A simple method for estimating the odds ratio in matched case-control studies with incomplete paired data

Paired data from matched case-control studies are commonly used to estimate the association between the exposure to a risk factor and the occurrence of a disease. The odds ratio is typically used to quantify this association. Difficulties in estimating the true odds ratio with matched pairs arise, however, when the exposure status is unknown for one of the individuals in one or more pairs. In this article, we propose a simple method for estimating the odds ratio when the sample consists of a combination of complete and incomplete matched pairs; that is, some of the pairs have exposure data for both the case and the control, some of the pairs have exposure data just for the case, and the remaining pairs have exposure data just for the control. This method uses a weighted average of the odds ratio estimator that is most commonly used when the sample consists entirely of complete paired observations and the odds ratio estimator that is most commonly used when the sample consists entirely of unpaired observations. The proposed estimator has simple closed-form expressions for the estimate of the odds ratio and its approximate variance. We compare our method to existing methods via simulation and show that our method is comparable to or better than the other methods in terms of bias, mean squared error, and confidence interval coverage probability and width.