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Ann Thorac Surg 1997;63:903-908
© 1997 The Society of Thoracic Surgeons
Division of Cardiothoracic Surgery, University of Florida Health Science Center, Jacksonville, Florida; University of Colorado Health Science Center, Denver, Colorado; and Summit Medical Systems, Minneapolis, Minnesota
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Abstract |
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 TopFootnotes Abstract IntroductionMaterial and MethodsResultsCommentReferences |
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Methods. Logistic regression analysis was used to develop a risk model for each calendar year. A standard "training set/test set" approach was used for each model.
Results. Five validation techniques were used to evaluate the reliability of the risk models. All models were found to predict operative mortality with good accuracy in this population.
Conclusions. The new risk models for isolated coronary artery bypass operations serve as reliable predictors of operative mortality for the most recent harvest of patient data from The Society of Thoracic Surgeons National Cardiac Surgery Database.
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Introduction |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentReferences |
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The changing profile of patients undergoing cardiac operations requires continuous updating and revision of the models to accurately reflect the current clinical milieu. With each new harvest of data, several different models based on a variety of statistical techniques have been compared. Before the most recent harvest, a Bayesian model had proven most accurate and was made available to participants as an integral part of the software package [1]. The patient data covering the 1990 to 1994 time frame, however, have been most accurately modeled by a logistic regression algorithm. The purpose of this report is to present the data and techniques used to develop this model of CABG operative mortality so that surgeons may be fully informed of the statistical tools used in the most current update of the STS Database.
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Material and Methods |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentReferences |
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). The definition of each risk factor in Table 1 is consistent with published guidelines [2].
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The modeling process followed a standard "training set/test set" approach in which patients were randomly assigned into one of two groups of approximately equal size. The "training set" population was used to develop the model, whereas the "test set" was used to test the model against observed results.
Statistical Analysis System (SAS) software (Version 6.09 for Windows; SAS Institute, Cary, NC) was used for all analyses. Each risk factor contained in the STS Database form was considered for inclusion in the models. A stepwise multivariate analysis of these risk factors was carried out to determine those patient variables that were independently associated with operative mortality. Variables were entered and removed by a stepwise selection process in which residual Wald 
2 p values for entry and retention were 0.2 and 0.1, respectively. These entry and retention values were selected so as to allow liberal inclusion of risk factors in the model.
After determining the appropriate risk factors, a standard stepwise logistic regression analysis was performed using the "training set" population to develop a risk equation of the form:
 | (1) |
where P = the probability of postoperative death; and X = B0X0 + B1X1 + ...BkXk, where each B value is a constant associated with a specific risk factor, and the X values denote the status of the risk factor for a given patient. It should be mentioned that this equation, like any other, consists of constants and variables. The constants (B values) are derived from the patient population, whereas the variables consist of the presence or absence of each risk factor for a given patient. After the risk factors for a specific patient are entered into the model, the mathematic calculations are carried out to yield the predicted probability of operative mortality for that patient. All patients in the "test set" population were used to determine the validity of the model.
Validation of the Models
Risk factors for each patient in the "test set" population were entered into the logistic risk equation to calculate the probability of operative death for that patient. To ensure validity, the models were subjected to several statistical tests.
The most direct approach is simply to compare the predicted mortality against the observed mortality for the entire "test set" population encompassed by the model. As shown in Table 2, there was excellent agreement for each of the models.
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shows the comparison using generally accepted clinical subgrouping. Another well-accepted technique involves the development of subgroups by dividing the population into deciles based on predicted operative mortality [3]. In this approach, the "test set" patients are arranged according to predicted operative mortality and then divided into ten subgroups of equal size. Predicted versus observed results can then be compared for each of the ten deciles (Fig 2).
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), which evaluates the calibration of the model, and the c-index (see Table 3), which assesses the ability of the model to discriminate between possible outcomes.
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Results |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentReferences |
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shows the calculated odds ratios for each of the patient risk factors. As one may see from the table, there was some minor variation in the significant risk factors from year to year. For each year, the patient risk factors found to be significant have an associated odds ratio listed in Table 4; those indices that were not significant have no specified odds ratio.
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; Figs 1, 2). This method of validation is the most direct and meaningful way to assess the clinical reliability of the model.
Other approaches to model validation involve more theoretic statistical techniques. The Hosmer-Lemeshow test determines calibration, which is a measure of performance across the risk spectrum. This test reflects the reliability of the model in low-, moderate-, and high-risk patients. The population is arranged from lowest to highest risk and divided into ten groups of equal size. A 2 test is then applied using a 2 x 10 matrix with 8 degrees of freedom. A p value less than 0.05 indicates a statistically significant deviation in model performance across the risk spectrum. As shown in Table 3, the 1994 model demonstrated poor calibration, but the other tests of validity were very favorable for this model. In particular, its c-index confirms good discrimination (see Table 3) and, most important, there is excellent agreement between predicted and observed results (see Figs 1E, 2E). These favorable validation findings appear to outweigh the issue of calibration in this case, and one may justifiably conclude that the 1994 model is a reliable predictor of CABG operative mortality.
The c-index reflects the ability of the model to discriminate between possible outcomes (survival versus nonsurvival in this case). A useless model would have a c-index of 0.5, indicating that the model would predict one outcome to be just as likely as any other. A c-index of 1.0 would be found in a "perfect" model. Generally, values greater than 0.75 are consistent with an excellent ability to discriminate between possible outcomes. In each of the five STS models, the c-index was in this range (see Table 3).
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Comment |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentReferences |
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Risk-assessment models are most commonly used as a quality assurance/quality improvement tool. In this setting, data from a group of patients are run through the model to determine the predicted mortality adjusted for patient risk. Practically speaking, if this predicted mortality is X percent, the following may be stated: "Based on the accumulated national experience of the STS Database, a group of patients having these risk factors would be expected to have an operative mortality of X percent." The extensive nature of the STS Database and the scrutiny to which its data are subjected suggest that this predicted mortality represents an acceptable standard. Predicted mortality is then compared with the actual observed mortality. There is universal agreement that this method of risk stratification is absolutely essential for a meaningful analysis of operative results.
Risk assessment is a continuous process in which the harvest of new data necessitates a reassessment of modeling techniques. New patient data are brought into the STS Database annually. These new data are analyzed, modeled, and tested with a variety of statistical algorithms. The technique that provides the best results is presented to the STS National Database for Thoracic Surgery Committee and to the STS Database Liaison Committee for further examination. Upon approval, thenew models are made available to STS Database participants.
The initial models were based on a Bayesian algorithm and generally performed very well [1]. One of the major advantages of Bayesian models is the ability to handle incomplete data, which were more common in the early stages of database development. In recent years, more careful data entry, better familiarization with the process, and detailed auditing techniques have led to a marked improvement in data quality. Possibly because of this enhanced data quality, we have found that Bayesian advantages now have a lesser impact, and logistic regression techniques are most suitable for modeling current patient data.
In conclusion, the latest risk models developed from the STS Database provide a reliable and statistically valid method to stratify CABG patients into appropriate risk categories. These predictive models of CABG operative mortality have become practical tools that surgeons may use to analyze operative results, facilitate patient counseling, and enhance medical decision making.
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Footnotes |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentReferences |
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A. L. W. Shroyer, F. L. Grover, and F. H. Edwards 1995 Coronary Artery Bypass Risk Model: The Society of Thoracic Surgeons Adult Cardiac National Database Ann. Thorac. Surg., March 1, 1998; 65(3): 879 - 884. [Abstract] [Full Text] [PDF]
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