Detection of associations between diseases in animal carcinogenicity experiments

We present a statistical test for the hypothesis of independence of two disease processes in animal carcinogenicity experiments. It is assumed that the diseases are occult (detectable only at death via necropsy), and progressive, in that each passes (potentially) through three states in each animal: absent, nonlethally present, and lethally present. The test is based on the combination of statistics from a series of age-stratified 3 x 3 tables in which the animals that die in each age interval are cross-classified into one of these three states for each disease. This test utilizes all the data, whether obtained by sacrifice or by "natural death." It avoids the biases due to lethality noted by Breslow et al. (1974, Journal of the National Cancer Institute 52, 233-239) for the test based on age-stratified 2 x 2 tables, where the nonlethal and lethal occurrences are pooled. In a simulation experiment, we show that such biases (which usually conceal true positive associations and produce spurious negative associations) can be very severe indeed, whereas our test preserves the nominal significance level quite well. The power of the test appears to vary widely, depending on the incidence, time to onset, and rate of progression of each disease. As an example of the application of our method, we assess the association between liver tumors and reticulum cell sarcoma in a radiocarcinogenesis experiment involving approximately 1,000 C3H female mice.