Causality, Learning and Forgetting in Surgery

In this paper we distinguish between two causal explanations for the volume-outcome relationship, learning-by-doing and selective referral. We use data on three surgical procedures for which a volume-outcome relationship has been documented, the Whipple, coronary artery bypass graft (CABG) and repair of abdominal aortic aneurysm (AAA). We distinguish between the competing explanations by estimating the relationship between mortality and volume in a non-linear system of equations where volume is endogenous and where predicted volume is used to “instrument” for volume. In this system, we also allow for the possibility of forgetting. This model will identify learning-by-doing by the extent to which differences in expected volume based on variation in the numbers of competitors and patients near the hospital affect mortality at the hospital. For AAA and CABG increased volume appears to cause lower mortality, while the direction of causality is less certain for the Whipple. Using the assumption that volume is exogenous, we find that a significant amount of the learning is retained from quarter to quarter for the Whipple and AAA. For CABG, the impact of an exogenous increase in contemporaneous volume on mortality depreciates from one quarter to the next.