Learning by Doing and Endogenous Patient-Physician Matching: Evidence from Cardiac Surgeons in New York State

In this paper, we examine the dynamic patient allocation problem of hospitals whose goals are to improve patient outcomes while training new physicians. We focus on cardiac surgeries in New York State, where the Report Cards system monitors and discloses physician and hospital performance annually. Our research is motivated by two empirical observations: (a) senior, top-rated cardiac surgeons do not seem to exhibit any advantage in the risk adjusted mortality rates (RAMR) of their patients, where risk adjustment is based on observable patient characteristics; (b) a surgeon’s performance over time does not display significant learning by doing effects, i.e., her RAMR does not decline as she treats more cases.

We seek to explain the puzzling empirical patterns by allowing for endogenous sorting of patients to physicians based on unobservable patient types. To this end, we develop a dynamic model of hospital-level decision-making. Hospitals in our model optimize their patient-physician matches over time, trying to strike the optimal balance between the learning by doing of junior physicians and the superior performance by experienced physicians. One implication of the model is that hospitals will assign junior physicians to treat relatively easy patients, defined as those expected to have lower ex-ante mortality rates based on unobservable characteristics. Then the junior physicians hone their skills via learning by doing, and will be assigned to treat more complicated cases over time.

We draw upon the New York Statewide Inpatient Database (SID) from 2003 to 2014 for empirical evidence, and supplement it with a collection of data on physician ratings by both patients and fellow physicians. The SID is ideal for our study for several reasons. First, it covers the universe of inpatient care within the state, with detailed case-level information on diagnoses, procedures, and outcomes. Second, it allows us to track physicians across hospitals and years, thereby retrieving their uninterrupted history of cardiac surgery cases. Third, it contains rich variations that help identify key parameters in the dynamic model. Of particular importance is the switching of a physician between different hospitals, where her relative seniority differs depending on a hospital’s portfolio of physicians. The corresponding change in performance is then most likely the result of the physician being assigned different types of patients, rather than discontinuous changes in her skills.

We identify coronary artery bypass graft (CABG) cases over the 12 sample years using the ICD-9 procedural codes. The main sample includes 121,801 cases (121,090 distinct patients) treated by 1,106 operating physicians at 53 hospitals. The sample features frequent physician turnover and switching: 43% of physicians practice at more than one hospital; 72% of the hospital-year combinations see at least one physician entry; 70% see at least one exit.

We estimate the dynamic model of hospital-level patient-physician matching on the SID data. By recovering the structural parameters of the endogenous sorting mechanism, we are able to provide a more precise characterization of physician performance, and also estimate the true learning curve that captures how a physician’s latent quality improves with her caseload.