Relationship between prevalence rate ratios and odds ratios in cross-sectional studies

Background. Cross-sectional data are frequently encountered in epidemiology and published results are predominantly presented in terms of prevalence odds ratios (FOR), A recent debate suggested a switch from FOR, which is easily obtained via logistic regression analysis available in many statistical packages, to prevalence rate ratios (PRR). We thought it useful to explore the mathematical relationship between PRR and FOR and to evaluate the degree of divergence of the two measures as a function of the prevalence of disease and exposure. Methods. With the use of some algebra and the common definitions of prevalence of the disease (Pr(D)), prevalence of the exposure (Pr(E)), PRR, and FOR in a 2x2 table, we have identified a useful formula that represents the mathematical relationship between these four quantities. Plots of FOR versus PRR for selected values of Pr(D) and Pr(E) are reported. Results. Mathematically speaking the general relationship takes the form of a second order curve which can change curvature and/or rotate around the point FOR = PRR = 1 according to the values of Pr(D) and Pr(E), with FOR being always further from the null value than is PRR. The discrepancies are much more influenced by variations in Pr(D) than in Pr(E). Conclusions. We think that the choice between FOR or PRR in a cross-sectional study ought to be based on epidemiological grounds and not on the availability of software tools. The paper offers a formula and some examples for a better understanding of the relationship between PRR and FOR as a function of the prevalence of the disease and the prevalence of the exposure.