Relative effect sizes for measures of risk

TLDR

Effect sizes are crucial for design, analysis, and interpretation, yet relative effect size benchmarks for risk measures such as relative risk, odds ratio, hazard ratio, rate ratio, and Mantel–Haenszel odds ratio are underexplored. This study extends relative effect size benchmarks to relative risk, odds ratio, hazard ratio, rate ratio, and Mantel–Haenszel odds ratio for related samples. The authors adapted existing relative effect size frameworks to derive thresholds for these risk metrics. For equal group allocation, small, medium, and large effect sizes correspond to 1.22, 1.86, and 3.00, respectively, while for non‑rare events the thresholds are 1.32, 2.38, and 4.70.

Abstract

Effect sizes are an important component of experimental design, data analysis, and interpretation of statistical results. In some situations, an effect size of clinical or practical importance may be unknown to the researcher. In other situations, the researcher may be interested in comparing observed effect sizes to known standards to quantify clinical importance. In these cases, the notion of relative effect sizes (small, medium, large) can be useful as benchmarks. Although there is generally an extensive literature on relative effect sizes for continuous data, little of this research has focused on relative effect sizes for measures of risk that are common in epidemiological or biomedical studies. The aim of this paper, therefore, is to extend existing relative effect sizes to the relative risk, odds ratio, hazard ratio, rate ratio, and Mantel–Haenszel odds ratio for related samples. In most scenarios with equal group allocation, effect sizes of 1.22, 1.86, and 3.00 can be taken as small, medium, and large, respectively. The odds ratio for a non rare event is a notable exception and modified relative effect sizes are 1.32, 2.38, and 4.70 in that situation.