Sample Size in Studies of Multiple Associations: Events-Per- Predictor-Parameter-Based Calculators for Case-Control, Cohort, and Cross-Sectional Designs

Abstract

Background: Observational studies examining associations between multiple predictor variables and health outcomes frequently use sample size calculation methods designed for single hypotheses, which is inadequate. Objective: To present sample size calculators based on the events per predictor parameter method for observational studies examining multiple associations, implemented for four classic epidemiological designs: case-control, closed cohort, open cohort with survival analysis, and analytical cross-sectional. Methods: We developed four calculators implemented as R packages, each specific to an epidemiological design. All use the events per predictor parameter (EPP) criterion, with EPP = 20 as the default planning criterion. Each package includes functions to generate scenarios with different EPP values (10–50), logistical planning (recruitment capacity, eligibility, refusal, and losses), and post-study verification of observed EPP. We applied the calculators to representative theoretical scenarios and compared the sample sizes obtained with those derived from traditional power-based methods for a single hypothesis. Results: The calculators determine sample sizes from the number of predictor parameters, the frequency of the event of interest, and logistical study conditions. Applied examples include a case-control study of acute myocardial infarction (12 parameters, EPP = 20, 2:1 control-to-case ratio, requiring 240 cases and 480 controls), a cohort study of prediabetes progression to diabetes (10 parameters, EPP = 20, 8% cumulative incidence over 36 months, requiring 2,500 participants), and a cross-sectional study of metabolic syndrome (15 parameters, EPP = 20, 25% prevalence, requiring 1,200 participants). EPP-based sample sizes were 78–108% larger than the power-based comparators. Five theoretical scenarios showed exact agreement (100%) between manual calculations and calculator results, confirming formula implementation in the tested scenarios. Conclusions: EPP-based calculators provide a transparent and reproducible framework for planning observational studies of multiple associations by linking an explicit event target to model complexity, expected outcome frequency, and recruitment feasibility.