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The Statistician's Page

Cumulative Sum Curves and Their Prediction Limits

Medical Data Research Center, Providence Health & Services, Portland, Oregon

^_* Address correspondence to Dr Wu, 9205 SW Barnes Rd, Suite 33, Portland, OR 97225 (Email: yingxing.wu@providence.org).

The first 300 words of the full text of this article appear below.

	Introduction

 
In this issue of The Annals of Thoracic Surgery, Dr Brevig and colleagues [1] describe their program to reduce blood transfusions in cardiac surgery. Their analysis of the changes in operative mortality during this process uses the risk-adjusted cumulative sum (CUSUM) of observed minus expected deaths. We previously discussed this method [2], but the "bullet-shaped" prediction limits that we used, which give rise to an expanding interval over time, raised some concern. Recently a statistically sophisticated cardiac surgeon asked, "Why do these intervals get wider, rather than narrower, as the number of patients increase?" The December 2004 issue of The Journal of Thoracic and Cardiovascular Surgery contained five important and enlightening articles on CUSUM methods, including a tutorial [3], two commentaries [4, 5], a clinical article [6], and an editorial [7]; the latter called the bullet-shaped prediction limits "nonintuitive." The present study was undertaken primarily to convince us that these bullet-shaped prediction limits are indeed reasonable and appropriate. Our secondary purpose is to provide a basic introduction to the CUSUM method of risk-adjustment, and to illustrate the concepts underlying this important analytical and graphical methodology.

	Risk Adjustment

 
Measuring the results of a surgical intervention is essential to determining its effectiveness. Public reporting and comparisons are proceeding, with the ultimate goal of identifying the best providers, whose permissions and reimbursements might be determined by their results. For this task, risk adjustment is imperative; because of differences in patient profiles, no two patients, and thus their intrinsic risks of death and other complications, are exactly the same. Among medical procedures, cardiac surgery has led the way in this area, contributing many risk models for mortality and other serious complications. For each patient, these risk models provide a predicted probability of the . . . [Full Text of this Article]

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Blood Transfusion Reduction in Cardiac Surgery: Multidisciplinary Approach at a Community Hospital

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Ann. Thorac. Surg. 2009 87: 532-539. [Abstract] [Full Text] [PDF]

This article has been cited by other articles:

				R. Jin, A. P. Furnary, S. C. Fine, E. H. Blackstone, and G. L. Grunkemeier Using Society of Thoracic Surgeons Risk Models for Risk-Adjusting Cardiac Surgery Results Ann. Thorac. Surg., March 1, 2010; 89(3): 677 - 682. [Abstract] [Full Text] [PDF]