Minimal Clinically Important Difference (MCID) of Effect Sizes other than Mean Difference

It is recommended to report both a P value < 0.05 and an effect size exceeding the minimal clinically important difference (MCID) to assert a meaningful difference or association between two clinical measurements. However, MCIDs for effect sizes other than mean difference has not been established. We aimed to propose study-level MCIDs, based on distribution method and Cohen’s d, for various effect sizes other than the mean difference, such as the hazard ratio (HR), risk ratio (RR), odds ratio (OR), absolute risk difference (ARD), correlation coefficient (r), and area under the receiver operating characteristic curve (AUC). Our primary innovation lies in the conversion between Cohen's d and effect sizes and in introducing flexible MCID for effect sizes not on an interval scale. The proposed MCIDs of the HR are 0.64, 0.76, and 0.83 for d = 0.5, 0.3, and 0.2, respectively, along with their reciprocals. For RR, OR, and ARD, d = |inverse_Φ(risk for experiment) – inverse_Φ(risk for control)|, where Φ represents the cumulative distribution function. For correlation coefficient, d = |f(r for experiment) − f(r for control)|, where f(r) = 2·r/√(1 – r^2). For AUC, d = |√2·inverse_Φ(AUC for experiment) − √2·inverse_Φ(AUC for control)|.The proposed MCID is especially useful for evaluating intergroup differences in meta-analyses, where statistical significance is more easily achieved, for setting detectable differences in superiority trials, and for determining non-inferiority margins in non-inferiority trials.