Determining the late effect parameter in the Fleming-Harrington test using asymptotic relative efficiency in cancer immunotherapy clinical trials

Abstract

ABSTRACT The delayed treatment effect, which manifests as a separation of survival curves after a change point, has often been observed in immunotherapy clinical trials. A late effect of this kind may violate the proportional hazards assumption, resulting in the non-negligible loss of statistical power of an ordinary log-rank test when comparing survival curves. The Fleming-Harrington (FH) test, a weighted log-rank test, is configured to mitigate the loss of power by incorporating a weight function with two parameters, one each for early and late treatment effects. The two parameters need to be appropriately determined, but no helpful guides have been fully established. Since the late effect is expected in immunotherapy trials, we focus on the late effect parameter in this study. We consider parameterizing the late effect in a readily interpretable fashion and determining the optimal late effect parameter in the FH test to maintain statistical power in reference to the asymptotic relative efficiency (ARE). The optimization is carried out under three lag models (i.e. linear, threshold, and generalized linear lag), where the optimal weights are proportional to the lag functions characterized by the change points. Extensive simulation studies showed that the FH test with the selected late parameter reliably provided sufficient power even when the change points in the lag models were misspecified. This finding suggests that the FH test with the ARE-guided late parameter may be a reasonable and practical choice for the primary analysis in immunotherapy clinical trials.