Attributing Effects to Treatment in Matched Observational Studies

An effect is attributable to treatment if it would not have been observed had the individual been exposed to control instead. Extending earlier results on attributable effects in unmatched groups, a method of exact randomization inference and sensitivity analysis is developed for case-referent, case-crossover, and cohort studies with matched sets, and a large sample approximation to the exact inference is given. The unmatched case, considered previously, has certain symmetries that the matched case, considered here, does not have. As a result, approximation for the matched case requires the use of the recently developed method of asymptotic separability, which was not needed in the unmatched case. Several examples are presented, including a case-referent study of Helicobacter pylori infection as a cause of myocardial infarction, a case-crossover study of alcohol as a cause of injury, a cohort study of women who gave birth at home, and a study of the effects of cadmium exposure with a continuous outcome measuring kidney function. Unlike tests of no effect, inference about attributable effects has a different form in case-referent and cohort studies.