Testing Treatment Effect in Randomized Clinical Trials with Possible Non-proportional Hazards

Abstract

Many randomized clinical trials include right censored time to event data, comparing an experimental treatment with a standard treatment or placebo control. In this comparison, one tests whether the two treatments have the same survival function or equivalently the same hazard function over a given time period in order to evaluate effect of treatment. The methodological development of survival analysis for randomized clinical trials with right-censored data that have had the most profound impact are the log-rank test for comparing the equality of two or more survival distributions, and the Cox proportional hazards model for examining the covariate(s) effects on the hazard function. However, when comparing treatments in terms of their time to event distribution, there may be reason to believe that the hazard curves will cross, and in such cases standard comparison techniques could lead to misleading results [16]. Hence, in this study, the performance of new methods for testing treatment effect on randomized clinical trials when the proportional hazards assumption is not satisfied was evaluated based on simulation studies and on two real datasets. New proposed methods are based on combination of early/late treatment effects obtained from stopped/left truncated Cox or equivalently from extended Cox and the overall treatment effect from Cox proportional hazards model. These methods were compared with Cox proportional hazards model [8], pseudo values regression approach based on mean restricted survival time [1, 13] and extended Cox for the time dependent treatment effect [20]. Type I error rate and power of the proposed tests were illustrated based on simulated data under five possible treatment effect. The results of simulations and real data examples on cancer clinical trials showed that the new proposed methods performed reasonably well in case of crossing survival curves compared to Cox proportional hazards model and pseudo values regression approach based on restricted mean survival time. However, they performed about the same compared to extended Cox model. Furthermore, they performed about the same compared to Cox proportional hazards model and extended Cox under the late treatment effect. Using the proposed methods under proportional hazards alternative did not generally yield dramatic decrease in power compared to the Cox model and they allow adjusting for covariate(s).