The odds ratio from a case-control study of the "cumulative-incidence" type can be used as an estimate of the relative risk of a disease attributable to exposure to an agent only when the incidence of the disease is low. The odds ratio can be modified to obtain an accurate estimate of the relative risk, regardless of the incidence of the disease. This modification of the odds ratio can be performed with any one of four types of auxiliary information: overall probability of disease, probability of disease in the unexposed population, probability of disease in the exposed population, or overall probability of exposure. For "incidence density" case-control studies, the odds ratio equals the relative risk when the estimate of exposure in the comparison group can be considered to be an estimate of the overall probability of exposure in the population at risk. Under certain conditions, such "case-exposure" studies may be preferable to cohort studies and to cumulative-incidence case-control studies. The authors present an approach to hypothesis testing for crude and stratified data from a case-exposure study.