Hazard ratio inference in stratified clinical trials with time-to-event endpoints and limited sample size

The stratified Cox model is commonly used for stratified clinical trials with time-to-event endpoints. The estimated log hazard ratio is approximately a weighted average of corresponding stratum-specific Cox model estimates using inverse-variance weights; the latter are optimal only under the (often implausible) assumption of a constant hazard ratio across strata. Focusing on trials with limited sample sizes (50-200 subjects per treatment), we propose an alternative approach in which stratum-specific estimates are obtained using a refined generalized logrank (RGLR) approach and then combined using either sample size or minimum risk weights for overall inference. Our proposal extends the work of Mehrotra et al, to incorporate the RGLR statistic, which outperforms the Cox model in the setting of proportional hazards and small samples. This work also entails development of a remarkably accurate plug-in formula for the variance of RGLR-based estimated log hazard ratios. We demonstrate using simulations that our proposed two-step RGLR analysis delivers notably better results through smaller estimation bias and mean squared error and larger power than the stratified Cox model analysis when there is a treatment-by-stratum interaction, with similar performance when there is no interaction. Additionally, our method controls the type I error rate while the stratified Cox model does not in small samples. We illustrate our method using data from a clinical trial comparing two treatments for colon cancer.