Estimation and testing of the relative risk of disease in case-control studies with a set of k matched controls per case with known prevalence of disease.
The analysis of case-control studies with matched controls per case is well documented in the medical literature. Of primary interest is the estimation of the relative risk of disease. Matched case-control studies fall into two scenarios: the probability of exposure is constant within each of the case and control groups, or the probability of exposure varies within each group. Numerous estimation procedures have been developed for both scenarios. Often these procedures are developed under the rare disease assumption, where the relative risk of disease is approximated by the odds ratio. In this paper, without making the rare disease assumption, we develop consistent estimators of the relative risk of disease for both scenarios. Exact derivations of the relative risk of disease are provided. Estimators, confidence intervals, and test statistics for the relative risk of disease are developed. We then make the following observations based on extensive simulations. First, our estimators are as close or closer to the relative risk of disease than other estimators. Second, our estimators produce mean square errors for the relative risk of disease that are as good as or better than these other estimators. Third, our confidence intervals provide accurate coverage probabilities. Therefore, these new estimators, confidence intervals, and test statistics can be used to either estimate or test the relative risk of disease in matched case-control studies.
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