Versatile tests for window mean survival time

Window mean survival time (WMST) evaluates the mean survival between a lower time horizon, tau 0$$ {\tau}_0 $$, and an upper time horizon, tau 1$$ {\tau}_1 $$. As a flexible extension of restricted mean survival time, specific clinically relevant windows of time can be assessed for survival difference accompanied by a communicable interpretation of estimates and tests. In its original application, WMST required the pre-specification of a window through the selection of appropriate window bounds, tau 0$$ {\tau}_0 $$ and tau 1$$ {\tau}_1 $$. In the instance of severe window misspecification of tau 0$$ {\tau}_0 $$ and tau 1$$ {\tau}_1 $$, the analysis may suffer from low power and a less meaningful interpretation. In this article, we introduce versatile tests whose procedures are based on the simultaneous use of multiple WMST test statistics that are asymptotically normal under the null hypothesis of no difference between two groups. Simulations are performed to examine the power of the tests in moderate sample sizes when the data are uncensored to heavily censored with a ramp-up enrollment period. The survival scenarios chosen for simulation are intended to imitate those which are commonly encountered in oncology, especially in trials involving immunotherapies. Implementation of the procedures is discussed in two real data examples for illustration. Functions for performing versatile WMST tests are provided in the survWMST package in R.