Department of Biostatistics Seminar/Workshop Series

Sizing up the Odds Ratio: Strengths, Limitations, and Misconceptions

Andrew J. Tomarken, PhD

Associate Professor of Psychology

Vanderbilt University

The odds ratio (OR) is among the most commonly used statistical measures of association or effect. It is by far the most commonly reported measure when dependent variables are binary and it is ubiquitous in studies focusing on the association between risk factors and disease outcomes. It is also among the most frequently misunderstood and heavily criticized indices. Unfortunately, even critiques of the OR sometimes overlook important features. All in all, it is challenging to arrive at a balanced and coherent assessment of the OR that takes into account multiple considerations. I will review what I consider to be the primary strengths and limitations of the OR. Relative to commonly cited alternative measures (e.g., the relative risk [RR] and risk difference [RD]), the OR has several desirable features including symmetry and the potential for insensitivity to variations in marginal probabilities, invariance across different reference points, and non-restricted range. Together, these features allow the OR to provide a single, uniform summary of effects across widely varying probabilities. In contrast, particularly when continuous predictors are used, it is often impossible for the RR and RD to demonstrate effects that are constant across all values of other predictors. Ironically, however, the scaling of probabilities that produces such beneficial effects exaggerates small differences at the extremes and makes the OR a less useful and non-intuitive measure that is difficult to understand. In addition, the concise summary of effects provided by the OR can mask a variety of problematic features related to the discrimination of a model, and non-collapsibility renders conclusions based on the OR surprisingly circumscribed. I will conclude by discussing two common misconceptions demonstrated by users based on a recent review of the literature in psychology and allied fields: (1) Mistaking the OR for the RR; and (2) Failing to acknowledge the difference between the multiplicative model associated with the OR and additive models more commonly used in other contexts. In short, conclusions about the nature, functional form, and magnitude of effects derived from the OR may often not generalize to alternatives. Thus, exclusive reliance on the OR can provide a selective or even misleading picture of the phenomenon under study.