Estimation of the relative risk following group sequential procedure based upon the weighted log-rank statistic

TL;DR

This paper develops a method to estimate the relative risk in group sequential survival trials using a weighted log-rank statistic, providing a way to derive p-values, confidence intervals, and bias correction.

Contribution

It introduces a bijection between the weighted log-rank statistic and a weighted average logged relative risk, enabling consistent estimation during interim analyses.

Findings

Bijection between WLR statistic and relative risk established

Method for deriving design-adjusted p-values and confidence intervals

Application to the NLST trial interim analysis

Abstract

In this paper we consider a group sequentially monitored trial on a survival endpoint, monitored using a weighted log-rank (WLR) statistic with deterministic weight function. We introduce a summary statistic in the form of a weighted average logged relative risk and show that if there is no sign change in the instantaneous logged relative risk, there always exists a bijection between the WLR statistic and the weighted average logged relative risk. We show that this bijection can be consistently estimated at each analysis under a suitable shape assumption, for which we have listed two possibilities. We indicate how to derive a design-adjusted p-value and confidence interval and suggest how to apply the bias-correction method. Finally, we document several decisions made in the design of the NLST interim analysis plan and in reporting its results on the primary endpoint.