Treatment–covariate interaction is often used in clinical trials to assess the homogeneity of treatment effects over these subgroups defined by a baseline covariate, which is frequently conducted after primary analysis including all patients is completed. When the endpoint is the time to an event, as in the cancer clinical trials, the Cox proportional hazard model with an interaction term has been used exclusively to test the significance of treatment-covariate interaction in oncology literature. But the proportional hazards assumption may not be satisfied by the data from clinical trials. Although there are several procedures proposed in statistical literature to assess the interaction based on a nonparametric measure of interaction or nonparametric models, some of these procedures do not take into the account of the nature of the data well, while some are very complicated which may have limited their applications in practice. In this thesis, a non-parametric procedure based on the smoothed estimate of Patel–Hoel measure is first derived to test the interaction between the treatment and a binary covariate with censored data. The theoretical distribution of the test statistic of the proposed procedure is derived. The proposed procedure is also evaluated through Monte-Carlo simulations and applications to data from a cancer clinical trial. Jackknifed versions of two test statistics based on nonparametric models are then derived by simplifying these test statistics and applying the jackknife method to estimate their variances. These jackknifed tests are also compared with the smoothed test and other related tests. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2011-09-27 11:09:28.449