An approximate randomisation-respecting adjustment to the hazard ratio for time-dependent treatment switches in clinical trials

We consider a clinical trial with a survival outcome, in which subjects may switch in a non-randomised manner from their randomised treatment to control treatment during follow-up. We extend a method for binary outcomes, due to Sommer and Zeger, by viewing a survival outcome as a sequence of binary outcomes. This leads to a simple expression for the hazard ratio among non-switchers at each time in terms of the unadjusted hazard ratio and the proportion of switchers among subjects who experience events. We also estimate an overall adjusted hazard ratio. Although our method is approximate, it has the advantage of preserving the significance level of the log rank test. A simulation study shows that the method works well for the overall adjusted hazard ratio but that interval-specific estimates are under-adjusted as the degree of switching increases and as the association between switching and events becomes stronger. The method is illustrated using data from the Concorde trial of immediate versus deferred treatment in HIV infection.