Exact statistical tests for any carcinogenic effect in animal bioassays

Standard statistical treatment of data from carcinogenicity bioassays generally involves separate analyses of data from many tumor responses in each sex in two species. There are two serious difficulties with this approach: the excessive probability of one or more false positive findings due to the large number of individual tests applied and the lack of mutual support among the separate tests (e.g., results that are close to significant from several organs should be allowed to reinforce each other, but such mutual support does not formally occur in statistical tests currently employed). In this paper we propose a class of tests that deals with both of these difficulties. The test statistics proposed are functions of p values from multiple conventional tests. The significance levels are computed by a Monte Carlo randomization procedure that treats individual animals (rather than tumor-specific response scores) as units of variation, so that the assumption of independence of tumors at different sites is not required. A single overall test statistic is derived from results from all individual tumor sites; thus there is proper control for the false positive rate. Mutual support from results from different tumor sites can be obtained by using a test statistic such as the product of the K smallest p values from conventional tests. Suggestions are made regarding specific tests that could be applied routinely to carcinogenesis bioassay data. The usefulness of the proposed tests is demonstrated by applying them to data from a National Toxicology Program bioassay of decabromodiphenyl oxide.