Overcoming Bias in Estimating the Volume–Outcome Relationship


  • Alexander C. Tsai,

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    • Address correspondence to Alexander C. Tsai, Ph.D., Department of Epidemiology and Biostatistics, Case Western Reserve University School of Medicine WG-57, 10900 Euclid Avenue, Cleveland, OH 44106-4945. Mark Votruba, Ph.D., Assistant Professor of Economics, is with the Department of Economics, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH. John F. P. Bridges, Ph.D., Leader of the Junior Group, is with the International Health Economics and Outcomes Research, Department of Tropical Hygiene and Public Health, University of Heidelberg Medical School, Heidelberg, Germany. Randall D. Cebul, M.D., Director, is with the Center for Health Care Research and Policy at MetroHealth Medical Center, Cleveland, OH and also Professor of Medicine, Epidemiology, and Biostatistics at Case Western Reserve University, Cleveland, OH.

  • Mark Votruba,

  • John F. P. Bridges,

  • Randall D. Cebul


Objective. To examine the effect of hospital volume on 30-day mortality for patients with congestive heart failure (CHF) using administrative and clinical data in conventional regression and instrumental variables (IV) estimation models.

Data Sources. The primary data consisted of longitudinal information on comorbid conditions, vital signs, clinical status, and laboratory test results for 21,555 Medicare-insured patients aged 65 years and older hospitalized for CHF in northeast Ohio in 1991–1997.

Study Design. The patient was the primary unit of analysis. We fit a linear probability model to the data to assess the effects of hospital volume on patient mortality within 30 days of admission. Both administrative and clinical data elements were included for risk adjustment. Linear distances between patients and hospitals were used to construct the instrument, which was then used to assess the endogeneity of hospital volume.

Principal Findings. When only administrative data elements were included in the risk adjustment model, the estimated volume–outcome effect was statistically significant (p=.029) but small in magnitude. The estimate was markedly attenuated in magnitude and statistical significance when clinical data were added to the model as risk adjusters (p=.39). IV estimation shifted the estimate in a direction consistent with selective referral, but we were unable to reject the consistency of the linear probability estimates.

Conclusions. Use of only administrative data for volume–outcomes research may generate spurious findings. The IV analysis further suggests that conventional estimates of the volume–outcome relationship may be contaminated by selective referral effects. Taken together, our results suggest that efforts to concentrate hospital-based CHF care in high-volume hospitals may not reduce mortality among elderly patients.