Introduction to Logistic Regression and Odds Ratios

Abstract

Logistic regression is commonly used to model binary outcomes because it restricts predicted probabilities to be between zero and one. Odds ratios are often reported in published papers, but it is challenging to interpret the effect of a change in an explanatory variable on the outcome and the magnitude of an odds ratio cannot be compared across studies because they are scaled by a factor that is undefined. One consequence of this scaling is that the magnitude of the odds ratio depends on the variables included in the model, something that does not happen in linear regression or marginal effect measures (risk differences, risk ratios). Instead of reporting odds ratios, we recommend reporting marginal effects, such as risk differences or risk ratios. This paper summarizes different ways to report results from logistic regression and makes recommendations for best practice.