A multivariate Bayesian model for assessing morbidity after coronary artery surgery

INTRODUCTION: Although most risk-stratification scores are derived from preoperative patient variables, there are several intraoperative and postoperative variables that can influence prognosis. Higgins and colleagues previously evaluated the contribution of preoperative, intraoperative and postoperative predictors to the outcome. We developed a Bayes linear model to discriminate morbidity risk after coronary artery bypass grafting and compared it with three different score models: the Higgins' original scoring system, derived from the patient's status on admission to the intensive care unit (ICU), and two models designed and customized to our patient population. METHODS: We analyzed 88 operative risk factors; 1,090 consecutive adult patients who underwent coronary artery bypass grafting were studied. Training and testing data sets of 740 patients and 350 patients, respectively, were used. A stepwise approach enabled selection of an optimal subset of predictor variables. Model discrimination was assessed by receiver operating characteristic (ROC) curves, whereas calibration was measured using the Hosmer-Lemeshow goodness-of-fit test. RESULTS: A set of 12 preoperative, intraoperative and postoperative predictor variables was identified for the Bayes linear model. Bayes and locally customized score models fitted according to the Hosmer-Lemeshow test. However, the comparison between the areas under the ROC curve proved that the Bayes linear classifier had a significantly higher discrimination capacity than the score models. Calibration and discrimination were both much worse with Higgins' original scoring system. CONCLUSION: Most prediction rules use sequential numerical risk scoring to quantify prognosis and are an advanced form of audit. Score models are very attractive tools because their application in routine clinical practice is simple. If locally customized, they also predict patient morbidity in an acceptable manner. The Bayesian model seems to be a feasible alternative. It has better discrimination and can be tailored more easily to individual institutions

A comparative analysis of predictive models of morbidity in intensive care unit after cardiac surgery – Part II: an illustrative example

<p>Abstract</p> <p>Background</p> <p>Popular predictive models for estimating morbidity probability after heart surgery are compared critically in a unitary framework. The study is divided into two parts. In the first part modelling techniques and intrinsic strengths and weaknesses of different approaches were discussed from a theoretical point of view. In this second part the performances of the same models are evaluated in an illustrative example.</p> <p>Methods</p> <p>Eight models were developed: Bayes linear and quadratic models, <it>k</it>-nearest neighbour model, logistic regression model, Higgins and direct scoring systems and two feed-forward artificial neural networks with one and two layers. Cardiovascular, respiratory, neurological, renal, infectious and hemorrhagic complications were defined as morbidity. Training and testing sets each of 545 cases were used. The optimal set of predictors was chosen among a collection of 78 preoperative, intraoperative and postoperative variables by a stepwise procedure. Discrimination and calibration were evaluated by the area under the receiver operating characteristic curve and Hosmer-Lemeshow goodness-of-fit test, respectively.</p> <p>Results</p> <p>Scoring systems and the logistic regression model required the largest set of predictors, while Bayesian and <it>k</it>-nearest neighbour models were much more parsimonious. In testing data, all models showed acceptable discrimination capacities, however the Bayes quadratic model, using only three predictors, provided the best performance. All models showed satisfactory generalization ability: again the Bayes quadratic model exhibited the best generalization, while artificial neural networks and scoring systems gave the worst results. Finally, poor calibration was obtained when using scoring systems, <it>k</it>-nearest neighbour model and artificial neural networks, while Bayes (after recalibration) and logistic regression models gave adequate results.</p> <p>Conclusion</p> <p>Although all the predictive models showed acceptable discrimination performance in the example considered, the Bayes and logistic regression models seemed better than the others, because they also had good generalization and calibration. The Bayes quadratic model seemed to be a convincing alternative to the much more usual Bayes linear and logistic regression models. It showed its capacity to identify a minimum core of predictors generally recognized as essential to pragmatically evaluate the risk of developing morbidity after heart surgery.</p

A comparative analysis of predictive models of morbidity in intensive care unit after cardiac surgery – Part I: model planning

<p>Abstract</p> <p>Background</p> <p>Different methods have recently been proposed for predicting morbidity in intensive care units (ICU). The aim of the present study was to critically review a number of approaches for developing models capable of estimating the probability of morbidity in ICU after heart surgery. The study is divided into two parts. In this first part, popular models used to estimate the probability of class membership are grouped into distinct categories according to their underlying mathematical principles. Modelling techniques and intrinsic strengths and weaknesses of each model are analysed and discussed from a theoretical point of view, in consideration of clinical applications.</p> <p>Methods</p> <p>Models based on Bayes rule, <it>k-</it>nearest neighbour algorithm, logistic regression, scoring systems and artificial neural networks are investigated. Key issues for model design are described. The mathematical treatment of some aspects of model structure is also included for readers interested in developing models, though a full understanding of mathematical relationships is not necessary if the reader is only interested in perceiving the practical meaning of model assumptions, weaknesses and strengths from a user point of view.</p> <p>Results</p> <p>Scoring systems are very attractive due to their simplicity of use, although this may undermine their predictive capacity. Logistic regression models are trustworthy tools, although they suffer from the principal limitations of most regression procedures. Bayesian models seem to be a good compromise between complexity and predictive performance, but model recalibration is generally necessary. <it>k</it>-nearest neighbour may be a valid non parametric technique, though computational cost and the need for large data storage are major weaknesses of this approach. Artificial neural networks have intrinsic advantages with respect to common statistical models, though the training process may be problematical.</p> <p>Conclusion</p> <p>Knowledge of model assumptions and the theoretical strengths and weaknesses of different approaches are fundamental for designing models for estimating the probability of morbidity after heart surgery. However, a rational choice also requires evaluation and comparison of actual performances of locally-developed competitive models in the clinical scenario to obtain satisfactory agreement between local needs and model response. In the second part of this study the above predictive models will therefore be tested on real data acquired in a specialized ICU.</p

A straightforward approach to designing a scoring system for predicting length-of-stay of cardiac surgery patients

Background: Length-of-stay prediction for cardiac surgery patients is a key point for medical management issues, such as optimization of resources in intensive care units and operating room scheduling. Scoring systems are a very attractive family of predictive models, but their retraining and updating are generally critical. The present approach to designing a scoring system for predicting length of stay in intensive care aims to overcome these difficulties, so that a model designed in a given scenario can easily be adjusted over time or for internal purposes. Methods: A naive Bayes approach was used to develop a simple scoring system. A set of 36 preoperative, intraoperative and postoperative variables collected in a sample of 3256 consecutive adult patients undergoing heart surgery were considered as likely risk predictors. The number of variables was reduced by selecting an optimal subset of features. Scoring system performance was assessed by cross-validation. Results: After the selection process, seven variables were entered in the prediction model, which showed excellent discrimination, good generalization power and suitable sensitivity and specificity. No significant difference was found between AUC of the training and testing sets. The 95% confidence interval for AUC estimated by the BCa bootstrap method was [0.841, 0.883] and [0.837, 0.880] in the training and testing sets, respectively. Chronic dialysis, low postoperative cardiac output and acute myocardial infarction proved to be the major risk factors. Conclusions: The proposed approach produced a simple and trustworthy scoring system, which is easy to update regularly and to customize for other centers. This is a crucial point when scoring systems are used as predictive models in clinical practice

A naïve approach for deriving scoring systems to support clinical decision making

Scoring systems are frequently proposed in medicine to summarize a set of qualitative and quantitative items by means of a numeric score. Their design often requires modelling ability and subjective judgments. This can make it difficult to adapt a scoring system to a clinical setting different from that in which the system was developed. The objective of this study was to discuss an approach to derive scoring systems, which can be easily modified and matched to any scenario

Importance of sociodemographic and morbidity aspects in measuring health-related quality of life: performances of three tools

Comparison, Euroqol, Health-related quality of life, Health Utility Index, SF-36,