SAMPLE-SIZE DETERMINATION FOR MULTIPLE CONTINUOUS RISK-FACTORS IN CASE-CONTROL STUDIES

For a desired power of detecting the association between a disease and several potential risk factors in case-control studies, Yang (1978, Biometrika 65, 635-640) and Halperin (1980, Biometrika 67, 577-580) proposed a probit risk model and derived approximate sample size formulas, respectively. The lack of direct interpretation of the parameters in the probit risk model and the complexity of these appropriate sample size formulas, however, limit the application of Yang's and of Halperin's procedures in practice. In this paper, we assume an exponential risk model for the incidence rate. Under our model assumptions, we derive an exact sample size calculation procedure that is simpler and easier to use than Yang's and Halperin's. Furthermore, when we consider many potential risk factors simultaneously and thus may have difficulty choosing an appropriate value for each parameter in the alternative hypothesis, we include a discussion on the application of the strategy similar to that proposed by Yang (1978) to solve this problem as well.