Overcoming bias in estimating the volume-outcome relationship

Twenty-five years ago (Luft, Bunker, and Enthoven 1979), documented an inverse volume–outcome relationship for surgical care. Subsequent studies in this literature (Halm, Lee, and Chassin 2000) have generated similar results. Accordingly, organizations such as the Leapfrog Group have encouraged patients undergoing high-risk procedures to seek care at high-volume hospitals (Birkmeyer, Finlayson, and Birkmeyer 2001). Congestive heart failure (CHF) is a particularly important area of investigation for improving quality of care, because of its high prevalence and considerable cost to the U.S. Medicare program, where the average charge for a CHF admission exceeds $10,000 (U.S. Centers for Medicare and Medicaid Services 2003). Despite technological advances, 5-year survival rates for CHF have failed to improve. This is commonly attributed to the complexity of medical management of patients with CHF (Akosah et al. 2002), suggesting that a learning by doing effect should be observed in the care of such patients. However, few studies have estimated the volume–outcome relationship for nonprocedural care (Halm, Lee, and Chassin 2000). Only one previous study has been performed so in the context of CHF. Burns and Wholey (1991) analyzed 1,988 statewide administrative data on nearly 6,000 CHF admissions and concluded that there was no suggestion of an inverse relationship between hospital volume and in-hospital mortality. Interpreting previous work on the inverse volume–outcome relationship, however, is subject to two important caveats, both of which are remedied in our study. The first caveat to the volume–outcome literature is that the estimated relationship may reflect unmeasured differences in the illness severity of patients admitted to low- versus high-volume hospitals. Most volume–outcome studies, including the one by Burns and Wholey (1991), have not used detailed clinical data for appropriate risk adjustment (Halm, Lee, and Chassin 2000) and may therefore be subject to unpredictable biases resulting from unmeasured severity of illness. Our analyses are based on clinical data that contain a much greater level of detail than that which is found in typical discharge abstract summaries. We then compare estimates based on administrative versus clinical risk adjustment models in order to illustrate the importance of appropriate risk adjustment. The second caveat is that the estimated relationship may reflect reverse causality, as providers known for high quality care will attract greater numbers of patients through “selective referral” (Luft 1980). Without the benefit of randomization, conventional estimates of the volume–outcome effect may be contaminated by selective referrals and will therefore exaggerate the importance of learning by doing. To identify the volume–outcome effect, previous studies have used the method of instrumental variables (IV), with the total number of hospital beds serving as an instrument (Luft, Hunt, and Maerki 1987; Hughes et al. 1988; Farley and Ozminkowski 1992; Norton et al. 1998). Using hospital bed size as an instrument, however, is not without its weaknesses. A legitimate instrument must also be conditionally unrelated with the dependent variable of interest except through its effect on the potentially endogenous regressor of interest. If patients are being selectively referred to generally higher-quality hospitals, then one would expect these hospitals to be larger in size, and CHF-specific quality of care is likely to be correlated with general quality of care provided by a given hospital. To remedy the shortcomings inherent in previous IV analyses, we construct an instrument that is based on the linear distances between patients and hospitals. This new instrument can serve as a plausibly exogenous source of variation in hospital CHF volume, which we use to appropriately identify the volume–outcome effect.