Impact of a non-constant baseline hazard on detection of time-dependent treatment effects: a simulation study

Restricted mean survival time to estimate an intervention effect in a cluster randomized trial

For time-to-event outcomes, the difference in restricted mean survival time is a measure of the intervention effect, an alternative to the hazard ratio, corresponding to the expected survival duration gain due to the intervention up to a predefined time t*. We extended two existing approaches of restricted mean survival time estimation for independent data to clustered data in the framework of cluster randomized trials: one based on the direct integration of Kaplan-Meier curves and the other based on pseudo-values regression. Then, we conducted a simulation study to assess and compare the statistical performance of the proposed methods, varying the number and size of clusters, the degree of clustering, and the magnitude of the intervention effect under proportional and non-proportional hazards assumption. We found that the extended methods well estimated the variance and controlled the type I error if there was a sufficient number of clusters (≥ 50) under both proportional and non-proportional hazards assumption. For cluster randomized trials with a limited number of clusters (< 50), a permutation test for pseudo-values regression was implemented and corrected the type I error. We also provided a procedure to estimate permutation-based confidence intervals which produced adequate coverage. All the extended methods performed similarly, but the pseudo-values regression offered the possibility to adjust for covariates. Finally, we illustrated each considered method with a cluster randomized trial evaluating the effectiveness of an asthma-control education program.

Examining evidence of time-dependent treatment effects: an illustration using regression methods

BACKGROUND

For the design and analysis of clinical trials with time-to-event outcomes, the Cox proportional hazards model and the logrank test have been the cornerstone methods for many decades. Increasingly, the key assumption of proportionality-or time-fixed effects-that underpins these methods has been called into question. The availability of novel therapies with new mechanisms of action and clinical trials of longer duration mean that non-proportional hazards are now more frequently encountered.

METHODS

We compared several regression-based methods to model time-dependent treatment effects. For illustration purposes, we used selected endpoints from a large, community-based clinical trial of low dose daily aspirin in older persons. Relative and absolute estimands were defined, and analyses were conducted in all participants. Additional exploratory analyses were undertaken by selected subgroups of interest using interaction terms in the regression models.

DISCUSSION

In the trial with median 4.7 years follow-up, we found evidence for non-proportionality and a time-dependent treatment effect of aspirin on cancer mortality not previously reported in trial findings. We also found some evidence of time-dependence to an aspirin by age interaction for major adverse cardiovascular events. For other endpoints, time-fixed treatment effect estimates were confirmed as appropriate.

CONCLUSIONS

The consideration of treatment effects using both absolute and relative estimands enhanced clinical insights into potential dynamic treatment effects. We recommend these analytical approaches as an adjunct to primary analyses to fully explore findings from clinical trials.