive
epidemiological evidence for human carcinogenicity. Since the
agent is not genotoxic, the credibility of the use of low dose
linearity would also be low, perhaps 0.25. If this were the case,
the overall credibility of the risk estimate would be 0.06; the
S.E.F. would equal 1.38. The risk standard would be 5.5 x 10%.

Discussion

According to the Oxford English Dictionary, the term credible
means "capable of being believed, trustworthy, reliable." They
illustrate by quotation from Lithgow (1682), "It is holden to be
so credible as if an oracle had spoken it." There is usage of
credibility in decision making. In medicine, the credibility of a
diagnosis gains strength when multiple tests point to the same
diagnosis. Similarly, the credibility of a particular cause of a
disease in epidemiologic studies becomes greater with the number
of independent studies that show the same response under
different circumstances. The fable about the boy who cried wolf
is an example of the role of credibility in determining a social
response. What is novel in this proposal, is that the credibility
of the risk assessment is graded and related linearly to the
likelihood of a zero carcinogenic effect. We posit that an agent,
which is 100% certain to act as a human carcinogen at low doses,
should have a 100% certainty of a zero risk. Conversely, as the
credibility that an agent is a human carcinogen at low doses
approaches zero, the requirement for a probability of a zero
carcinogen effect should also approach zero. It is not illogical,
that the degree of belief that an agent will act as a human
carcinogen at low doses should correspond to the degree of belief
in a zero carcinogen risk.

The calculated risk standards are relatively insensitive to
differences in the degree of credibility in the risk assessment.
This is largely because of the narrow range of variability in the
cancer rate for the USA as a whole. This makes the standard
error equivalent to a small increment in the cancer risk, namely
4x10%. By the same token, the risk standards are relatively
insensitive to the shape of the curves, shown in Figure 2,
relating the level of credibility of the risk assessment and the
likelihood of a zero carcinogen effect. For the calculated risk
standards to approach the level of 10°, there would have to be an
extrordinarily high level of belief in the credibility of the
risk assessment, namely, 99.9997%.

The EPA describes the results of the linear non-threshold
extrapolation as a plausible upper limit assessment of risk,
which is not likely to be exceeded but could be substantially
lower(6). It is impossible to know what, if any, incremental
effect on the cancer rate a carcinogen will have when the risk is
below the detection limit of animal and epidemiologic studies.
We make judgements about the validity of such estimates based on
existing scientific knowledge, but the validity cannot be
established by direct observation. We can only put bounds on what
the observed carcinogen effect would be even if the estimated
increase were correct because of the variable forces that affect
the background cancer rate and which are substantial in relation
to the low-dose carcinogen effects. However, there is an equal
likelihood that the response would be greater or smaller than
predicted, so that the estimated increment is most probable.

The proposed approach is best used in terms of total cancer
mortality. If specific types of cancer are used as an endpoint,
for example, lung cancer, the variability does not increase a
great deal, e.g., the fractional standard error increases from
1.8x10° to about 3.0 x 10%. However, the lifetime probability of
death from lung cancer is much lower than from cancer as a whole
and risk based standard would be correspondingly lower. It is an
advantage, therefore, to use the total cancer experience in the
country as a whole for several other reasons. The regulation of
carcinogens is a public health program aimed at the reduction of
the total burden of cancer. There is little preference in dying
of any one form of cancer. Basing the variability of the cancer
rate on national statistics is a conservative approach. The
larger the population, the smaller the variability. Another
conservative aspect of the proposed approach is that the entire
population of the country is assumed to be exposed to each
carcinogen. This compensates for the effect of multiple
carcinogen exposures, since many carcinogens expose limited
numbers of people.

The proposed approach has a number of advantages. 1- It uses the
weight of evidence for human carcinogenicity, which at present,
is ignored; e.g.,it does not seem appropriate to use the same
standard for known human carcinogens and for those which are
probable or possible human carcinogens. 2-The proposed approach
uses scientific judgement about the credibility of low dose
linearity, which is also presently ignored. The level of
credibility for low dose linearity varies with the type of
carcinogen; it is greater for high LET radiation than for low LET
ionizing radiation and higher for genotoxic chemical carcinogens
compared to those which are not. 3~ The approach avoids use of a
culturally based de minimis risk standard such as 10°, which has
a relatively flimsy ‘basis: 4- The approach does not tailor the
risk to the size of the exposed population because when a
standard is based on the induction of excess cancer cases, the
risk to the individual can be high when small numbers of people
are exposed. 5-In the case of chemical carcinogens that are
identified by animal bioassay, the use of total cancers avoids
the issue of where the cancers are likely to occur in humans.
A disadvantage of the proposal is the need for a delphic approach
to determining the level of credibility in the risk assessment.
But at least the credibility is based on scientific judgement
about the nature of the evidence that supports carcinogenicity
and low dose linearity. However, judgements depend on the status
of scientific knowledge about low- dose mechanisms of
carcinogenesis, and this is expected to increase with continuing
research. The judgements may, therefore, have to be modified in
time.

The use of the variability in the background of exposure to
ionizing radiation(14) and chemicals(15) as the basis for
formulating exposure standards that are small in relation to
background variability is not new. However, the approach used
here is different in that the background variability in cancer
rates determines the odds of a zero carcinogen effect.

There are various forms of uncertainty in risk assessments. For
example, there are uncertainties in the assessment of exposure or
the statistical uncertainties in the extrapolation of data from
the higher, observable dose range, to the low dose region. The
only uncertainties that are included in the proposed approach are
those that relate to the likelihood that the agent in question
will behave as a human carcinogen.

The approach to relating the credibility of the risk assessment
to the likelihood of a zero carcinogen effect on a proportional
basis is contrary to the legal mind-set where judgements are
dichotomous: agents are regulated either as carcinogens or as
non-carcinogens. There is little flexibility to the regulatory
process in this regard. The approach proposed here is consistent
with the scientific tradition of making judgements on the basis
of the weight of evidence.

APPENDIX

The Taylor series expansion is a generalized expression that
provides the value of a function (e.g., a normal distribution) at
points in the vicinity of the maximum, in terms of the distance
from the maximum and the value of the function at the maximun.
The Taylor series can be written as follows:

F(@) = F(@,) + (8-6,) F’(6,) + 1/2(6-6,)? F’’(®,)
+ 1/3!(@-@,)? F’’"’(@,)...
Where F(6) is the value of the function at 6; F’(6) is the

differential rate of change; F(®,) is the value of the function
at the maximum, and F’(8,) is zero.
Neglecting the cubic term and higher order terms and since (€-6€,)
F’(8,) is zero, we have

F(@) = F(®@,) + 1/2 (@-8,)? F’’ (@,)

Rearranging terms, we have

2 [F(®) - F(®,)] = (@-@,)? F’’(@,)

Let —1 = -W where W is equivalent to the variance of

Qo and thecefore W is equivalent to the standard deviation of @,.

Rearranging terms, we have

(2(F(8,)-F(@))]'? = 8-80
W

 

Let F(6,) = 1 and let F(@) = a as in Figure 1, we get
F(@,) b
STANDARD ERROR FRACTION (SEF) = 9-8, = [2(1-a) ]'?
W b

REFERENCES
1. Pesticide Chemical News, 1975,3, p.10.

2. Council for Agricultural Science and Technology, Report
No.54. The Environmental Protection Agency’s Nine
"Principles" of Carcinogenicity. January 19, 1976

3. The Lancet. Seventeen principles about cancer, or something.
1:571-573, March 13, 1976

4. Albert, R.E., R.E. Train and E. Anderson. Rationale
Developed by the Environmental Protection Agency for the
Assessment of Carcinogenic Risks. J. Natl. Cancer Inst.
58(5):1537-1541, (May, 1977).

5. United States Environmental Protection Agency. (U.S.EPA).
1976. Interim Procedures and guidelines for Health risk
and Economic Impact Assessments of suspected Carcinogens.
Federal Register 41:21402.

6. Anderson, E.L. and the Carcinogen Assessment Group of the
U.S. Environmental Protection Agency. Quantitative
Approaches in use to assess cancer risk. Risk Analysis
3:277, 1983

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10.

11.

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13.

14.

15.

Albert, R.E. U.S. Environmental Protection Agency Revised
Interim Guidelines for the Health Assessment of Suspect
Carcinogens. In: Banbury Report 19: Risk Quantitation and
Regulatory Policy, Cold Spring Harbor Laboratory, 1985, pp.
307-329.

National Research Council (NRC), 1983, Risk Assessment in
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S.M. Goodman and R. Royall "Evidence and Scientific
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A.W.F. Edwards, Likelihood _( Cambridge University Press, New
York, 1976)

R.E.Albert and R. Shukla, The Use of Statistical
Insignificance in the Formulation of Risk-Based Standards
for Carcinogens. In : Comparative Risk Assessment. Ed. E.
Richard Cothern. Lewis Publishers, Chelsea, Michigan. In
Press.

U.S. Cancer Mortality by County: 1950-1969. U.S. Dept. of
Health, Education, and Welfare. (PHS) T.J. Mason &
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Cancer Mortality in the United States: 1950-77. NCI
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Adler, H.I. and A.M. Weinberg, "An Approach to Setting
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Travis, Curtis C. and Samantha A. Richter. On Defining a
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11
Table 1. THE RELATIONSHIP BETWEEN THE LIKELIHOOD RATIO (ZERO EFFECT)
AND THE STANDARD ERROR FRACTION

Likelihood Ratio (Zero Effect) 0.99 0.95 0.90 0.75 0.50

Standard Error Fraction 0.14 0.32 0.46 0.71 1.00

12
FIGURE LEGENDS

Figure 1. Schematic of the Likelihood Ratio where a/b represents the likelihood of a zero
carcinogen effect.

Figure 2. The relationship between the credibility of the carcinogen risk assessment and
the likelihood of a zero incremental cancer risk

C:\ Risk

13
 

 

 

 

Vv

Likelihood Ratio = —

Figure 1. The Likelihood Ratio
 

    
    

More Protective ——

Likelihood
Of A Zero
Incremental
Cancer Risk

Less Protective

 

 

 

Credibility Of The
Risk Assessment
>

Figure 2.