Properties of the weighted log-rank test in the design of confirmatory studies with delayed effects

TL;DR

This paper examines how the weighted log-rank test can be effectively used in clinical trial designs with delayed effects, addressing challenges in sample size calculation and analysis when proportional hazards assumptions are violated.

Contribution

It provides an empirical evaluation of the weighted log-rank test's performance in delayed effect scenarios and offers practical guidelines for its application in adaptive trial designs.

Findings

Weighted log-rank test maintains power with delayed effects.

Incorporating Fleming-Harrington weights improves test efficiency.

Recommendations depend on trial characteristics and delay estimates.

Abstract

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. This assumption not only affects the analysis part but also the sample size calculation. The presence of delayed effects causes a change in the hazard ratio while the trial is ongoing since at the beginning we do not observe any difference between treatment arms and after some unknown time point, the differences between treatment arms will start to appear. Hence, the proportional hazards assumption no longer holds and both sample size calculation and analysis methods to be used should be reconsidered. The weighted log-rank test allows a weighting for early, middle and late differences through the Fleming and Harrington class of weights, and is proven to be more efficient when the proportional hazards assumption does not hold. The Fleming and Harrington class of weights, along with the estimated delay, can be incorporated into the sample size calculation in order to maintain the desired power once the treatment arm differences start to appear. In this article, we explore the impact of delayed effects in group sequential and adaptive group sequential designs, and make an empirical evaluation in terms of power and type-I error rate of the of the weighted log-rank test in a simulated scenario with fixed values of the Fleming and Harrington class of weights. We also give some practical recommendations regarding which methodology should be used in the presence of delayed effects depending on certain characteristics of the trial.