Quantifying the Effect Size of Exposure-Outcome Association Using δ-Score: Application to Environmental Chemical Mixture Studies

Epidemiologists often study the associations between a set of exposures and multiple biologically relevant outcomes. However, frequently used scale-and-context-dependent regression coefficients may not offer meaningful comparisons could further complicate interpretation if these outcomes do have similar units. Additionally, when scaling up hypothesis-driven based on preliminary data, knowing how large to make sample size is major uncertainty for epidemiologists. Conventional p-value-based calculations emphasize precision might lead small- moderate-effect sizes. This asymmetry utility costly detection irrelevant effects. Here, we introduce “δ-score” concept, by modifying Cohen’s f2. δ-score scale independent circumvents challenges coefficients. Further, under new hypothesis testing framework, it quantifies maximum f2 with certain optimal properties. We also introduced “Sufficient size”, which minimum required attain δ-score. Finally, data adults from 2017–2018 U.S. National Health Nutrition Examination Survey demonstrate sufficient reduced finding mixtures per-and polyfluoroalkyl substances metals serum high-density low-density lipoprotein cholesterol.