Randomization-based inference in the presence of selection bias

For the analysis of clinical trials, the study participants are usually assumed to be representative sample of a target population. This assumption is rarely fulfilled in clinical trials, and particularly not if the sample size is small. In addition, covariate imbalances may affect the trial. Randomization tests provide a nonparametric analysis method of the treatment effect that does not rely on population-based assumptions. We propose a nonparametric statistical model that yields a formal basis for randomization tests. We adapt the model for the presence of covariate imbalance in the form of selection bias and investigate the effects of bias on the rejection probability of the randomization test using Monte Carlo simulations. Finally, we show that ancillary statistics can be used to control for the influence of bias. We show that covariate imbalance leads to an inflation of the type I error probability. The proposed nonparametric model allows for the use of ancillary statistics that yield an unbiased adjusted randomization test.