Sample sizes for estimation of exposure-specific disease rates in population-based case-control studies

Abstract

This paper discusses sample sizes for estimation of exposure-specific disease rates for population-based case-control studies. Neutra and Drolette's confidence limits, which are based on the approximate normality of the logarithm of the ratio of independent binomial exposure rates, are used to determine the sample sizes required for precise estimation of exposure-specific disease rates. It is shown that, for large sample sizes, the disease rate in the exposed population is more precisely estimated than the disease rate in the unexposed population when more than 50% of the cases are exposed, and that the converse is true when fewer than 50% of the cases are exposed. Expressions are derived for the optimal case and control sample sizes that ensure the required level of precision and minimize the total study size. The optimum control-to-case ratio is found to be equal to the square root of the exposure odds ratio. The optimum number of cases and the total study size are found to be smaller for precise estimation of the disease rate in the exposed population than for precise estimation of the exposure odds ratio when the disease is rare.