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 log-rank 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(rho,gamma) 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.