Relationships among three popular measures of differential risks: relative risk, risk difference, and odds ratio

The relative risk, risk difference, and odds ratio are the three most commonly used measures for comparing the risk of disease between different groups. Although widely popular in biomedical and psychosocial research, the relationship among the three measures has not been clarified in the literature. Many researchers incorrectly assume a monotonic relationship, such that higher (or lower) values in one measure are associated with higher (or lower) values in the other measures. In this paper we discuss three theorems and provide examples demonstrating that this is not the case; there is no logical relationship between any of these measures. Researchers must be very cautious when implying a relationship between the different measures or when combining results of studies that use different measures of risk.