Optimal case-control matching in practice

We illustrate modern matching techniques and discuss practical issues in defining the closeness of matching for retrospective case-control designs (in which the pool of subjects already exists when the study commences). We empirically compare matching on a balancing score, analogous to the propensity score for treated/control matching, with matching on a weighted distance measure. Although both methods in principle produce balance between cases and controls in the marginal distributions of the matching covariates, the weighted distance measure provides better balance in practice because the balancing score can be poorly estimated. We emphasize the use of optimal matching based on efficient network algorithms. An illustration is based on the design of a case-control study of hepatitis B virus infection as a possible confounder and/or effect modifier of radiation-related primary liver cancer in atomic bomb survivors.