Abstract
For many surgical procedures, apparent volume–outcome relationships may reflect differences in patient risk-profiles as well as quality of care. As some important patient profile differences may be unobserved, we use fixed effects (FE) regression to estimate the relationship between operative mortality and surgeon and hospital volumes, and compare this method with the more commonly used random effects (RE) regression approach. The 1998 and 1999 Medicare Inpatient and Denominator files for Medicare Fee for Service enrollees aged 65–99. Operative mortality rates are estimated for different surgeon and hospital volume tertiles (high, medium, low) using FE and RE regression methods, adjusted for patient demographics and morbidities. The data were collected by the Centers for Medicare and Medicaid Services (CMS). FE regression estimates that lowest volume tertile hospitals have 1.4 and lowest volume tertile surgeons have 1.6 additional operative deaths (for every 100 CABG surgeries) compared to their highest volume tertile counterparts. The corresponding RE estimates are 0.5 and 1.4 respectively. The substantially higher FE hospital volume effect compared to RE indicates the presence of unobserved “protective” characteristics in lower volume providers, including a less complicated patient profile. Lower hospital and surgeon volumes are associated with substantially higher excess operative mortality from CABG surgeries than previously estimated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
As the term “fixed effects” used in the econometrics literature is quite different from that in the applied statistics/biostatistics literature, a clarification is in order. In regressions involving multilevel or hierarchical data, fixed effects regression is an approach in the econometrics literature wherein only intra-level variation is used to obtain regression coefficient estimates. For instance, in the context of longitudinal person-level data, fixed effects regression estimates are obtained by comparing only the temporal changes in measures, not the levels between individuals. The strength of this approach is that each individual is treated as a control for himself/herself. Random effects estimates utilize both within- and between-individual variation. (Johnston and DiNardo 1997; Wooldridge 2002). Alternately, in the applied statistics literature, the terms “fixed effects” and “random effects” are used to specify the nature of the regression coefficients in a multilevel regression. If a coefficient is permitted to vary—say across individuals in a longitudinal data framework—then it could be specified as a random variable; however, if a coefficient is not permitted to vary then it is described as a “fixed effect” (Raudenbush and Bryk 2002). Such a distinction does not arise in this study as none of the regression coefficients are random.
Fixed effects logistic regression (also known as conditional logistic regression) requires at least one decedent and survivor from each fixed level (surgeon, hospital) (Chamberlain 1980). As 507 of the 2772 surgeons have no decedents, we have instead followed previous studies (Tsai et al. 2006) and chosen to use the linear probability specification that has the advantage of retaining data from all surgeons and hospitals.
References
Auerbach, A.D., Hilton, J.F., Maselli, J., Pekow, P.S., Rothberg, M.B., Lindenauer, P.K.: Shop for quality or volume? Volume, quality, and outcomes of coronary artery bypass surgery. Ann. Intern. Med. 150(10), 696–704 (2009)
Birkmeyer, J.D.: Should we regionalize major surgery? Potential benefits and policy considerations. J. Am. Coll. Surg. 190(3), 341–349 (2000)
Birkmeyer, J.D.: Understanding surgeon performance and improving patient outcomes. J. Clin. Oncol. 22(14), 2765–2766 (2004)
Birkmeyer, J.D., Siewers, A.E., Finlayson, E.V.A., Stukel, T.A., Lucas, F.L., Batista, I., Welch, H.G., Wennberg, D.E.: Hospital volume and surgical mortality in the United States. N. Engl. J. Med. 346(15), 1128–1137 (2002)
Birkmeyer, J.D., Stukel, T.A., Siewers, A.E., Goodney, P.P., Wennberg, D.E., Lucas, F.L.: Surgeon volume and operative mortality in the United States. N. Engl. J. Med. 349(22), 2117–2127 (2003)
Birkmeyer, N.J.O., Birkmeyer, J.D.: Strategies for improving surgical quality—should payers reward excellence or effort? N. Engl. J. Med. 354(8), 864–870 (2006)
Chamberlain, G.: Analysis of covariance with qualitative data. Rev. Econ. Stud. 47, 225–238 (1980)
Christiansen, C. L., Morris, C. N.: Improving the statistical approach to health care provider profiling. Ann Intern Med 127(8_Part_2):764–768 (1997)
Dranove, D., Kessler, D., McClellan, M., Satterthwaite, M.: Is more information better? The effects of “report cards” on health care providers. J. Polit. Econ. 111(3), 555 (2003)
Farley, D.E., Ozminkowski, R.J.: Volume–outcome relationships and in-hospital mortality: the effect of changes in volume over time. Med. Care 30(1), 77–94 (1992)
Fredenheim, M.: To find a doctor, mine the data. The New York Times, New York City (2005)
Gaynor, M., Seider, H., Vogt, W.B.: The volume-outcome effect, scale economies, and learning-by-doing. Am. Econ. Rev. 95(2), 243–247 (2005)
Gowrisankaran, G., Town, R.J.: Estimating the quality of care in hospitals using instrumental variables. J. Health Econ. 18(6), 747–767 (1999)
Gowrisankaran, G., Ho, V., Town, R.: Causality, Learning and Forgetting in Surgery. Working Paper, John M. Olin School of Business, Washington University in St. Louis. St. Louis (2005)
Halm, E.A., Lee, C., Chassin, M.R.: How is Volume Related to Quality in Health Care? A Systematic Review of the Research Literature. Institute of Medicine, Washington, D.C. (2000)
Halm, E.A., Lee, C., Chassin, M.R.: Is volume related to outcome in health care? A systematic review and methodologic critique of the literature. Ann. Intern. Med. 137(6), 511–520 (2002)
Hamilton, B.H., Ho, V.: Does practice make perfect? Examining the relationship between hospital surgical volume and outcomes for hip fracture patients in Quebec. Med. Care 36(6), 892–903 (1998)
Hewitt, M.: Interpreting the Volume–Outcome Relationship in the Context of Health Care Quality: Workshop Summary. Institute of Medicine, Washington, D.C. (2000)
Jha, A.K., Orav, E.J., Li, Z., Epstein, A.M.: Concentration and quality of hospitals that care for elderly black patients. Arch. Intern. Med. 167(11), 1177–1182 (2007)
Johnston, J., DiNardo, J.: Econometric Methods, 4th edn. McGraw-Hill, New York, NY (1997)
Krumholz, H.M., Brindis, R.G., Brush, J.E., Cohen, D.J., Epstein, A.J. , Furie, K., Howard, G., Peterson, E.D., Rathore, S.S., Smith, S.C., Jr., Spertus, J.A., Wang, Y., Normand, S.L.: Standards for statistical models used for public reporting of health outcomes: an American Heart Association Scientific Statement from the Quality of Care and Outcomes Research Interdisciplinary Writing Group: cosponsored by the Council on Epidemiology and Prevention and the Stroke Council. Endorsed by the American College of Cardiology Foundation. Circulation 113(3):456–62 (2006)
Kumbhani, D.J., Cannon, C.P., Fonarow, G.C., Liang, L., Askari, A.T., Peacock, W.F., Peterson, E.D., Bhatt, D.L.: Association of hospital primary angioplasty volume in ST-segment elevation myocardial infarction with quality and outcomes. JAMA 302(20), 2207–2213 (2009)
Losina, E., Wright, E.A., Kessler, C.L., Barrett, J.A., Fossel, A.H., Creel, A.H., Mahomed, N.N., Baron, J.A., Katz, J.N.: Neighborhoods matter: use of hospitals with worse outcomes following total knee replacement by patients from vulnerable populations. Arch. Intern. Med. 167(2), 182–187 (2007)
Luft, H.S.: The relation between surgical volume and mortality: an exploration of causal factors and alternative models. Med. Care 18(9), 940–959 (1980)
Luft, H.S., Bunker, J., Enthoven, A.: Should operations be regionalized? The empirical relation between surgical volume and mortality. N. Engl. J. Med. 301(25), 1364–1369 (1979)
Normand, S.-L.T., Glickman, M.E., Gatsonis, C.A.: Statistical methods for profiling providers of medical care: issues and applications. J. Am. Stat. Assoc. 92(439), 803–814 (1997)
O’Brien, S.M., DeLong, E.R., Peterson, E.D.: Impact of case volume on hospital performance assessment. Arch. Intern. Med. 168(12), 1277–1284 (2008)
Post, P.N., Kuijpers, M., Ebels, T., Zijlstra, F.: The relation between volume and outcome of coronary interventions: a systematic review and meta-analysis. Eur Heart J (2010)
Raudenbush, S.W., Bryk, A.S.: Hierarchical Linear Models, 2nd edn. Sage Publications, Thousand Oaks, CA (2002)
Schneider, E.C., Epstein, A.M.: Influence of cardiac-surgery performance reports on referral practices and access to care—a survey of cardiovascular specialists. N. Engl. J. Med. 335(4), 251–256 (1996)
Schwartz, L.M., Woloshin, S., Birkmeyer, J.D.: How do elderly patients decide where to go for major surgery? Telephone interview survey. BMJ 331(7520), 821–827 (2005)
Shahian, D.M., Normand, S.-L.T.: The volume–outcome relationship: from Luft to Leapfrog. Ann. Thorac. Surg. 75(3), 1048–1058 (2003)
Shahian, D.M., Torchiana, D.F., Shemin, R.J., Rawn, J.D., Normand, S.-L.T.: Massachusetts cardiac surgery report card: implications of statistical methodology. Ann. Thorac. Surg. 80(6), 2106–2113 (2005)
StataCorp.: Stata Statistical Software: Release 9. StataCorp LP, College Station, TX (2005)
Tsai, A.C., Votruba, M., Bridges, J.F.P., Cebul, R.D.: Overcoming bias in estimating the volume–outcome relationship. Health Serv. Res. 41(1), 252–264 (2006)
Wooldridge, J.M.: Econometric analysis of cross-section and panel data. The MIT Press, Cambridge, MA (2002)
Acknowledgment
This study was funded by an AHRQ Grant (R03 HS015617-01A1).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hanchate, A.D., Stukel, T.A., Birkmeyer, J.D. et al. Surgery volume, quality of care and operative mortality in coronary artery bypass graft surgery: a re-examination using fixed-effects regression. Health Serv Outcomes Res Method 10, 16–32 (2010). https://doi.org/10.1007/s10742-010-0063-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10742-010-0063-1