Estimating the Power of a Case-Control Study Conducted Within a Cohort

Power of epidemiologic studies can be studied via simulation, but simulations can require substantial computational effort and time. We describe a method for estimating power in matched and nested case-control studies using the noncentral Chi-square approximation to the distribution of the log-likelihood ratio test statistic. The non-centrality parameter is estimated by computing the likelihood ratio statistic using the expected values of the parameters under the null and alternative hypotheses. The method is compared to simulation results from an actual study evaluating various numbers of matched controls. There was reasonably close agreement between simulated and calculated values of the mean likelihood ratio test statistics, but the power estimates differed, perhaps due to small sample failure of the asymptotic distribution assumption.