Sample size determination in case-control studies: the influence of the distribution of exposure

In the design of case-control studies, the determination of the required number of cases and controls is based on consideration of the strength of the relationship between the disease and exposure to the putative cause, the variability in exposure within the population under study, and the desired size and power of the statistical test. This paper derives sample size equations for studies with a continuous exposure which allow the investigator to specify the strength of the relationship between disease and exposure in terms of relative risk, etiologic fraction or the slope of an exposure response relationship. With these formulations it becomes apparent that the size of the sample increases with decreasing variability in exposure in the population under study, a finding not apparent in the use of conventional methods of sample size determination for continuous data. The ability of a case-control study to detect a significant association between disease and exposure therefore depends critically on the distribution of exposure which exists in the community to be studied. Implications of these findings for studies of diet and cancer are discussed.