Simultaneous inference on treatment effects in survival studies with factorial designs

A clinical trial with a 2×2 factorial design involves randomization of subjects to treatment A or A‾ and, within each group, further randomization to treatment B or B‾. Under this design, one can assess the effects of treatments A and B on a clinical endpoint using all patients. One may additionally compare treatment A, treatment B, or combination therapy AB to A‾B‾. With multiple comparisons, however, it may be desirable to control the overall type I error, especially for regulatory purposes. Because the subjects overlap in the comparisons, the test statistics are generally correlated. By accounting for the correlations, one can achieve higher statistical power compared to the conventional Bonferroni correction. Herein, we derive the correlation between any two (stratified or unstratified) log‐rank statistics for a 2×2 factorial design with a survival time endpoint, such that the overall type I error for multiple treatment comparisons can be properly controlled. In addition, we allow for adjustment of prognostic factors in the treatment comparisons and conduct simultaneous inference on the effect sizes. We use simulation studies to show that the proposed methods perform well in realistic situations. We then provide an application to a recently completed randomized controlled clinical trial on alcohol dependence. Finally, we discuss extensions of our approach to other factorial designs and multiple endpoints.