Interpreting relative risks and odds ratios after propensity score matching: practical guidance for clinical research

In observational studies, using relative risks (RRs) or odds ratios (ORs) influences the interpretation and generalizability of results, particularly after propensity-score matching (PSM). Here, we explain the theoretical and practical differences between the RR and OR across varying event probabilities and examine the influence of PSM. We illustrate the behaviors of the RR, OR, and their ratios mathematically and graphically across event probabilities. Using a simulated dataset with a binary outcome and three covariates (age, sex, and body mass index), we demonstrate how PSM can change event rates, RRs, ORs, and RR collapsibility. The OR departs from unity more steeply than does the RR as the event probabilities diverge, whereas both measures converge for probabilities below 0.10. When groups have similar event probabilities, the OR and RR diverge minimally, even at high probabilities. PSM shifts the covariate distributions and alters the event rates, RRs, and ORs. The difference between the RR and OR increases when the event rate exceeds 0.10, but remains small at lower event rates. The weighted averages of sex-specific RRs closely approximate the marginal RR, illustrating the collapsibility of an RR. Interpreting the RR and OR after PSM requires caution. While the OR may overestimate or underestimate associations, depending on the event rates, the RR is generally suitable as a marginal measure, but PSM modifies the study population, making the matched sample a product of statistical modeling. Reporting ORs after PSM is generally appropriate, but cross-checking with a collapsible measure, such as the marginal RR, can help to evaluate effect estimate robustness.