Inference Under Covariate-Adaptive Randomization Using Random Center-Effect

The minimization method is a popular choice for covariate-adaptive randomization in multicenter trials. Existing literature suggests that the type-I error is controlled if minimization variables are included in the statistical analysis. However, in practice, minimization variables with many categories, such as the recruitment center, are often not included in the model. In this paper, we propose including the minimization variable "center" as a random effect and assess its performance using simulations for Gaussian, binary, and Poisson endpoint variables. Our simulation study suggests that the random-effect model controls type-I error and preserves maximum power for all three endpoints under varied clinical trial settings. This approach offers an alternative to the re-randomization test, which regulatory authorities often suggest for sensitivity analysis.