Interim analysis on survival data: its potential bias and how to repair it

We consider interim analyses in clinical trials or observational studies with a time-to-event outcome variable where the survival curves are compared using the hazard ratio resulting from a proportional hazards (PH) model or tested with the logrank test or another two-sample test. We show and illustrate with an example that if the PH assumption is violated, the results of interim analyses can be heavily biased. This is due to the fact that the censoring pattern in interim analyses can be completely different from the final analysis. We argue that, when the PH assumption is violated, interim analyses are only sensible if a fixed time horizon for the final analysis is specified, and at the time of the interim analysis sufficient information is available over the whole time interval up to the horizon. We show how the bias can then be remedied by introducing in the estimation and testing procedures an appropriate weighting that reflects the weights to be expected in the final analysis. The consequences for design and analysis are discussed and some practical recommendations are given.