Sensitivity Analysis for Restricted Mean Survival Time When Survival Curves Have Divergent Tails

Abstract

New immunotherapy methods are being developed to provide cancer patients with survival benefit. The tail effect of immuno-oncology (IO) therapy resulting in diverse tails of survival curves between treatment arms may provide important information for physicians to guide treatment decisions in clinical practice. The hazard ratio (HR) and the log-rank test may not be suitable for quantifying and interpreting the between-group difference in IO clinical trials because the underlying assumption that the HR is constant over time is not valid. As an alternative summary measure, the restricted mean survival time (RMST) has been attracting more attention for comparing survival curves. The RMST is defined as the mean survival time to a specific threshold timepoint τ and is calculated as the area under the curve within a specific time window from 0 to τ. Although physicians may wish to compare the RMST up to the end timepoint of a longer curve to elucidate the tail effect of the IO treatment, with the currently available statistical methods, τ is required to be set at the end timepoint of a shorter curve or before. To address this issue, we propose a sensitivity analysis approach to evaluating the between-group difference in the RMST at any timepoint that clinical investigators consider clinically relevant, thus being free from such a statistical constraint. Notably, this analysis can only provide complementary results; thus, it cannot function as the primary analysis.

Keywords: Immunotherapy; Randomized clinical trial; Restricted mean survival time; Sensitivity analysis; Tail effect; Time-to-event outcome.