The Relative Merits of Risk Ratios and Odds Ratios

Abstract

When a study outcome is rare in all strata used for an analysis, the odds ratio estimate of causal effects will approximate the risk ratio; therefore, odds ratios from most case-control studies can be interpreted as risk ratios. However, if a study outcome is common, the odds ratio will be further from 1 than the risk ratio. There is debate regarding the merits of risk ratios compared with odds ratios for the analysis of trials and cohort and cross-sectional studies with common outcomes. Odds ratios are conveniently symmetrical with regard to the outcome definition; the odds ratio for outcome Y is the inverse of the odds ratio for the outcome not Y. Risk ratios lack this symmetry, so it may be necessary to present 1 risk ratio for outcome Y and another for outcome not Y. Risk ratios, but not odds ratios, have a mathematical property called collapsibility; this means that the size of the risk ratio will not change if adjustment is made for a variable that is not a confounder. Because of collapsibility, the risk ratio, assuming no confounding, has a useful interpretation as the ratio change in average risk due to exposure among the exposed. Because odds ratios are not collapsible, they usually lack any interpretation either as the change in average odds or the average change in odds (the average odds ratio).