Keywords: Time-to-event data, non-proportional hazards, hazard rate
Typically, the time-to-event survival type of data in clinical trials is analyzed utilizing log-rank test or Cox proportional hazards model assuming proportionality in hazard rates over time. But many a times this assumption is violated. It is not uncommon to observe the magnitude of hazard rates change over time due to mechanism of action of treatment that can trigger sometimes a lagged or early treatment effect. Although many a times the direction of treatment effect remains same, there may be scenarios when the hazard rates cross each other changing the direction of treatment effect. It is well known that the log-rank test or Cox model can lose efficiency (sometime substantially) under deviation from the proportional hazards assumption. There has been lot of research activities recently to develop methodology under non-proportional hazards that are easy to implement and interpret. We will review various alternative methods accounting for non-proportional hazards for implementation guidance, including the piecewise exponential model and the choice of cut-points, and examine their performance under variety of non-proportionality scenarios.