Sample Size Determination and Information Fraction Based on the Weighted log-rank Test with the Fleming—Harrington Class of Weights and a Test of the Difference in Restricted Mean Survival Time

Abstract

Many clinical research studies evaluate a time-to-event outcome, illustrate survival functions and compare them between groups. Because actual relationships between survival curves are various, the use of conventional methods such as the log-rank test and a test of hazard ratio by Cox proportional hazards model are potentially underpowered compared with the planned power under the proportional hazards assumption, especially if a proportional hazards assumption is invalid. Therefore, when it is difficult to expect the proportional hazards assumption in the study planning phase, it is considered to use an alternative more efficient test method instead of the log-rank test or an alternative summary measure instead of the hazard ratio from statistical point of view. In this paper, we focus on the sample size determination and the information fraction, which are required for planning a study design and monitoring accrual progress, for each of the weighted log-rank test with Fleming– Harrington class of weights and a statistical significance test of the difference in the restricted mean survival time between groups as the summary measure of treatment effect. Also, they are illustrated by an application example.