Sample Size and Statistical Power Calculation in Multivariable Analyses: Development and Implementation of "SampleSizeMulti" Packages in R
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.074 | 0.311 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.023 | 0.011 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".