Ann Thorac Surg 2003;75:1820-1825
© 2003 The Society of Thoracic Surgeons
Original article: cardiovascular
A simple model to predict coronary disease in patients undergoing operation for mitral regurgitation
Eric Lim, MB ChB, MRCSa*,
Ziad A. Ali, MB ChBa,
Clifford W. Barlow, DPhil, FRCS (CTh)a,
Christopher H. Jackson, PhDb,
Amir-Reza Hosseinpour, FRCSa,
James C. Halstead, MRCSa,
John B. Barlow, MD, FRCPc,
Francis C. Wells, MS, FRCSa
a Department of Cardiothoracic Surgery, Papworth Hospital, Cambridge, United Kingdom
b Medical Research Council Biostatistics Unit, Cambridge, United Kingdom
c Division of Cardiology, Department of Internal Medicine, University of Witwatersrand and Johannesburg Hospital, Johannesburg, South Africa
Accepted for publication January 16, 2003.
* Address reprint requests to Mr Lim, Department of Cardiothoracic Surgery, The Royal Brompton Hospital, Sydney Street, London SW3 6NP, United Kingdom.
e-mail: ericlim2{at}hotmail.com
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Abstract
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BACKGROUND: Coexistent coronary disease can be identified in a third of patients with mitral valve disease. This study aims to evaluate candidate selection strategy using risk factor identification and logistic regression and to develop an additive model for the prediction of coexistent coronary disease.
METHODS: The sample is a consecutive series of patients who had mitral repair from 1987 to 1999. Sensitivities and specificities were calculated for each risk factor. Variables for prediction of coronary disease were entered into a univariate analysis, and predictors were entered into a forward and backward stepwise multivariate logistic regression model to form a predictive score. An additive model was derived from transformation of the logistic model. Receiver operating characteristic curves were used to compare discrimination and precision quantified by the Hosmer-Lemeshow statistic.
RESULTS: The American Heart Association and American College of Cardiology risk factor identification selection criteria for the 359 patients who had screening coronary angiography yielded 100% sensitivity and 1% specificity. Risk prediction with our logistic model produced a receiver operating characteristic curve area of 0.91 and Hosmer-Lemeshow score of 3.4 (p = 0.9). Similar discriminating ability for our patients was achieved by the Cleveland Clinic logistic model (receiver operator characteristic curve area of 0.79; Hosmer-Lemeshow score of 12; p = 0.1). Our five-item additive model produced receiver operating characteristic curve area of 0.91 and Hosmer-Lemeshow score of 3.81 (p = 0.80).
CONCLUSIONS: Simple risk factor identification has excellent sensitivity but is limited by specificity. Logistic regression modeling is an accurate risk prediction method but is difficult to apply at the bedside. Simplicity and accuracy may be achieved by the logistic regression-derived simple additive model.
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Introduction
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Coexistent coronary disease can be identified in up to a third of patients with mitral valve disease [1,2]. Ischemic heart disease is not only important as an etiology for mitral regurgitation but is also an independent predictor of mortality [3]. The presence of significant coronary stenosis alters the operative strategy, requiring revascularization in addition to valve operation, and increases operative risk [4]. Accurate identification of the presence of significant coronary disease is therefore an important component of the workup to mitral valve operation.
Recent advances in the diagnostic utility of echocardiography have helped to establish it as the standard noninvasive diagnostic tool for the assessment of valvular regurgitation [5]. The ability of echocardiography to diagnose and quantify the severity of regurgitation may obviate the need for cardiac catheterization in most patients [6]. Therefore screening coronary angiography is now undertaken as an additional procedure for selected patients scheduled for mitral valve operation who are at risk of coronary artery disease.
Controversy exists regarding the target population at risk of coexistent coronary disease in mitral regurgitation. It has been suggested that all patients with operable mitral valve disease should undergo screening angiography [7], whereas others recommend age as the sole indication [8]. Currently, the most widely used criteria are the American Heart Association and the American College of Cardiology (AHA/ACC) guidelines, where patients are selected for screening angiography based on risk factor identification [9]. The Cleveland Clinic group recently described a logistic regression model to increase the accuracy of risk prediction and further refine the selection process [10].
The aims of this study are to (1) evaluate the strategies of candidate selection for screening angiography in patients undergoing surgical repair for mitral regurgitation using risk factor identification (AHA/ACC guidelines) and logistic regression modeling and (2) to develop an additive model for the prediction of coexistent coronary artery disease.
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Material and methods
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The sample population was identified from a database consisting of a consecutive series of patients who had mitral valve repair between 1987 and 1999 by a single surgeon (FCW). Routine screening coronary angiography was performed as standard procedure for patients scheduled for elective mitral valve operation. Experienced cardiologists reviewed coronary angiograms, and the degree of luminal narrowing was obtained by visual estimation. The presence of significant coronary disease was defined as luminal narrowing of 50% in two or more views. Of 400 patients, angiographic details were unavailable in 12 (3%), and 29 (7.5%) had no angiography because of emergent status (24 with and 5 without AHA/ACC defined indications). Therefore angiographic data were available in a total of 359 (92.5%) patients.
Risk factors for coronary artery disease were defined as follows: age (35 years or more for men, 51 years or more for women), family history (first-degree relative with a myocardial infarction before the age of 50 years in men and 60 in women), smoking, diabetes, and hypercholesterolemia (defined as receiving medication for hypercholesterolemia or serum cholesterol of 5.0 mmol/L [193 mg/dL] or more). Evaluated AHA/ACC indications were history of angina or myocardial infarction or the presence of one or more risk factors for coronary artery disease. The presence of ischemic changes on echocardiography (ECG) was defined as resting ST or T wave abnormalities on the ECG. Etiology for mitral regurgitation was determined by operative assessment in conjunction with histopathologic examination of valve specimens.
Statistical methods
Sensitivities, specificities, and likelihood ratios were calculated for each of the AHA/ACC criteria for screening angiography. The analytic methods used to create and validate the logistic regression model were based on the work by Lin and colleagues [10]. Clinical variables for the prediction of coexistent coronary artery disease were entered into a univariate analysis. The criterion for variable retention was significance at the 0.2 level. Predictors of coronary artery disease were then entered into a forward and backward stepwise multivariate logistic regression model. Independent predictors were included in the following multivariate model:
where 
is a constant, ß is the coefficient of the variable, and X represents the respective variables. The percentage risk of coexistent coronary artery disease risk is calculated as:
Refinement of our model was undertaken using the bootstrapping technique [11], which utilizes 1,000 random samples to assess the stability of our odds ratio estimates with random variation.
Creating an additive model
We created an additive model by using 100% sensitivity as a criterion and using a probability of coexistent coronary artery disease of greater than 0.02 as a cut off. Age was reclassified into intervals of 5 years over the age of 50 years; each beta coefficient was multiplied by a factor of two and rounded to the nearest whole number.
Comparing the various models
Receiver operating characteristic (ROC) curves were used to compare discrimination of the AHA/ACC guidelines, our logistic model, Lin’s logistic model [10] (on both the general population and that of degenerative disease alone), and our simple additive model for the prediction of coexistent coronary artery disease. Precision was quantified by the Hosmer-Lemeshow goodness-of-fit statistic for each of the specified models.
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Results
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The analyses were based on angiographic data obtained from 359 patients. Baseline characteristics of our population are presented in Table 1.
Risk factor identification
The AHA/ACC risk factor identification selection criteria for the 359 patients who had screening coronary angiography yielded 100% sensitivity and 1% specificity. The proportion of patients fulfilling the criteria of angina or previous myocardial infarction or more than one risk factor was 99.4%. Similar results could be achieved by using age as the single criterion for angiography with 98.1% proceeding to angiography, yielding 100% sensitivity and 3% specificity.
In 248 patients without a history of angina or previous myocardial infarction, the risk factors, in decreasing order of utility (likelihood ratio positive) for the prediction of coexisting coronary disease, were hypertension (1.98), hypercholesterolemia (1.85), smoking (1.77), diabetes (1.30), and family history (1.01). The results are summarized in Table 2.
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Table 2. Sensitivities, Specificities, and Likelihood Ratios for American Heart Association and the American College of Cardiology Guidelines
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Logistic regression modeling
The univariable risk factors for the prediction of coexistent coronary disease are presented in Table 3.
Using logistic regression, diabetes did not reach the significance cut-off for variable retention. Using multivariable logistic regression, the best fit yielded the following predictive model:
Further validation using bootstrapping provided similar results confirming the stability of the odds ratios of our model with random variation and is presented in Table 4.
Our additive model
With 100% sensitivity as a criterion, we chose a probability of coexistent coronary disease of greater than 0.02 as a cut-off. The logistic regression equation was modified accordingly and simplified into an additive model of five variables, presented in Table 5.
A score of 3 or more would be an indication for angiography. Details of the derivation from ordinal logistic regression are available in the Appendix.
Comparison of discrimination between the various models
Our logistic regression model produced an ROC area of 0.91 (Fig 1). The Hosmer-Lemeshow test revealed good fit with a value of 3.4 (p = 0.9). Similar discriminating ability was achieved by Lin’s model on our unselected patient population (ROC area of 0.79) and our patients with degenerative disease (ROC area of 0.77). The Hosmer-Lemeshow statistic revealed good fit for both populations with values of 12 (p = 0.1) and 6.5 (p = 0.6), respectively. The simple additive model yielded similar goodness of fit and discrimination, with a Hosmer-Lemeshow score of 3.81 (p = 0.80) and ROC area of 0.91.
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Comment
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Surgically important lesions of the coronary arteries that are not revascularized are associated with diminished survival in patients who have mitral valve operations [4]. Therefore, screening guidelines aim to produce recommendations that identify all patients with coexistent coronary disease (complete sensitivity). However, this is often undertaken at the expense of unacceptably low specificity, resulting in many patients being exposed to the morbidity and cost of an additional investigation.
Simple risk factor identification is the most widespread strategy for the selection of patients to undergo screening angiography before mitral valve operation. Although this is an excellent method to correctly detect the presence of concomitant coronary artery disease, the limited clinical utility of this approach is best reflected by its likelihood ratio of 1.01 (a ratio of 1.0 implies a test of no diagnostic utility) with similar results obtained by using only age as a criterion.
One of the best predictive features of coexistent coronary disease is a history of angina, even though it has been regarded by many to be unreliable in the presence of mitral regurgitation [8]. Interestingly, we expected a history of previous myocardial infarction to be completely predictive of coexistent coronary disease, but this held true in only 95% of cases. However, the overall discriminating ability of any single risk factor for the presence of coronary arterydisease is disappointing, as most of our patients had one or more risk factors.
Logistic regression models have been used to provide a more accurate estimation for the presence of coronary artery disease [10, 12]. We have validated the model proposed by Lin and colleagues on our patients, resulting in congruent discriminatory power, even though their model was derived from a cohort of patients with isolated degenerative disease. The clinical applicability of a model derived from an unselected cohort of patients (including candidates with coronary artery disease as an etiologic factor for mitral regurgitation) is greater, as it may be difficult to determine the definitive etiology with any certainty before operative and histopathologic assessment.
Predictive accuracy of logistic regression models has its own limitation and can be compromised by converting continuous values (systolic and diastolic blood pressure, serum cholesterol levels) into dichotomous variables (eg, hypertensive, normotensive, hypercholesterolemic, normocholesterolemic). Moreover biologic measurements fluctuate, interact with other variables (such as cholesterol and high-density lipoprotein), and are potentially modifiable by medication, all contributing to the limitation of the precision of risk estimation. To account for each and every variable and interaction would produce a model that would be too cumbersome for clinical use.
However, the versatility of logistic regression prediction can be utilized to determine levels of risk and direct clinical decisions. The model of Lin and colleagues, using a 5% risk cut off, eliminated approximately one third of patients for screening but at the cost of missing 1.3% patients with significant coronary artery disease. Although no patient with a prognostically significant configuration was missed, the mathematical model does not take into account number, site, or severity of stenosis (apart from significant disease). In our logistic model, we used a more conservative cut off at 2% probability of coexistent coronary disease while achieving a sensitivity of 100%. Compared with the AHA/ACC guidelines, the overall reduction in the frequency of angiography was 11% Table 6
(Table 6).
Clinical implications
The main benefit of risk factor identification for the selection of candidates for screening angiography is simplicity and sensitivity (at the expense of specificity). Although logistic regression estimates of risk are much more accurate, bedside calculation of clinical risk is cumbersome. Using a simple additive model, the simplicity of risk factor identification is combined with the accuracy of logistic regression.
As mathematical modeling can specify different cut-offs for various risks, ultimately the balance of risk and benefit rests on the decision of how many patients a clinician is prepared to expose the morbidity and cost of screening angiography to identify significant coexistent coronary disease.
Potential limitations
Evaluation of our risk models was undertaken in a cohort of patients extracted from a specific mitral valve repair database that did not include mitral valve replacements. However, studies have shown that patients who had mitral repair had greater frequency of concomitant coronary artery revascularization and more severe disease compared with patients who had mitral valve replacement [13, 14]. In our sample population, diabetes was not found to be a predictor of coronary artery disease by using logistic regression analysis, and this may be due to the relatively small number of diabetic patients in our cohort.
Although we achieved 100% sensitivity with our model, further validation of our logistic regression–derived simple additive model in other populations would be desirable to assess the performance of our scoring system in different populations.
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Conclusions
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Simple risk factor identification (AHA/ACC guidelines) has excellent sensitivity to detect coexistent coronary artery disease in patients but is limited by specificity, thereby exposing many patients to the morbidity and cost of coronary angiography. Logistic regression modeling is an accurate risk prediction method but is difficult to apply at the bedside. Simplicity and accuracy may be achieved by our logistic regression–derived simple additive model.
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Acknowledgments
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The authors would like to acknowledge the contribution of Christopher Jackson for the derivation of the simple additive model.
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Appendix
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Derivation of the simple additive model
With 100% sensitivity as a criterion, we chose a probability of coexistent coronary artery disease of greater than 0.02 as a cut off. This corresponded to a model score of –3.9. To determine the logistic score required to achieve these values, 3.9 was subtracted from the original intercept, to yield the following expression:
Age was then rescaled as a variable with intervals of 5 years when above 50 years old (Interval age = [age at operation –50]/5). The equation was modified using principles of algebra as follows:
Multiplying each coefficient by a factor of 2 and rounding off the values to the nearest whole number, we created a simple additive model as presented in Table 5. A model score of 3 or more would be an indication for angiography. Echocardiographic evidence of ischemia yielded a score of 6. However, any score more than 3 would be an indication for angiography; therefore, we reassigned this variable a value of 3 to simplify the values in our additive model.
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Abstract
Introduction
