Relevance of the C-Statistic When Evaluating Risk-Adjustment Models in Surgery

• Published in: Journal of the American College of Surgeons Vol. 214; no. 5; pp. 822 - 830
• Main Authors: Merkow, Ryan P., MD, Hall, Bruce L., MD, PhD, MBA, FACS, Cohen, Mark E., PhD, Dimick, Justin B., MD, MPH, FACS, Wang, Edward, PhD, Chow, Warren B., MD, MS, Ko, Clifford Y., MD, MS, MSHS, FACS, Bilimoria, Karl Y., MD, MS
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.05.2012; Elsevier
• Subjects: Adult; Aged; Biological and medical sciences; Calibration; Cohort Studies; Colorectal Surgery - mortality; Elective Surgical Procedures - mortality; Female; General aspects; Humans; Male; Medical sciences; Middle Aged; Models, Statistical; Outcome Assessment (Health Care) - methods; Quality Improvement - statistics & numerical data; Risk Adjustment - methods; Surgery; Medicine; Relevance; Treatment; Surgery; Risk factor; Risk; Models; Statistics
• ISSN: 1072-7515; 1879-1190
• DOI: 10.1016/j.jamcollsurg.2011.12.041

Background The measurement of hospital quality based on outcomes requires risk adjustment. The c-statistic is a popular tool used to judge model performance, but can be limited, particularly when evaluating specific operations in focused populations. Our objectives were to examine the interpretation and relevance of the c-statistic when used in models with increasingly similar case mix and to consider an alternative perspective on model calibration based on a graphical depiction of model fit. Study Design From the American College of Surgeons National Surgical Quality Improvement Program (2008−2009), patients were identified who underwent a general surgery procedure, and procedure groups were increasingly restricted: colorectal-all, colorectal-elective cases only, and colorectal-elective cancer cases only. Mortality and serious morbidity outcomes were evaluated using logistic regression-based risk adjustment, and model c-statistics and calibration curves were used to compare model performance. Results During the study period, 323,427 general, 47,605 colorectal-all, 39,860 colorectal-elective, and 21,680 colorectal cancer patients were studied. Mortality ranged from 1.0% in general surgery to 4.1% in the colorectal-all group, and serious morbidity ranged from 3.9% in general surgery to 12.4% in the colorectal-all procedural group. As case mix was restricted, c-statistics progressively declined from the general to the colorectal cancer surgery cohorts for both mortality and serious morbidity (mortality: 0.949 to 0.866; serious morbidity: 0.861 to 0.668). Calibration was evaluated graphically by examining predicted vs observed number of events over risk deciles. For both mortality and serious morbidity, there was no qualitative difference in calibration identified between the procedure groups. Conclusions In the present study, we demonstrate how the c-statistic can become less informative and, in certain circumstances, can lead to incorrect model-based conclusions, as case mix is restricted and patients become more homogenous. Although it remains an important tool, caution is advised when the c-statistic is advanced as the sole measure of a model performance.