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In the analysis of clinical trials, study participants are often assumed to be a representative sample of a study population. This assumption is rarely fulfilled as covariate imbalances may affect the trial. Randomization tests provide a nonparametric analysis method that does not rely on population-based assumptions. The objective of this investigation is to revisit the foundations of randomization tests and investigate their susceptibility to covariate imbalance in clinical trials.
We propose a nonparametric statistical model that yields a formal basis for randomization tests, and adapt it for the presence of covariate imbalance. We use Monte-Carlo simulations to assess the effects of bias on the rejection probability of the randomization test, and show that ancillary statistics can be used to control for the influence of bias.
While covariate imbalance leads to an inflation of the type I error probability and power, the proposed nonparametric model allows for the use of ancillary statistics that yield an unbiased adjusted randomization test. In conclusion, randomization tests provide valid statistical inference for clinical trials when covariate imbalance is present.
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