BACKGROUND: The planning and analysis of multi-regional clinical trials (MRCTs) has increased in the pharmaceutical industry to facilitate global research and development. The ICH E17 guideline emphasizes the importance of considering the potential for regional differences, which may arise from shared intrinsic and extrinsic factors among patients within the same region in MRCTs. These differences remain as challenges in the design and analysis of MRCTs. METHODS: We introduce and investigate hierarchical linear models (HLMs) that account for regional differences by incorporating known factors as covariates and unknown factors as random effects. Extending previous studies, our HLMs incorporate random effects in both the intercept and slope, enhancing the model's flexibility. The proposed figures that depict the observed distribution of the primary endpoint and covariates facilitate understanding the proposed models. Moreover, we investigate the test statistics for the overall treatment effect and derive the required sample size under the HLM, considering both a fixed number of regions and real-world budgetary constraints. RESULTS: Our simulation studies show that when the number of regions is sufficient, HLM with random effects in the intercept and slope provides empirical type I error rates and power close to the nominal level. However, the estimate for the regional variabilities remains challenging for the small number of the regions. Budgetary constraints impact the required number of regions, while the required number of patients per region is influenced by the variability of treatment effects across regions. CONCLUSIONS: We offer a comprehensive framework for understanding and addressing regional differences in the primary endpoint for MRCTs. Through the proposed strategies with figures and required sample size considering the budget constraints, designs for MRCT could be more efficient.