Weighted Mean Survival Test Statistics: a Class of Distance Tests for Censored Survival Data

A class of test statistics is introduced which is sensitive against the alternative of stochastic ordering in the two-sample censored data problem. The test statistics for evaluating a cumulative weighted difference in survival distributions are developed while taking into account the imbalances in base-line covariates between two groups. This procedure can be used to test the null hypothesis of no treatment effect, especially when base-line hazards cross and prognostic covariates need to be adjusted. The statistics are semiparametric, not rank based, and can be written as integrated weighted differences in estimated survival functions, where these survival estimates are adjusted for covariate imbalances. The asymptotic distribution theory of the tests is developed, yielding test procedures that are shown to be consistent under a fixed alternative. The choice of weight function is discussed and relies on stability and interpretability considerations. An example taken from a clinical trial for acquired immune deficiency syndrome is presented.