An age‐adjusted bootstrap‐based Poly‐k test

Abstract

The assumption of an asymptotic normal distribution of some test statistics may be invalid in certain dose-response trend tests. For instance, the survival-adjusted Cochran-Armitage test, known as the Poly-k test, is asymptotically standard normal under the null hypothesis. However, the asymptotic normality is not valid if there is a deviation from the tumour onset distribution that is assumed in this test or if the competing risks survival rates differ across groups. We develop an age-adjusted bootstrap-based method to assess the significance of assumed asymptotic normal tests for animal carcinogenicity data. The proposed method differs from conventional bootstrap methods in the aspect of preserving the mortality rate in each dose group under the null hypothesis of equal tumour incidence rates among the groups. We investigate an empirical distribution of the Poly-3 (P3) trend test statistic using the proposed age-adjusted bootstrap-based method and compare it with the P3 test statistic referenced to the assumed standard normal distribution. A simulation study is conducted to evaluate the robustness of these tests to various Weibull-family tumour onset distributions. The proposed method is applied to National Toxicology Program data sets to evaluate a dose-related trend of a test substance on the incidence of neoplasms.