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.

Xu R ，Mehrotra DV ，Shaw PA 《-》

An efficient alternative to the stratified Cox model analysis.

Consider a typical two-treatment randomized clinical trial involving a time-to-event endpoint, with randomization stratified by a categorical prognostic factor (for example gender). At the design stage, it is often assumed that the treatment hazard ratio (HR) is constant across the strata, and the data are commonly analyzed using the stratified Cox proportional hazards model. We caution that this ubiquitous approach is needlessly risky because departures from the assumption of the HR being the same for all the strata can result in a notably biased and/or less powerful analysis. An alternative approach is proposed in which first the [log] HR is estimated separately for each stratum using an unstratified Cox model, and then the stratum-specific estimates are combined for overall inference using either sample size or 'minimum risk' stratum weights. The advantages of the proposed two-step analysis versus the common one-step stratified Cox model analysis are illustrated using simulations that were conducted to support the design of a vaccine clinical trial.

Mehrotra DV ，Su SC ，Li X 《-》

The stratified win ratio.

Dong G ，Qiu J ，Wang D ，Vandemeulebroecke M ... -  《-》

The Average Hazard Ratio - A Good Effect Measure for Time-to-event Endpoints when the Proportional Hazard Assumption is Violated?

In many clinical trial applications, the endpoint of interest corresponds to a time-to-event endpoint. In this case, group differences are usually expressed by the hazard ratio. Group differences are commonly assessed by the logrank test, which is optimal under the proportional hazard assumption. However, there are many situations in which this assumption is violated. Especially in applications were a full population and several subgroups or a composite time-to-first-event endpoint and several components are considered, the proportional hazard assumption usually does not simultaneously hold true for all test problems under investigation. As an alternative effect measure, Kalbfleisch and Prentice proposed the so-called 'average hazard ratio'. The average hazard ratio is based on a flexible weighting function to modify the influence of time and has a meaningful interpretation even in the case of non-proportional hazards. Despite this favorable property, it is hardly ever used in practice, whereas the standard hazard ratio is commonly reported in clinical trials regardless of whether the proportional hazard assumption holds true or not. There exist two main approaches to construct corresponding estimators and tests for the average hazard ratio where the first relies on weighted Cox regression and the second on a simple plug-in estimator. The aim of this work is to give a systematic comparison of these two approaches and the standard logrank test for different time-toevent settings with proportional and nonproportional hazards and to illustrate the pros and cons in application. We conduct a systematic comparative study based on Monte-Carlo simulations and by a real clinical trial example. Our results suggest that the properties of the average hazard ratio depend on the underlying weighting function. The two approaches to construct estimators and related tests show very similar performance for adequately chosen weights. In general, the average hazard ratio defines a more valid effect measure than the standard hazard ratio under non-proportional hazards and the corresponding tests provide a power advantage over the common logrank test. As non-proportional hazards are often met in clinical practice and the average hazard ratio tests often outperform the common logrank test, this approach should be used more routinely in applications.

Rauch G ，Brannath W ，Brückner M ，Kieser M ... -  《-》

Introducing a new estimator and test for the weighted all-cause hazard ratio.

Ozga AK ，Rauch G 《-》