Three Risk Indices: Risk Ratio, Odds Ratio, and Risk Difference, Which is the Most Effective in Measuring the Treatment Effect?

Abstract

Quantifying the causal effect of an intervention on a binary outcome is a cornerstone of epidemiological research. While the risk ratio (RR), odds ratio (OR), and risk difference (RD) are standard measures, they are not monotonic transformations of one another and often yield inconsistent rankings of treatment effects. This study introduces a principled framework to evaluate the statistical effectiveness of these indices by unifying them through a shared “win-loss-tie” structure. We derive the non-centrality parameters for the Wald-type tests associated with each measure to provide an objective, mathematical criterion for index selection. Our analytical results demonstrate that the optimal measure depends strictly on the direction of the treatment effect: the RD-based test maximizes statistical power when the treatment increases risk (p1 > p0), whereas the OR-based test is most informative when the treatment is protective (p1 < p0). Notably, the RR is consistently outperformed by either the OR or the RD across both scenarios. Extensive Monte Carlo simulations confirm these power hierarchies across varied sample sizes and risk levels. Applying this framework to the Physicians’ Health Study I confirms that the OR is the most sensitive measure for nonfatal myocardial infarction (a protective effect), while the RD is superior for ischemic stroke (a harmful effect). These findings provide essential guidance for study design, allowing researchers to pre-specify the most powerful risk measure based on the hypothesized direction of effect.