Sample size determination for case-control studies: the influence of the joint distribution of exposure and confounder.

In case-control studies, the results about how the exposure distribution affects sample size are well known. This paper extends previous results by incorporating the effect of a confounder into the calculation of sample size for a desired size and power of a statistical test. The paper also includes a quantitative discussion on the influence of the joint distribution for exposure to a putative cause and a a confounder on required sample sizes. The results show that, to detect a specified alternative for a given size and power, the required sample size decreases as either the variance of exposure or the effect of exposure on disease increases. The required sample size, however, increases as either the variance of the confounder or the effect of the confounder on disease increases. Generally, the higher is the absolute value of the simple correlation between the exposure and the confounder, the larger is the required sample size.