# On Window Mean Survival Time With Interval‐Censored Data

## TL;DR

This paper introduces a new method for analyzing survival data in cancer trials, especially when survival curves cross or show late differences, using window mean survival time with interval-censored data.

## Contribution

The paper proposes a novel WMST inference method for interval-censored data using one-point imputations and Turnbull's method.

## Key findings

- The proposed WMST method using mid-point imputation performs comparably to Turnbull's method for interval-censored data.
- WMST testing has higher power than RMST in late difference and early crossing survival scenarios.
- WMST maintains higher power than RMST even when the pre-specified time point is not clinically optimal.

## Abstract

In recent years, cancer clinical trials have increasingly encountered non proportional hazards (NPH) scenarios, particularly with the emergence of immunotherapy. In randomized controlled trials comparing immunotherapy with conventional chemotherapy or placebo, late difference and early crossing survival curves scenarios are commonly observed. In such cases, window mean survival time (WMST), the area under the survival curve within a pre‐specified interval τ0,τ1, has gained increasing attention due to its superior power compared to restricted mean survival time (RMST), the area under the survival curve up to a pre‐specified time point. Considering the increasing use of progression‐free survival as a co‐primary endpoint alongside overall survival, there is a critical need to establish a WMST estimation method for interval‐censored data; however, sufficient research has yet to be conducted. To bridge this gap, this study proposes a WMST inference method utilizing one‐point imputations and Turnbull's method. Extensive numerical simulations demonstrate that the WMST estimation method using mid‐point imputation for interval‐censored data exhibits comparable performance to that using Turnbull's method. Since the former facilitates standard error calculation, we adopt it as the standard method. Numerical simulations on two‐sample tests confirm that the proposed WMST testing method have higher power than RMST in late difference and early crossing survival curves scenarios, while having compatible power to the log‐rank test under the PH. Furthermore, even when pre‐specified τ0 deviated from the clinically desirable time point, WMST consistently maintains higher power than RMST in late difference and early crossing survival curves scenarios.