Sample Size and Statistical Power Calculation in Multivariable Analyses: Development and Implementation of "SampleSizeMulti" Packages in R

This paper presents advanced methodological approaches and practical tools for sample size calculation in epidemiological studies involving multivariable analyses. Traditional sample size calculation methods often fail to account for the complexity of modern statistical analyses, particularly regarding the correlation between covariates in multivariable models. We introduce a series of R packages (SampleSizeMulti) designed to address these limitations. These packages offer two distinct calculation approaches: one based on the multiple correlation coefficient between covariates (rho-based method) and another utilizing standard errors from previous studies (SE-based method). These complementary approaches provide comprehensive solutions for different association measures commonly used in epidemiological research: prevalence ratios, odds ratios, risk ratios, and hazard ratios. The rho-based method innovatively incorporates the explicit consideration of the multiple correlation coefficient between covariates, significantly impacting required sample sizes in multivariable analyses. The SE-based method leverages information from previous studies through their confidence intervals, offering an alternative when correlation estimates are unavailable but published results exist. Furthermore, both approaches integrate crucial logistical considerations, including rejection rates, eligibility criteria, and expected losses to follow-up, providing researchers with realistic estimates of recruitment requirements and timelines. Seven detailed case studies covering various epidemiological study designs and analytical scenarios demonstrate the practical application of these methods. These examples illustrate how correlation values, standard errors, and logistical factors influence sample size calculations and study planning. The implementation in R ensures accessibility and reproducibility, while the incorporation of logistical planning tools bridges the gap between theoretical calculations and practical research requirements. These methods represent a significant advancement in study design methodology, potentially improving the quality and efficiency of epidemiological research by ensuring adequate statistical power while optimizing resource utilization.