In multi-regional clinical trials, hierarchical linear models have been actively studied because they can reflect that patients in the same region share common intrinsic and extrinsic factors. In this paper, we investigate the statistical properties of the hierarchical linear model including a random effect in the intercept. The big advantage of the random intercept hierarchical linear model is that it can control the type I error rates of testing the overall treatment effect when there are no or clinically negligible regional differences in the treatment effect. Moreover, we compare the pros and cons with the hierarchical linear model in which the random effect is included in the slope. For the two hierarchical linear models, the model selection criteria are determined according to the magnitude of the difference in treatment effect across the regions, and we provide the criteria through simulation studies.
