Background: Many articles provide only odds ratios (OR) and not relative risks (RR) as the effect estimate. For a variety of important reasons, multiple logistic regression used to adjust for confounders routinely provides only the adjusted OR (ORadj). However, from the clinician's perspective, the ORadj is only easily interpretable when it approximates the adjusted RR (RRadj). In general, the relationship between the OR and RR (adjusted or non-adjusted) is dependent on prevalence of disease in the control group (Po) and has always been presented as non-linear. Therefore, it is difficult for the clinician to convert the OR to RR when reading published data. A formula was proposed by Zhang and Yu, but the relationship remains non-linear.

Objectives: To develop a simple formula that can convert OR to RR without the use of computer.

Methods: Algebraic manipulation.

Results: Through algebraic manipulation, we show that although the OR and RR relationship is non-linear over the range Po, the ratio OR/RR has a linear relationship with Po with a slope of 'OR-1': 0R/RR = (OR-1)*Po + 1. Previous problems with confidence intervals noted with the Zhang and Yu formula remain (i.e. they are too narrow under some conditions) and the result should be interpreted with this limitation. Relationships between ORadj and risk difference or number needed to treat remain curvilinear but some overall approximations can be made. See Figures below.

Conclusion: A simple relationship exists that allows readers to easily convert ORadj to RRadj. Limitations of the approach remain but appear to be less restrictive than the limitations of not converting ORadj to RRadj.