The Case-Control Approach Can be More Powerful for Matched Pair Observational Studies When the Outcome is Rare

In an observational study, to investigate the treatment effect, one common strategy is to match the control subjects to the treated subjects. The outcomes between the two groups are then compared after the TC (treatment-control) match. However, when the outcome is rare, detection of an outcome difference can be challenging. An alternative approach is to compare the treatment or exposure discrepancy after matching subjects with the outcome (cases) to subjects without the outcome (referents). Throughout the article, we follow the tradition to call this the matched “case-control” approach instead of the matched “case-referent” approach. We reserve “control” to mean not taking the treatment, and the abbreviation TC and CC (case-control) when possible confusion may arise. We derive conditions when the matched CC approach has more power for testing the treatment effect and examine its empirical performance in simulations and in our data example. We also show that the CC approach gives better match quality in our study of the effect of long vs. short stay in the hospital after joint surgery.