A non-parametric approach for estimating the correlation between log-rank test statistics with applications to a conjunctive power calculation

TL;DR

This paper introduces a non-parametric method to estimate the correlation between log-rank test statistics for different endpoints, aiding in clinical trial design by providing realistic power calculations based on subject-level data.

Contribution

The paper presents a novel iid decomposition-based approach for correlation estimation that is assumption-lean and applicable to any alternative hypothesis.

Findings

Method provides unbiased, consistent correlation estimates in finite samples.

Simulation confirms robustness under various censoring scenarios.

Application demonstrates improved power calculation for clinical trial planning.

Abstract

We present a method for estimating the correlation between log-rank test statistics evaluating separate null hypotheses for two time-to-event endpoints. The correlation is estimated using subject-level data by a non-parametric approach based on the independent and identically distributed (iid) decomposition of the log-rank test statistic under any alternative. Using the iid decomposition, we are able to make an assumption-lean estimation of the correlation. A motivating example using the developed approach is provided. Here, we illustrate how the suggested approach can be used to give a realistic quantification of expected conjunctive power that can guide the design of a new randomized clinical trial using historical data. Finally, we investigate the method's finite sample properties via a simulation study that confirms unbiased and consistent behavior of the proposed approach. In addition, the simulation study gives insight into the effects of censoring on the correlation between the log-rank test statistics.