Omnibus test for restricted mean survival time based on influence function

The restricted mean survival time (RMST), which evaluates the expected survival time up to a pre-specified time point t , has been widely used to summarize the survival distribution due to its robustness and straightforward interpretation. In comparative studies with time-to-event data, the RMST-based test has been utilized as an alternative to the classic log-rank test because the power of the log-rank test deteriorates when the proportional hazards assumption is violated. To overcome the challenge of selecting an appropriate time point t , we develop an RMST-based omnibus Wald test to detect the survival difference between two groups throughout the study follow-up period. Treating a vector of RMSTs at multiple quantile-based time points as a statistical functional, we construct a Wald ?(2) test statistic and derive its asymptotic distribution using the influence function. We further propose a new procedure based on the influence function to estimate the asymptotic covariance matrix in contrast to the usual bootstrap method. Simulations under different scenarios validate the size of our RMST-based omnibus test and demonstrate its advantage over the existing tests in power, especially when the true survival functions cross within the study follow-up period. For illustration, the proposed test is applied to two real datasets, which demonstrate its power and applicability in various situations.

Automated summary

The restricted mean survival time (RMST) is widely used to summarize survival distribution due to its robustness and interpretation. In comparative studies, the RMST-based test is used as an alternative to the log-rank test. We developed an RMST-based omnibus Wald test to detect survival differences between two groups throughout the study follow-up period, considering multiple quantile-based time points.