United States
Environmental Protection
Agency
Office of Health and
Environmental Assessment
Washington DC 20460
Research and Development
EPA/600/S8-89/068 Feb. 1990
4>EPA Project Summary
Application of an Exact
NOAEL - Procedure for
Dichotomous Data from
Animal Experiments
A statistical method has been
developed that utilizes a step-wise
hypothesis testing procedure to esti-
mate the distribution of the no-
observed-adverse-effect level
(NOAEL), and thereby to estimate the
expected value of the NOAEL and its
variability. The methodology is
dependent upon the sum of the dose
group sizes, the expected response
rates, experimental dose levels, and
the type I error rates. The technique
may be employed to evaluate the
reliability of the NOAEL and to
provide a measure of its variability.
This Project Summary was devel-
oped by EPA's Environmental Criteria
and Assessment Office, Cincinnati,
OH, to announce key findings of the
research project that Is fully docu-
mented in a separate report of the
same title (see Project Report order-
ing information at back).
Introduction
In the risk assessment of systemic
toxicity, the no-observed-adverse-effect
level (NOAEL) is the highest experimental
dose level at which one does not reject
the hypothesis that the expected re-
sponse rate is the same as in the control
group. The NOAEL is then scaled
downward, usually by a factor of 10, 100
or 1000, to obtain the reference dose
(RfD). The RfD is an estimate (with
uncertainty spanning perhaps an order of
magnitude) of a daily exposure to the
human population (including sensitive
subgroups) that is likely to be without an
appreciable risk of deleterious effects
during a lifetime.
There is a need to estimate the vari-
ability of the NOAEL (and consequently
of the RfD) and to estimate the false
negative rate, which is indicative of
unacceptable increases in added risk
over a specified background rate. A
statistical method has been developed
that addresses these issues (Brown et al.,
1986). This project illustrates with real
data sets how this method can be used in
evaluating noncarcinogenic risks, and in
measuring uncertainties in the process.
The expected value of the NOAEL, its
variability, and the relationship between
Type I errors (false positive rates) and
type II errors (false negative rates), are all
interrelated and are dependent upon
sample sizes, the expected (but un-
known) response rates, dose values and
the statistical analysis employed.
Results and Conclusions
The statistical procedure is applicable
to experiments that produce dichotomous
response data (presence/absence of a
response of interest). The responses for
each dose group are assumed to be
independently distributed from binomial
distributions. For example, the response
rates for an experiment with control, low,
and high dose groups are represented by
the binomial population parameters po, PI
and p2, respectively. The approach util-
izes methods of isotonic inference to
incorporate a priori knowledge that PQ £
Pi < pa- (The inequalities could also be
reversed.) The long-term relative fre-
quency (probability) with which the
NOAEL would take each dose value in
repeated sampling is derived. From this
distribution an estimate of the expected
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value (long-term average) of the NOAEL
and its standard deviation are obtained.
The power for detecting a treatment
effect at any dose can be calculated for
any background rate and value of added
risk. This is particularly useful for deter-
mining the added risk that can be
detected with a specified power, and to
specify an upper limit of added risk that
is consistent with the data even when no
treatment effect has been detected.
Recommendations
The step-wise hypothesis procedure
produces conditional probabilities for the
second hypothesis test, which depend on
the results of the first hypothesis test.
Therefore, the testing of the second
hypothesis and the determination of its
corresponding type II error rate are
accomplished using only part of the
available data. Also, the entire procedure
is dependent on the choice of values for
the type I error rates. These observations
lead to the recommendation that an in-
depth analysis of this method be made.
It is apparent that the method will
require extensive amounts of computer
time when the dose group sizes are large
or when there are more than three to four
dose groups to analyze. The limits of this
procedure because of data processing^
requirements should also be investigated.^
References
Brown, K. G., L. M. LaVange, T. S.
Farrell, and S. C. Wheeles. 1986. An
Exact NOAEL—Procedure for Dichot-
omous (Incidence) Data, and Its Statis-
tical Properties. Research Triangle
Institute Report, RTI/3510,3516, Con-
tract No. 68-01-6826, Statistical Policy
Branch, U.S.EPA, 401 M Street, S.W.,
Washington, DC 20460.
This Pro/ect Summary was prepared by staff of the Environmental Criteria and
Assessment Office, Cincinnati, OH 45268.
Jeff Swartout is the EPA Project Officer (see below).
The complete report, entitled "Application of an Exact NOAEL—Procedure for
Dichotomous Data from Animal Experiments," (Order No. PB 90-145 780/AS;
Cost: $15.00, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
For information contact:
Environmental Criteria and Assessment Office
U.S. Environmental Protection Agency
Cincinnati, OH 45268
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
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