Analysis of factorial survival experiments

Several new methodological issues that arise within two-way factorial designs for survival experiments are discussed within the framework of asymptotic theory for the proportional hazards model with two binary treatment covariates. These issues include: the proper formulation of null hypotheses and alternatives, the choice among log-rank and adjusted or stratified log-rank statistics, the asymptotic correlation between test statistics for the separate main effects, the asymptotic power (under the various possible methods of analysis) of tests to detect main effects and interactions, the comparison of power to detect main effects within a 2 x 2 factorial design with power in a three-group trial where no patients are randomized simultaneously to both treatments, and the problems of analysis arising when accrual or exposure to one of the treatments is terminated early for ethical reasons.