Since the purpose of the report is to recommend guidelines and priorities for selecting chemicals for human use without direct experimental toxicological evaluation, the lack of consideration of irreversible long-term toxic effects (which would not be ruled out by the suggested criteria) makes the suggested approach practically inapplicable and potentially dangerous.

APPENDIX III—A METHOD FOR DETERMINING THE DOSE COMPATIBLE WITH SOME "ACCEPTABLE" LEVEL OF RISK

(Contributed by Dr. M. A. Schneiderman)

INTRODUCTION

In establishing the concept of an "acceptable" risk dose (ARD) we must bear in mind that the dose level arrived at gives a tolerable risk only for the species for which the extrapolation has been made. Given this caveat, to make a conservative' estimate of an ARD, two assumptions need to be made:

A. The dose-responsive curve at low response levels is concave upward (e.g. the left-hand tail of the common S-shaped curve). The upper (dose) limit of this S-shaped curve is a straight line going through the 0,0 point (no dose= no response). The true dose-response curve is shallowest at this point.

B. A given set of data will provide an estimate for the upper limit of the other point through which the straight line must pass (which then gives the upper limit of the slope of the dose-response curve).

As an example of the use of the ARD concept, let us suppose that we have observed 100 control animals and 100 treated animals at a given dose rate, d, and have seen no tumors in either group. The upper 95% confidence limit on such a result is 3/100 (i.e. the data are consistent with the statement that with a true response rate of .03, we might expect to see zero tumor incidence in 95% of similar experiments). If the socially "acceptable" risk selected is to be one additional cancer case for each hundred thousand persons, it is now desired to establish an ARD which will produce a maximum lifetime tumor incidence of 1/100,000. We can then construct the graph:

The procedure outlined here is essentially the "one-hit" procedure and gives a somewhat more conservative answer than the procedure of Mantel and Bryan (4).

The line connecting the (0,0) point with the (d, .03) point has

and the equation of the line is:

Slope=.03/d

Response= (Dose) (.03/d)

If we wish to determine some dose (e.g. the ARD) which would be predicted to yield a response of not more than 1.10-5 we would write :

Dose (1.10-5) (d/.03)=3.3·10-'d)

ARD

Working towards an ARD this way has several consequences:

a. An increase in the experimental size (at the same dose, d, and with the same experimental result, i.e. no tumors) will reduce the upper confidence limit. Thus, if there were 200 animals in each contrast group, the upper 95% confidence limit would be about halved and the estimated ARD would be doubled.

b. An increase in the dose, d, at which the result (no tumors) occurred would increase the estimated ARD in direct proportion to the tested dose. Thus, if the initial experiment had been conducted at twice as high a dose with the same result, the estimated ARD would be twice as high as that determined from this experiment.

The procedure outlined has the virtue of lending greater credence to conclusions reached on the basis of larger experiments. Higher estimated ARD's will be found under such circumstances and the confusion between "hot statistically significantly different", and "not different" can be avoided.

It must be stressed that these calculations do not establish an "acceptable risk dose" for man. The procedures do not tell us for example what factors are required to extrapolate from animal to man, although the following factors must certainly be considered.

1. Dose-response curves in man (a grossly non-homogeneous animal) are likely to be much shallower than dose-response curves in experimental animals. This implies higher levels of response at low doses for man, other things being equal.

2. It is possible that even the use of the straight line between the 0,0 point and some experimentally determined dose-response point (plus upper confidence limit) may yield too high an estimated ARD for man.

3. Whether the proper blow-up factor for doses in man should be on a mg/kg. or mg/M2 basis, or any other basis, must be established independently.

4. Nothing in this procedure would enable one to know where the doseresponse curve for man belongs along the dose scale in comparison with the dose-response curve for the experimental animal. If man's curve lies much to the left of the experimental animal's curve, then an ARD for the experimental animal may be a gross overdose for man.

Where several species are studied, it would seem safest in the absence of better information, to accept for man an ARD no greater than the lowest ARD dose derived from the results for the several species. It has been suggested that an appropriate "safety factor" for man should involve a reduction in the ARD for animals by a factor of 100 to allow for species' differences, another factor of 100 to allow for interactions with other carcinogens, and another factor of 100 to hedge against the incorrect choice of "blow up" (weight, or surface area) from animals to man. This would imply an ARD in man of about 1 X 10-" the ARD in animals.

INSTRUCTIONS FOR CALCULATION OF THE ARD USING 95% AND CONFIDENCE LIMITS
(Experiment in which no animals in either treated or control group show a
response, e.g. development of a tumor): We need the following values:

C=Upper confidence limit on the result (computed as shown below).
S-Arbitrary "acceptable" response level.

d=Acceptable risk dose (ARD), that which causes no more than the arbitrarily allowed acceptable risk.

td Test dose, some multiple, t, of the tolerated dose. These values are related as shown:

S

d

td

(td, C)

From the above figure, we have the following relationships: C/S=(t'd)/d=t which can also be stated as C=St.

Since C is a function of the size of the experiment, N, we have a relationship between S, t, and N where N=sample size.

For zero positive responses, the upper a% confidence limit is St-C-1-e[1n (1-a)]/N, where in is the natural logarithm. From this rela. tionship, given any two of the values N, t, and S, we can solve for the third. The accompanying graphs have this relationship shown for difference values of N. Figure A1 s for a 95% confidence limit: Figure A2 is for a 99% confidence limit.

In any specific situation St is constant (=C), so that we can increase the range of the chart by dividing S (the tolerable risk level) by k while multiplying t (the dose multiplier) by k. Two sets of values for S and t are shown on each graph.

1. Given:

EXAMPLES OF HOW TO USE GRAPHS

a. That we agree to a socially "acceptable" risk level, say .00001 (1 in 100,000). b. The expected average dose in man is D, and we wish to determine whether it is compatible with the acceptable risk.

c. The maximum pharmacologically tolerated dose in our test species is tD, where, say, t=600, (i.e. this species can survive a dose 600 times larger than the average dose in man).

Procedure (Using "95%" figure)

a. Find t=600 along the bottom scale of the graph. Notice that it is in parenthesis. This means we must look for our S value in parenthesis, too. (Small arrow at bottom of graph.)

b. Find S=10(X10°). (Small arrow at side of graph.)

c. Find where the t=600 vertical line crosses the S=.00001 horizontal line. This is at the diagonal line labeled 500.

This means we must conduct an experiment with 500 animals in each group, yielding 0 positives, at a dose level 600 times the "average" dose in man, in order to have some assurance that the average dose in man is within the acceptable risk level, where acceptable risk is .00001. [This dose may be far too high, for it has been assumed that man's dose-response curve is the same (except for slope) as

the animal species in which we did the experiment. No "safety" factors have been applied.]

2. Given

To repeat the above experiment using a dose 300 X the expected ARD. S=.00001, and t=300.

Note the crossing point at diagonal N=1000.

This means if we test at a lower dose, we must have more test animals to achieve the same ARD.

3. Given

To repeat experiment 1 using only 100 animals. N=100; S=10(X10-")
Procedure

Follow along the horizontal line until you come to diagonal N=100
Look down to the t scale and note that we are at t=3000.

This means if we test with fewer animals, we can have assurance only that a dose 1/t times the test dose will yield less than the acceptable level. Fewer animals in a test imply a lower ARD. In this case the ARD is 1/3000 the test does as compared with 1/600 in Example 1.

APPENDIX IV-RELATIONSHIP BETWEEN CHEMICAL ANALYSIS,
BIOLOGICAL ASSAYS AND CARCINOGENIC RISKS TO MAN

The following set of Figures presents a conceptual scheme for dealing with the problems stated. In practice any or all of the steps may be rendered impossible by limitations in quantifying pertinent variables. Operational problems in implementing the plan result from uncertainties in the correspondence of human and animal dose response curves, extrapolation of animal data to extremely low response levels, differences in response from species to species, synergistic effects, etc. The scheme itself may be useful, however, in defining the specific areas in which further efforts should be made.

PROBLEM No. 1: GIVEN THE PRESENCE OF A CHEMICAL IN THE ENVIRONMENT, ESTIMATE ITS CARCINOGENIC HAZARD FOR MAN AND DETERMINE ITS COMPATI BILITY WITH A SOCIALLY "ACCEPTABLE" RISK

The inputs and the estimations required for this problem are represented in Figure 1 and discussed in the following paragraphs.

1. Analytical Detectability in the Environment-Limited by the sensitivity and specificity of the available analytical method.

2. Quantitative Distribution in Time and Space in the Environment-Preparation of "environmental profiles" limited chiefly by extent of sampling. Segments of the environment should not be considered non-contributory, because they fall below the minimum levels for analytical detection.