Statistical Inference with Mixed-Effect Model for Covariate-Adaptive Randomized Experiments

Recent clinical studies increasingly involve a long factor with many levels, e.g., investigation sites, resulting in a large number of strata that must be accounted for either through design or subsequent analysis. This complication has prompted concerns from the U.S. Food and Drug Administration (FDA, 2023) regarding the adequacy of standard statistical methods, whose performance may deteriorate, and their properties become unclear when the number of strata is relatively large. In this work, we offer a first-time rigorous solution by employing mixed-effect models in covariate-adaptive randomized experiments. We show that the mixed-effect estimate achieves lower variance in treatment effect estimation than its fixed-effect counterpart in the presence of the long factor with many levels. This variance reduction is attributable to marginal imbalances induced by the randomization procedure, suggesting that designs promoting finer covariate balance lead to more efficient inference and increased statistical power. Furthermore, we demonstrate that, as the sample size grows, the mixed- and fixed-effect estimators become asymptotically equivalent. Our theoretical findings are validated through simulations and a clinical trial case study, and provide new insights on the design and analysis of clinical trials in the presence of a large number of strata.