Assessing the impact of selection bias on test decisions in trials with a time-to-event outcome

If past treatment assignments are unmasked, selection bias may arise even in randomized controlled trials. The impact of such bias can be measured by considering the type I error probability. In case of a normally distributed outcome, there already exists a model accounting for selection bias that permits calculating the corresponding type I error probabilities. To model selection bias for trials with a time-to-event outcome, we introduce a new biasing policy for exponentially distributed data. Using this biasing policy, we derive an exact formula to compute type I error probabilities whenever an F-test is performed and no observations are censored. Two exemplary settings, with and without random censoring, are considered in order to illustrate how our results can be applied to compare distinct randomization procedures with respect to their performance in the presence of selection bias. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.