Consequences of Delayed Treatment Effects on Analysis of Time-to-Event Endpoints

The assumption of proportional hazard ratios is implicit in certain analyses of time-to-event endpoints such as Cox regression. Other statistical analyses, such as the nonparametric logrank test, possess some desirable properties only under the proportional hazards model. Data models for delayed effects of treatment on time-to-event endpoints such as survival violate the proportional hazards assumption. Fleming and Harrington's G^ρ,γ class of weighted log-rank tests, a new option in SAS 9.1, is appropriate to test against a broad range of alternative hypotheses, including delayed treatment effects. A model for delayed treatment effects is proposed, and it is demonstrated that weighted log-rank tests are more powerful under this model than the standard unweighted log-rank test.