Reducing mean squared error in the analysis of pair-matched case-control studies

The standard estimator of the common odds ratio for pair-matched case-control studies, the stratified estimate, is consistent but it ignores all information from the concordant pairs. At the other extreme, the pooled estimator is more efficient as it uses all the data, but is not consistent. In order to trade between bias and precision, Liang and Zeger (1988, Biometrics 44, 1145-1156) proposed an estimator that is a compromise between the stratified and pooled estimates. In the current paper, the possibility of optimizing the trade-off is explored. Specifically, the family of weighted averages of the stratified and pooled estimates is considered, and the weight that minimizes an asymptotic approximation of mean squared error is derived. In practice, the optimal weight must be estimated from the data so that the estimator is only approximately optimal. Small-sample properties are evaluated via simulations.