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Eur J Cardiothorac Surg 2004;26:1134-1140
© 2004 Elsevier Science NL

Logistic versus additive EuroSCORE. A comparative assessment of the two models in an independent population sample

Bartolo Zingone*, Aniello Pappalardo, Lorella Dreas

Division of Cardiac Surgery, Department of Cardiology, Ospedali Riuniti di Trieste, Trieste, Italy

Received 9 July 2004; received in revised form 1 September 2004; accepted 1 September 2004.

* Corresponding author. Vicolo degli Scaglioni, 22, 34141 Trieste, Italy, Tel.: +39 040 3994856; fax: +39 040 3994995. (E-mail: bartolo.zingone{at}aots.sanita.fvg.it).


   Abstract
Top
 Abstract
1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Limitations
 6. Conclusion
 References
 
Objective: Validation of EuroSCORE outside the boundaries of the original database has been limited to the additive model and has occasionally shown inconsistencies. Therefore we sought to validate the logistic model and assess its predictive performance compared to the additive approach. Methods: Twenty-four hundred and twenty-six consecutive patients were prospectively assigned individual expected risks of dying calculated by the logistic and the additive EuroSCORE algorithms. Discriminating ability of the two models was tested by Receiver Operating Characteristic (ROC) curves. Calibration was assessed by the Hosmer–Lemeshow (H-T) test and further explored by additional cross-tabulations. A percent difference among the estimates was calculated and plotted across score groups. The series was then sorted by date of operation and split in halves to separately explore the potential effect of variation of performance. Results: Observed mortality (5.6%) was not significantly different from the additive (5.3%) and the logistic estimates (6.9%). Both models satisfactorily discriminated outcomes (ROC areas of 0.80 and 0.79 for the logistic and the additive model, respectively). The H-T test showed that calibration was good for the logistic model (P=0.12) but turned out being inadequate for the additive model (P<0.0001). Further cross-tabulations confirmed a good correlation among observed and predicted death rates by the logistic model across all groups. The additive model, on the other hand, revealed a propensity to over-predict in medium-risk categories and under-predict in the very high-risk cases. Direct comparison of additive vs logistic estimates showed a similar behaviour demonstrating it as an intrinsic property of the additive approach. The split-file analysis revealed a significantly improved outcome for patients treated in the second half of the series though the predictive performance of the two models was unaltered. Conclusions: Logistic EuroSCORE reliably predicted outcomes in our series despite the higher risk profile compared to the reference EuroSCORE sample and the observed variation in clinical performance during the study period. The additive model was less precise, exhibiting a predictive distortion which should be accounted for, particularly when employing it at the individual patient level.


   1. Introduction
Top
 Abstract
 1. Introduction
2. Methods
 3. Results
 4. Discussion
 5. Limitations
 6. Conclusion
 References
 
EuroSCORE has gained wide popularity among risk-stratifying tools due to its ability to deal with almost the entire caseload of any adult cardiac surgery program, coupled with the ease of use of its simple additive algorithm [1,2]. It has also been repeatedly validated in a number of diverse population samples [3], and has successfully passed the comparison with a number of both proprietary and public domain competing models [4,5].

Although the predictive accuracy of EuroSCORE is now firmly established, it should be appreciated that the additive model alone has been subjected to validation out of the boundaries of the original database [3]. In addition to this, inconsistencies have been found among the popular additive version and the logistic model when applied to the higher risk segment of the original study population in the EuroSCORE database [3,6]. Indeed, details of the full logistic model including the numeric coefficients required to run the procedure had not been available before a recently published report [7].

We have been fortunate in obtaining the logistic EuroSCORE model as early as of January 1999 (P Michel, personal communication), and have used it prospectively within our quality improvement program ever since. We deemed therefore useful to report upon the first external validation of the logistic EuroSCORE in an independent population sample and comparatively assess the additive approach in the same dataset.


   2. Methods
Top
 Abstract
 1. Introduction
 2. Methods
3. Results
 4. Discussion
 5. Limitations
 6. Conclusion
 References
 
All patients operated upon in the period January 1999–April 2004 were prospectively enrolled in a dedicated database for the purpose of monitoring outcomes in our practice. The database had been running for some time and already included six different prognostic systems with their logistic models by the time EuroSCORE became available.

Data were collected at the time of surgery on a standardised A4 form by the surgeon's first assistant and next inputted in a PC database. Stored data were formatted (or subsequently transformed) so as to comply with the sometimes differing definitions stated from the various models. Data supervision was performed by the project coordinator for consistency, and aggregate outputs were periodically cross-checked against an independent clinical database.

The outcome of interest, death early after surgery, was defined as that occurring at any time during the hospital stay or within 30 days since surgery for discharged patients. Hospital stay includes transferral to other units and, occasionally, to other hospitals. Vital status of discharged patients was ascertained at ≥30 days by phone interviews. Predictors were prospectively defined according to EuroSCORE criteria but for extra-cardiac arteriopathy, for which the absence of peripheral pulses was also added to the set of criteria [1]. Missing categorical variables were considered absent. Moderate or severe left ventricular dysfunction were assigned by semi-quantitative echocardiographic or angiographic assessment in 144 and by any available measurement of ejection fraction in 620 cases.

The dataset was eventually imported and analysed in SPSS 10.1 (SPSS Inc, Chicago, IL). The individual probabilities of death were estimated by running a syntax code incorporating the regression coefficients and intercept developed by EuroSCORE [7]. An individual score was also calculated by a simple additive SPSS syntax. The percent difference among the two model estimates was computed on a patient basis by the formula: (logistic estimate–additive score)/logistic estimate.

The discriminating ability of the logistic and additive models was assessed by separately developing Receiver Operating Characteristic (ROC) curves [8]. Calibration was formally assessed by the Hosmer–Lemeshow test with 8 Degrees of Freedom comparing observed and predicted deaths in risk deciles separately generated for each model [9]. In order to provide additional insight two further grouping strategies were adopted, first by using a clinical risk classification generating low-, medium-, high-, and very high-risk groups based on additive scores [6]. Next, smaller interval scales were used to break down the sample in as a large number of groups as practical.

Finally, the series was split into two equal-sized consecutive groups in the search for temporal variation in performance and in order to verify whether this might affect the performance of the two EuroSCORE models.

Risk-adjusted mortality rates (RAMR) were calculated by multiplying the Observed/Expected ratio of death rates in the study sample by the 4.8% raw mortality in the EuroSCORE population [1]. The prevalence of categorical data were compared by the chi square test. Either chi square test or 95% Confidence Intervals around Risk Ratios were used for comparing the incidence of death among groups. The one sample t-test was employed to compare patient's ages among the EuroSCORE population and the study sample.

During the study period 2443 consecutive patients were enrolled. Seventeen cases (sixteen surviving) operated upon without requiring extra-corporeal circulation were excluded on the assumption that they would not satisfy the enrolment criteria of EuroSCORE, so leaving 2426 cases useful for analysis. Excluded patients underwent procedures for acute or chronic pericardial disease in 11 cases, exploratory thoracotomy in 3 cases, pacemaker procedures in 2 cases, and repair of cardiac rupture in 1 case. Patients undergoing off pump coronary artery bypass grafting (OPCABG, n=109) were included.

Surgical operations consisted in isolated coronary artery bypass grafting (CABG) in 1629 cases (67.1%), isolated valve surgery in 340 cases (14.0%), combined CABG and valve surgery in 234 cases (9.6%), thoracic aortic surgery in 140 cases (5.8%) and miscellaneous procedures in 83 cases (3.4%).


   3. Results
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
4. Discussion
 5. Limitations
 6. Conclusion
 References
 
The prevalence of predictors in both the EuroSCORE dataset and in our own population sample are shown in Table 1, which also illustrates a number of significant differences among the two populations.


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  		Table 1. Prevalence of predictors in the reference and in the study samples
 
There were 142 deaths among the 2426 study patients. The 5.9% observed death rate was higher than the 5.6% predicted by the additive EuroSCORE but lower than the 6.9% predicted by the logistic EuroSCORE, though neither difference reached statistical significance. The difference among the additive and logistic estimates was only ‘possibly’ significant (P=0.066).

Discriminating ability was good for both additive and logistic models, with areas under the ROC curve of 0.80 for the logistic model and 0.79 for the additive model (Fig. 1). Calibration was good for the logistic model (P=0.12) but turned out being inadequate for the additive model (P<0.0001).



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  		Fig. 1. ROC curves for logistic and additive models.

 
To further explore in a more usable way the question of calibration, we used a 4-group scheme using additive scores to separate groups (Table 2). Risk Ratios showed substantial agreement among observed and logistic-based predictions of death rates, both across the four groups and overall. As for the additive model, 95% CIs for Risk Ratios of observed/additive scores were well below the value of 1 in medium-risk cases on one hand, and well above the value of 1 in very high risk cases, in keeping with the already shown calibration problem.


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  		Table 2. Observed and predicted deaths by risk groups
 
The sample was then broken down in smaller groups. Fig. 2 shows that predictions based on logistic estimates closely anticipated observed death rates up to the 18% estimated death rate, covering over 92% of the population sample. Observations then spread out quite erratically for higher risk cases, though still including predicted rates within their widening 95% CIs. When it came to the additive-based breakdown (Fig. 3), observed death rates exceeded predictions in the very high risk segment, though involving only a distinct minority of patients. In a meaningful proportion of patients in the medium-risk segment, however, observed rates were lower than predicted.



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  		Fig. 2. Sample broken down into 17 groups by logistic estimates (cut-offs precise at the 3rd decimal, rounded for clarity). Data points are observed death rates with 95%CI. Straight reference line represents expected rates.

 


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  		Fig. 3. Sample broken down into 15 groups by additive estimates. Data points are observed death rates with 95%CI. Straight reference line represents expected rates.

 
In order to better clarify whether the noted divergence between observations and predictions should be attributed to peculiarity of performance or, rather, to inadequate calibration of the additive model, the percent difference among logistic and additive estimates was calculated and plotted in Fig. 4. Overestimation at medium risk and underestimation at very high risk on the part of the additive model were both confirmed.



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  		Fig. 4. Difference among additive and logistic estimates expressed as percentage of logistic estimate, plotted against additive scores.

 
Table 3 summarises the result of split file analysis in terms of expected and observed death rates. It contains a strong suggestion that performance improved over time. The areas under the ROC curves were 0.80 and 0.81 for the logistic model in groups A and B, respectively, and 0.79 for the additive model in both groups. Calibration was good for the logistic model in both groups (Group A: P=0.11; Group B: P=0.15) but remained inadequate for the additive model (Group A: P<0.0001; Group B: P<0.0001). The pattern of the percent difference among logistic and additive EuroSCORE estimates was almost identical among the two groups (Fig. 5).


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  		Table 3. Observed and predicted deaths in temporally consecutive groups
 


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  		Fig. 5. Difference among additive and logistic estimates expressed as percentage of logistic estimate, plotted against additive scores. Series sorted by date of surgery, Group A #1-1213, Group B #1214-2426.

 

   4. Discussion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
5. Limitations
 6. Conclusion
 References
 
External validation of a risk-predicting model seeks to verify whether it can be generalised outside the boundaries of the population it was built upon [10], as a preliminary to using it as a reference for quality assessment. Differences in the prevalence of both measured and unmeasured variables (and performance characteristics) among the reference population and the testing sample, however, are generally considered as a serious hindrance to such a validation process. In addition, and whatever the result, the often asked question is whether one is validating a predicting model or rather evaluating the quality of clinical performance in the study population. Stated differently, the issue is ‘who is assessing whom’.

Before we try to answer this question we would like to acknowledge that the characteristics of the population described in our study significantly differ from those of the EuroSCORE population in terms of prevalence of the predictive variables, resulting in higher predicted and observed death rates than measured in the original study [1]. Among others, the older age of our patients probably explain much of the variation and also justifies the greater prevalence of co-morbidity. We are also quite confident that adherence to strict definition criteria makes unstable angina, recent infarct, critical preoperative state and emergency truly more prevalent in our sample. They probably reflect the generally evolving attitude towards increasingly aggressive management of acute coronary syndromes in the time frame our population was enrolled, compared to the less recent EuroSCORE data collection. This having said, it should be noted that what is actually expected from a risk-stratifying tool is exactly the possibility of reliably predicting outcomes in practice experiences different from the one which the model was generated upon.

Being based on a large database collecting patients from 128 cardiac units throughout Europe, EuroSCORE has been shown to be quite robust in dealing with different populations. Despite major epidemiological differences, for instance, Nashef et al. obtained striking concordances with the Society of Thoracic Surgeons model on predicting death rates by EuroSCORE in a large North American cardiac surgical population [4]. Less of a surprise, EuroSCORE performed quite well in individual European countries [11]. Additional validations have been provided on a British population [12], on Japanese cardiovascular patients [13] and in Turkish patients [14]. Some studies concentrated themselves on the subset of patients undergoing isolated CABG [15–17] and some others further restricted their scope to high-risk CABG [18] or to thoracic aortic surgery [19]. Quite surprisingly, all of these studies but one possible exception [11] tested the additive EuroSCORE which transforms the original logistic coefficients into integer risk scores though, by so doing, may not necessarily reproduce the same discrimination and calibration properties demonstrated for the internally validated logistic model.

We therefore addressed the validation of the logistic model of EuroSCORE and compared its performance with its additive counterpart. Our study revealed that the logistic model has both a good discriminating ability and a fairly good calibration across the full range of risk values in our population. To the extent our split-series can be credited of, variation of outcomes due to changing performance over time does not affect the capacity of the logistic model to risk-stratify samples of different risk-profile compared to the reference EuroSCORE. On the other hand, the additive model appeared poorly calibrated in our study, and reproducibly so after multiple attempts at placing different cut-offs for risk grouping. Splitting our series in two temporal groups confirmed that such a limitation is indeed intrinsic to the additive model itself and cannot be attributed to variations in the level of clinical performance.

These findings are not entirely new. Several studies have already pointed to the strong propensity for the additive EuroSCORE to under-predict death rates in high risk settings [6,15,17]. Although high risk cases constitute a minority of the caseload in most cardiac programs they also express a significant proportion of the overall mortality, for which poor approximation in stratification cannot be easily tolerated [15]. On the other hand, an opposite trend towards over-predicting the risk of death has been shown for low-to-medium risk patients by Sergeant et al. [17] in CABG patients. Gogbashian et al. [3] further strengthened both these criticisms and expanded their scope to the whole caseload by reviewing the published reports on EuroSCORE validation in populations not participating to the original database. By directly comparing the estimates from the two models on the same population sample we found a consistent twist effect from over-predicting at medium-risk levels to under-predicting at high risk levels of the additive vs the logistic model.

We also confirmed that ROC curves alone cannot be taken as the only indicator of predictive models performance. Formal calibration by Hosmer–Lemeshow testing and additional breakdown tables are of utmost importance in understanding the possible limitations of different models showing similarly good c-statistics [10].


   5. Limitations
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Limitations
6. Conclusion
 References
 
EuroSCORE was devised to risk-stratify an adult population undergoing heart surgery with cardio-pulmonary bypass at a time when OPCABG was rarely employed. We elected to use OPCABG as a performance variable not to be used in selecting study cases, believing this would not violate the intended clause of EuroSCORE.

The process of external validation of stratifying models heavily relies on strict adherence to the variable definitions provided by the original model. To this regard, mild over-expression of the variable ‘extra-cardiac arteriopathy’ in our series should be considered a possible cause of excess risk estimation, though we would guess it was of trivial degree and did not consider it influential. Far more relevant deviations, such as defining mortality as within 30-days [20] or limiting the events to the in-hospital course [5,17] or ignoring stronger predictors such as pulmonary hypertension [5] may weaken the results of the validation procedure and should be discouraged.

Formal, external auditing was not available for our data. However, systematic supervision and periodical cross-checking as described captured (and corrected) a number of erroneous data inputs small enough to render the whole dataset satisfactorily reliable.


   6. Conclusion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Limitations
 6. Conclusion
References
 
Although our observations will need further confirmation by other independent studies, the alleged advantage of bedside counselling by paper and pencil calculation of risk by the additive EuroSCORE algorithm appears questionable. At the population level, risk assessment and institution- or surgeon-specific adjusted death rates may suffer from inaccurate approximation in case of imbalances towards the extremes of risk, and particularly so in small study samples. In the era of powerful hand-held calculators and on-line free availability of a logistic calculator (www.euroscore.org) the robustness and accuracy of the logistic EuroSCORE should make it the preferred instrument for both individual estimation of risk and for overall quality assessment of clinical performance.


   References
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Limitations
 6. Conclusion
 References
 

  1. Roques F, Nashef SAM, Michel P, Gauducheau E, de Vincentiis C, Baudet E, Cortina J, David M, Faichney A, Gabrielle F, Gams E, Harjula A, Jones MT, Pinna Pintor P, Salamon R, Thulin L. Risk factors and outcome in European cardiac surgery: analysis of the EuroSCORE multinational database of 19030 patients. Eur J Cardiothorac Surg 1999;15:816-823.[Abstract/Free Full Text]
  2. Nashef SAM, Roques F, Michel P, Gauducheau E, Lemeshow S, Salamon R, the EuroSCORE study group. European system for cardiac operative risk evaluation (EuroSCORE). Eur J Cardiothorac Surg 1999;16:9-13.[Abstract/Free Full Text]
  3. Gogbashian A, Sedrakyan A, Treasure T. EuroSCORE: a systematic review of international performance. Eur J Cardiothorac Surg 2004;25:695-700.[Abstract/Free Full Text]
  4. Nashef SAM, Roques F, Hammill BG, Peterson ED, Michel P, Grover FL, Wyse RKH, Ferguson TB. Validation of European System for Cardiac Operative Risk Evaluation (EuroSCORE) in North American cardiac surgery. Eur J Cardiothorac Surg 2002;22:101-105.[Abstract/Free Full Text]
  5. Asimakopoulos G, Al-Ruzzeh S, Ambler G, Omar RZ, Punjabi P, Amrani M, Taylor KM. An evaluation of existing risk stratification models as a tool for comparison of surgical performances for coronary artery bypass grafting between institutions. Eur J Cardiothorac Surg 2003;23:935-942.[Abstract/Free Full Text]
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  7. Roques F, Michel P, Goldstone AR, Nashef SAM. The logistic EuroSCORE. Eur Heart J 2003;24:1-2.[Free Full Text]
  8. Hanley JA, McNeil BJ. The meaning and use of area under a receiver operating characteristic (ROC) curve. Radiology 1982;143:29-36.[Abstract/Free Full Text]
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  12. Stoica SC, Sharples LD, Ahmed I, Roques F, Large SR, Nashef SAM. Preoperative risk prediction and intraoperative events in cardiac surgery. Eur J Cardiothorac Surg 2002;21:41-46.[Abstract/Free Full Text]
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ANN THORAC SURG ASIAN CARDIOVASC THORAC ANN EUR J CARDIOTHORAC SURG
J THORAC CARDIOVASC SURG ICVTS ALL CTSNet JOURNALS