Monte Carlo Results for the 3-Poly Test for Animal Carcinogenicity Experiments

Abstract

(4)]. Because the two-stage model and its extensions are complex enough to involve stochastic proliferation and differentiation of initiated cells and yet simple enough to be applicable to many data sets, this model has been suggested as the basic model for assessing risk of environmental agents (6).We will briefly describe the model and how Monte Carlo data can be generated; we will then apply the 3-poly methods to the data. To assess the efficiency and robustness of the test, we will compute the Monte Carlo size and the power of the test. Finally, we will discuss the results and some of the issues relevant to the method. The Model and Generation of Monte Carlo DataTo generate Monte Carlo studies, animal carcinogenicity experiments were carried out in which healthy animals were exposed to different dose levels of the carcinogen at to-0 and are followed up until time tM = tk.In the group of animals exposed to the carcinogen with dose level z, let a,(jlz) and a2(jIlz) denote the numbers of animals which died at time j without and with cancerous tumors, respectively; similarly, in the group of animals exposed to the carcinogen with dose level z, let b1(z) and b2(z) be the numbers of terminal sacrifices without and with cancerous tumors, respectively.To generate Monte Carlo data from such an experiment, we assign D as the random variable for the time to death, Tas the random variable for the time to the onset of cancer tumors, and Z as the variable for the dose level. Given Z=z, let o0(tjz), O(tls,z), (t > s), and ko(tlz) be the incidence func- For j < t < j+1, the survival functions associated with cx0(tl z), P,0(tl s,z), and ko(tl z) are given respectively by Bo(tli)for j >i, andwhere a (i) = J1 a. (xlz)dx, f3z(jls) = j0 t(xs x for j-12 s, and AZW = .f17lo(xIzkPc Assume that 300(tls,z) = 00(tli,z) for i-l < s < i and that during one time unit, the event of death and the event of developing cancerous tumors are independent of each other. Then Pz(tIs) = Pz(t Ii) for i-I < s < i < t, and the probabilities for generating