Estimating Covariate-Adjusted Log Hazard Ratios for Multiple Time Intervals in Clinical Trials Using Nonparametric Randomization Based ANCOVA

Abstract

The hazard ratio is a useful tool in randomized clinical trials for comparing time-to-event outcomes for two groups. Although better power is often achieved for assessments of the hazard ratio via model-based methods that adjust for baseline covariates, such methods make relatively strong assumptions, which can be problematic in regulatory settings that require prespecified analysis plans. This article introduces a nonparametric method for producing covariate-adjusted estimates of the log weighted average hazard ratio for nonoverlapping time intervals under minimal assumptions. The proposed methodology initially captures the means of baseline covariables for each group and the means of indicators for risk and survival for each interval and group. These quantities are used to produce estimates of interval-specific log weighted average hazard ratios and the difference in means for baseline covariables between two groups, with a corresponding covariance matrix. Randomization-based analysis of covariance is applied to produce covariate-adjusted estimates for the interval-specific log hazard ratios through forcing the difference in means for baseline covariables to zero, and there is variance reduction for these adjusted estimates when the time to event has strong correlations with the covariates. The method is illustrated on data from a clinical trial of a noncurable neurologic disorder.