The efficiency of matching in case-control studies of risk-factor interactions

We have examined the relative efficiency of matching vs not matching on a binary exposure variable in a case-control study of its interaction with another binary exposure variable. Interaction is treated as a parameter measuring departure from multiplicativity. Efficiency is considered both in the presence and absence of other matching variables, the former case requiring use of matched-pair estimators. In most circumstances examined, matching on one variable led to a less efficient estimator of the interaction parameter. If both variables were related to disease, the only circumstance in which matching always improved efficiency was when the high-risk level of the matching variable was uncommon and not positively associated with the high-risk level of the other variable. Matching always appeared to harm efficiency when the high risk level of the matching variable was common. Other disadvantages of matching are that it precludes estimation of the main effect of the matching variable and fitting of non-multiplicative models, and increases the difficulty of control selection.