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

2026-01-06

AI Summary

This study addresses the challenge of accurately estimating the correlation between log-rank statistics for two time-to-event endpoints in clinical trial power calculations, a task often hindered by restrictive assumptions about underlying distributions or covariance structures. The authors propose a nonparametric approach based on an independent and identically distributed (iid) decomposition that robustly estimates this correlation using only individual participant data, without relying on conventional modeling assumptions. The method is shown to be unbiased and consistent in finite samples, and extensive Monte Carlo simulations demonstrate its stability across various censoring scenarios. Applied successfully to historical data for quantifying joint power, this approach offers a flexible and reliable statistical tool for designing trials with complex, multiple time-to-event endpoints.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationConstraint Satisfaction and Optimization: Distributed CSP/OptimizationReasoning under Uncertainty: Relational Probabilistic Models

Application Category

User Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSecurity and Privacy: Large-scale security measurements

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.

Problem

• log-rank test
• correlation estimation
• time-to-event endpoints
• conjunctive power
• non-parametric

Innovation

• non-parametric
• log-rank test
• iid decomposition
• conjunctive power
• correlation estimation