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.

Odds ratios for a continuous outcome variable without dichotomizing

The loss of information from dichotomizing a continuous outcome is well documented in the literature. One advantage of dichotomizing is that it allows estimation of odds ratio parameters through a logistic regression analysis. The objective of this paper is to develop a new estimator of the same odds ratio parameters through regression analysis on the original continuous outcome without the inherent loss of information caused by dichotomizing. Through a mathematical, asymptotic development the relative sample sizes required to attain a specified power when testing the odds ratio parameter are compared for the dichotomizing procedure and the proposed approach. The comparison highlights the substantial sample size savings attained by the proposed approach, particularly for large values of the odds ratio parameter and for small proportions of dichotomized successes or failures. In a Monte Carlo simulation the variances and absolute biases of the two odds ratio estimators and the length of their respective confidence intervals again demonstrate the improvement attained by the proposed approach. In addition, coverage probabilities of the confidence intervals of the proposed approach converge quickly to the nominal levels. The cost savings due to the reduction in required sample size when using this method make it a very attractive study design and analysis tool for medical researchers.