Stratified Logrank Test of No Randomized Treatment Effect with Missing Stratum Information
A major objective in many clinical trials is to compare several competing treatments in a randomized experiment. In such studies, it is often necessary to adjust for some other important factor that affects the event rates in the treatment groups. When this factor is discrete, one usual approach uses a stratified version of the logrank test. In this article, we consider the problem that arises when the factor giving rise to the strata is missing at random for some of the study subjects. This article proposes a modified version of the stratified logrank test, in which the unobserved stratum indicators are replaced by an estimate of their conditional expectation given available auxiliary covariate measurements. The null asymptotic distribution of the proposed test statistic is investigated. Simulation experiments are also conducted to examine the finite-sample behavior of this test under both null and alternative hypotheses. Simulations indicate that the proposed test performs well, even under some moderate deviations to the at-random missingness assumption.