Finite-sample correction for the covariate-adjusted log-rank test

2026-08-11

AI Summary

In small-sample settings, covariate-adjusted log-rank tests are prone to inflated Type I error rates due to treatment allocation imbalance or a relatively large number of covariates. To address this issue, this work proposes a finite-sample correction method that explicitly accounts for the loss of residual degrees of freedom and the uncertainty in regression coefficient estimation by adjusting the denominator of the test statistic. This approach introduces, for the first time in covariate-adjusted log-rank testing, a correction mechanism that jointly incorporates both degrees-of-freedom reduction and parameter estimation uncertainty. Monte Carlo simulations demonstrate that the proposed correction substantially reduces Type I error rates across a range of scenarios, thereby enhancing the reliability of hypothesis testing in small samples.

Abstract

The covariate-adjusted log-rank test is a novel method for covariate adjustment in randomized trials with time-to-event endpoints, offering guaranteed efficiency gains compared to the standard log-rank test. However, it has been noted that, in small samples, this method may lead to type I error rate inflation. This issue is particularly pronounced in trials with imbalanced allocation and settings where the number of adjustment covariates is large relative to the sample size. We propose a finite-sample correction for the denominator of the covariate-adjusted log-rank test statistic that accounts for the loss of the residual degrees of freedom as well as the uncertainty in the unknown regression coefficients. In simulations, we show that applying this correction leads to a substantial reduction in the type I error rate inflation across multiple scenarios.

Problem

• covariate-adjusted log-rank test
• type I error inflation
• small samples
• imbalanced allocation
• high-dimensional covariates

Innovation

• finite-sample correction
• covariate-adjusted log-rank test
• type I error control
• residual degrees of freedom
• randomized trials