Use of Irwin's restricted mean as an index for comparing survival in different treatment groups--interpretation and power considerations.

In the analysis of survival data from clinical trials and other studies, the censoring generally precludes estimation of the mean survival time. To accommodate censoring, Irwin (1949) proposed, as an alternative, estimation of the mean lifetime restricted to a suitably chosen time T. In this article we consider the use of Irwin's restricted mean as an index for comparing survival in different groups, using as an example published data from a randomized clinical trial in patients with primary biliary cirrhosis. Irwin's method, originally based on the actuarial survival estimator, is extended to incorporate covariates into the analysis through the use of piecewise exponential models. For comparing two survival curves, the logrank test is known to be optimal under proportional hazards alternatives. However, comparison of restricted means may outperform the logrank test in situations involving nonproportional hazard rates. We examine the size and power of these two procedures under various proportional and nonproportional hazards alternatives, with and without covariate adjustment. For survival curves that separate early in time the censored data generalization of the Wilcoxon test is known to exhibit high power, and we examine how the comparison of restricted means performs relative to this procedure also.