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Ann Thorac Surg 2000;69:823-828
© 2000 The Society of Thoracic Surgeons

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Original Articles

Bedside estimation of risk as an aid for decision-making in cardiac surgery

^a Division of Surgical Research, Newark Beth Israel Medical Center, Newark, New Jersey, USA

Address reprint requests to Dr Bernstein, Newark Beth Israel Medical Center, 201 Lyons Ave, Newark, NJ 07112
e-mail: adbnbi{at}idt.net

	Abstract

Top Abstract Introduction Material and methods Results Comment References

 
Background. Evaluations of the cardiac-surgery mortality rates of hospitals and surgeons can be fair and realistic only when the observed mortality rates are compared with expected rates with preoperative risk factors taken into account. Risk-approximation calculations also can assist patients and physicians in discussing the risk of cardiac surgery, especially if the estimation of surgical mortality takes all of the important risk factors into account.

Methods. A logistic regression model was developed in which 47 potential risk factors were considered, and a method requiring only simple addition and graphic interpretation was designed for approximating the estimated risk easily and quickly, with paper and pencil alone.

Results. The estimates provided by the simplified model correlated well with the observed mortality rates.

Conclusions. A simple approximation of a logistic regression model has been found to be helpful in discussions between physicians and patients contemplating aortocoronary bypass or valve-related surgery.

	Introduction

Top Abstract Introduction Material and methods Results Comment References

 
The manifest need for risk-adjusted outcome evaluation in open-heart surgery has prompted the use of several statistical approaches in the retrospective and prospective estimation of operative mortality based on preoperative risk factors [1–9]. Predictive models are often used to compare the quality of care provided by individual institutions and surgeons in attempts to avoid the misunderstandings that can result from consideration of raw mortality rates alone.

Several problems in modeling preoperative risk have emerged. First, the acquisition of valid data requires clearly defined and uniformly applied definitions. This can best be accomplished when the risk factors (covariates) considered are amenable to objective measurement using standards recognized by all participants and applied in a uniform fashion. Second, the inclusion of covariates based even partly on subjective judgment, such as unstable angina, diffuseness of disease, and chronic obstructive pulmonary disease, contributes uncertainty that compromises the validity of the model. Third, the incorporation of generalized, extremely subjective risk factors such as operative priority contributes not only uncertainty but collinearity as well if those factors are represented implicitly elsewhere in the model. Fourth, the inclusion of covariates of this type that duplicate or reinforce other covariates already present in the model inevitably results in overestimation of preoperative risk.

Three additive (ie, linear) and progressively accurate models developed at our center have been used since 1989 for comparing cardiac surgery outcomes among hospitals and surgeons [10–12]. The most recent and contemporary model, described in this article, was derived by logistic regression, after which an approximate version of the model was then used as the basis for a simple paper-and-pencil method devised to estimate the risk of surgical mortality faced by an individual patient, as an aid to patients and physicians contemplating cardiac surgery.

	Material and methods

Top Abstract Introduction Material and methods Results Comment References

 
Statistical modeling
Data regarding 47 potential risk factors were acquired from 10 New Jersey centers for all consecutive open-heart procedures performed in 1994 and 1995. Among these were aortocoronary bypass (ACB), valve replacement or repair (VLV), and combinations of the two (COM) performed on 10,703 patients during those 2 years. The data were subjected to error-trapping routines and corrections then were made by the contributing hospitals. Data plausibility was assessed by analyzing the variations in risk-factor frequencies reported by the participating centers. In reporting risk factors, unreported factors were indistinguishable from factors actually absent, but the participating hospitals were motivated to provide complete profiles to avoid underestimation of expected mortality rates that might compare unfavorably with their observed mortality rates. Surgical mortality was defined as death at any time during the same hospital admission.

Every third patient record was separated out for use as a test set. Logistic regression was performed on the remaining 8,593 records with all covariates forced into the model (ie, stepwise regression was not used). For simplicity in calculation with the ultimate approximate model, every risk factor was expressed in dichotomous form. This required that continuous variables such as age and ejection fraction be separated into contiguous, mutually exclusive ranges. The resulting logistic regression model, designated System 97, is summarized in Table 1, together with the frequency of occurrence of each risk factor considered. The observed mortality rates were similar in the training (5.3%) and test (5.1%) sets.

Approximation of preoperative risk for use in discussions with patients
The logistic regression model described above was simplified to facilitate the rapid approximation of preoperative risk in discussions with patients or their families. All coefficients were rounded to the nearest half-integer and multiplied by 10, and some infrequent risk factors with negative coefficients (which occur rarely; see Table 1) were omitted. Two covariates with negative coefficients were assigned new weights on an empirical basis: refusal of blood products and repair of a ventricular septal defect were adjudged of equivalent risk to pulmonary hypertension and cardiogenic shock and were assigned the same weights (11 and 12, respectively). These empirical adjustments, based on clinical experience, were made only in low-prevalence covariates whose logistic regression coefficients had large standard errors. As shown below, these adjustments made predictions obtained by means of the approximate model more realistic than those determined using the original logistic regression model. A graph was plotted to allow the determination of the estimated risk from the total score obtained by summing the individual scores for the risk factors present. In calculating the curve shown in the graph, an adjustment was made to take the constant logistic regression intercept into account. A pair of curves was derived by polynomial regression from the binomial confidence limits calculated from the observed mortality rates to allow the determination of confidence limits associated with the risk estimates. Pocket-sized cards were made up for convenience during bedside consultations.

	Results

Top Abstract Introduction Material and methods Results Comment References

 
Figure 1 shows the expected and observed mortalities as calculated for the training set using the logistic regression model System 97. The accompanying table shows the corresponding ratios of observed to expected mortality rates (O/E ratios) for the same subgroups. This quantity, being normalized for expected risk, is useful for comparing the outcomes of surgery among hospitals or surgeons. In Figure 1, 95% binomial confidence limits calculated from observed mortality are superimposed. The new model was found to fit the observed mortality rates closely. The "C" statistic for the model (ie, the area under the receiver operating characteristic curve) was 0.811 for the training set and 0.785 for the test set. Because the observed mortality rates were lower than in previous studies, the expected-risk ranges chosen for displaying results were revised downward (0% to 3%, 3% to 6%, 6% to 9%, and > 9% instead of 0% to 5%, 5% to 10%, 10% to 15%, and > 15%, as used in past years) to achieve a realistic distribution of patients among the contiguous ranges.

View larger version (34K): [in this window] [in a new window]   Fig 1. Expected () and observed (•) mortality rates with 95% binomial confidence limits for aortocoronary bypass, valve, and combination procedures performed in 1994 and 1995 at 10 New Jersey hospitals. The risk ranges shown are used only for comparison of observed and estimated mortality rates. No ranges were involved in deriving the approximate model described in the text. (O/E = ratio of observed to expected mortality rates.)

View larger version (81K): [in this window] [in a new window]   Fig 2. Form for use in preoperative estimation of surgical risk. (A) Front; (B) Back. A similar worksheet derived from more recent (1996–1997) data may be obtained from the authors. (ACB = aortocoronary bypass; COPD = chronic obstructive pulmonary disease; CVA = cerebrovascular accident; IABP = intraaortic balloon pump; LV = left-ventricular; MI = myocardial infarction; PTCA = percutaneous transluminal coronary angioplasty.)

	Comment

Top Abstract Introduction Material and methods Results Comment References

The simplified model provided on a pocket-sized card (Fig 2) for assistance in estimating preoperative risk for open-heart surgery during preoperative discussions with patients is intended as an adjunct to clinical judgment based on experience, not as a substitute for it. The application to an individual patient of statistical estimates derived for cohorts of patients is questionable even when confidence intervals are provided. For example, the 95% confidence interval does not mean that there is a 95% probability that a single patient whose risk factors put him or her in a particular range of expected-mortality values will have the probability of mortality observed for patients in that range. It means only that if the experiment from which the confidence limits were derived is repeated (ie, another equivalent set of the same number of patients with the same risk factors is operated on in the same way by the same surgeons), there is a 95% probability that the mortality rate will fall somewhere within the confidence-limit range [13].

An example of the use of the form is shown in Figure 3. The total score (17) is determined on the first page by adding the individual scores associated with the four preoperative risk factors present in this example: female gender, age between 76 and 79 years, hypertension, and morbid obesity. Entering the graph on the reverse side of the form at 17 on the horizontal axis, as shown in Figure 4, the range of expected risk is estimated as approximately 2.5% to 3.5% by reading the corresponding values of the confidence-limit bands on the vertical axis. Because both System 97 and the bedside approximation are nonlinear predictive models, simple summations of the System 97 coefficients and bedside-approximation scores shown cannot be interpreted as estimates of the likelihood of operative mortality, but must be processed numerically or graphically by the appropriate logistic-regression formulas.

View larger version (45K): [in this window] [in a new window]   Fig 3. Example of the use of the bedside form: calculation of a patient’s total score. (ACB = aortocoronary bypass; COPD = chronic obstructive pulmonary disease; IABP = intraaortic balloon pump.)

View larger version (28K): [in this window] [in a new window]   Fig 4. Detail showing how to determine the estimated risk (vertical axis, approximately 2.5% to 3.5%) from the total score calculated by adding the appropriate risk-factor scores shown on the worksheet in Figure 3.

View larger version (27K): [in this window] [in a new window]   Fig 5. Scatter plot comparing the bedside approximation with System 97 estimates for 200 actual consecutive aortocoronary bypass procedures at a single hospital in 1996. The three outliers are addressed in Table 2.

There has been steady improvement in the results achieved by open-heart surgery from year to year in New Jersey. This evolution, together with the concomitant change in patient-risk profiles, makes it important to derive predictive models such as those discussed above periodically, using "training" sets of actual data based on successive and most recent years for which the data are complete. Although time must be allowed for optimizing the accuracy of the data through error checking and plausibility analysis, it is appropriate to derive updated models each year based on data sets "rolled forward" a year at a time.

In conclusion, the results of this study show that the use of logistic regression followed by the translation of the regression model into a simplified form that can be used with paper and pencil provides a potentially valuable resource for use in decision-making regarding cardiac surgery. Because two-thirds of patients who undergo cardiac surgery have no more than four risk factors, this method is both rapid and convenient. At the same time, its estimates reflect observed operative-mortality rates far more closely than did earlier linear models based on the assumption of risk factor independence. This approximation is extremely useful in preoperative discussions with patients and their families, assisting the surgeon in providing a realistic estimate of the potential risk of surgery.

	Acknowledgments

 
The authors acknowledge their indebtedness to the Sagamore Foundation and the New Jersey Department of Health and Senior Services for providing funding for this research, and to Mr Michael Gera for his assistance in the acquisition and initial processing of the data used in the study.

	References

Top Abstract Introduction Material and methods Results Comment References

 

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