Weighted re-randomization tests for minimization with unbalanced allocation

Re-randomization test has been considered as a robust alternative to the traditional population model-based methods for analyzing randomized clinical trials. This is especially so when the clinical trials are randomized according to minimization, which is a popular covariate-adaptive randomization method for ensuring balance among prognostic factors. Among various re-randomization tests, fixed-entry-order re-randomization is advocated as an effective strategy when a temporal trend is suspected. Yet when the minimization is applied to trials with unequal allocation, fixed-entry-order re-randomization test is biased and thus compromised in power. We find that the bias is due to non-uniform re-allocation probabilities incurred by the re-randomization in this case. We therefore propose a weighted fixed-entry-order re-randomization test to overcome the bias. The performance of the new test was investigated in simulation studies that mimic the settings of a real clinical trial. The weighted re-randomization test was found to work well in the scenarios investigated including the presence of a strong temporal trend.