Estimation of "safe doses" in carcinogenic experiments

The statistical methodology for carcinogenic safety testing here developed has the following advantages: (1) Rather than making possibly unwarranted assumptions about a minimum slope in a dose response relationship, the present method represents an objective data based method of estimating "safe" doses. It is applicable to any specified permissible risk (of exceeding the spontaneous rate) and the latter must of course be specified by F.D.A. (2) Although the model which is used for the estimation of safe doses and their lower confidence points is parametric it comprises an adequately large number of parameters to allow for differences in the idiosyncracies of suspected carcinogens, host species and to a limited degree for variations in the experimental protocols. (3) The same computer program will cover the analysis of an experiments in which times to tumor have been recorded as well as experiments in which only tumor incidence rates have been recorded or mixtures of the two. "Better experimentation" is "rewarded" in that the lower confidence limits for the "safe doses" should be higher and more closely approach the true safe dose as the experimental effort increases. (4) The maximum likelihood estimation procedure is sophisticated and has asymptotic optimality properties. It utilizes the latest techniques of "convex programming" and the computer algorithm is straightforward and fast. The methodology proposed here also has the following shortcomings: (1) The model is (multi)parametric. However, it is of the form of the product model for age specific hazard rates which is now widely accepted. (2) Robustness studies on the effect of model breakdown on the estimated safe doses are as yet limited and should be followed up with more extensive studies. (3) Obviously no estimates of "safe doses" can be made if the spontaneous incidence rate is zero and the experimental dose levels have been chosen too small and no tumors have been observed. Similarly if the experimental doses are too small and the tumor incidence rates are all comparable with the spontaneous rate the estimation procedure is afflicted by extremely large errors. The situation improves slightly if the incidence for the highest dose level is higher than that of the lower dose levels which are all approximately equal. In such situations more satisfactory experimental data are needed. Some general recommendations are as follows: (1) Whenever possible it is preferable to record times to tumor and not just incidence rates. However, for experiments of sufficiently long duration necropsies following the varying times of death will provide adequate information on the time dependence of tumor incidence. It may also be advisable to deliberately vary the times of sacrifice to two or three different times. (2) Other considerations being equal it is preferable to have a large number of dose levels rather than more animals per dose level...