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1.  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 naïve 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.
doi:10.1186/1472-6947-14-89
PMCID: PMC4203871  PMID: 25311154
Intensive care unit; Decision-support system; Prediction model; Scoring system
2.  A simple clinical model for planning transfusion quantities in heart surgery 
Background
Patients undergoing heart surgery continue to be the largest demand on blood transfusions. The need for transfusion is based on the risk of complications due to poor cell oxygenation, however large transfusions are associated with increased morbidity and risk of mortality in heart surgery patients. The aim of this study was to identify preoperative and intraoperative risk factors for transfusion and create a reliable model for planning transfusion quantities in heart surgery procedures.
Methods
We performed an observational study on 3315 consecutive patients who underwent cardiac surgery between January 2000 and December 2007. To estimate the number of packs of red blood cells (PRBC) transfused during heart surgery, we developed a multivariate regression model with discrete coefficients by selecting dummy variables as regressors in a stepwise manner. Model performance was assessed statistically by splitting cases into training and testing sets of the same size, and clinically by investigating the clinical course details of about one quarter of the patients in whom the difference between model estimates and actual number of PRBC transfused was higher than the root mean squared error.
Results
Ten preoperative and intraoperative dichotomous variables were entered in the model. Approximating the regression coefficients to the nearest half unit, each dummy regressor equal to one gave a number of half PRBC. The model assigned 4 units for kidney failure requiring preoperative dialysis, 2.5 units for cardiogenic shock, 2 units for minimum hematocrit at cardiopulmonary bypass less than or equal to 20%, 1.5 units for emergency operation, 1 unit for preoperative hematocrit less than or equal to 40%, cardiopulmonary bypass time greater than 130 minutes and type of surgery different from isolated artery bypass grafting, and 0.5 units for urgent operation, age over 70 years and systemic arterial hypertension.
Conclusions
The regression model proved reliable for quantitative planning of number of PRBC in patients undergoing heart surgery. Besides enabling more rational resource allocation of costly blood-conservation strategies and blood bank resources, the results indicated a strong association between some essential postoperative variables and differences between the model estimate and the actual number of packs transfused.
doi:10.1186/1472-6947-11-44
PMCID: PMC3141374  PMID: 21693020
3.  A bootstrap approach for assessing the uncertainty of outcome probabilities when using a scoring system 
Background
Scoring systems are a very attractive family of clinical predictive models, because the patient score can be calculated without using any data processing system. Their weakness lies in the difficulty of associating a reliable prognostic probability with each score. In this study a bootstrap approach for estimating confidence intervals of outcome probabilities is described and applied to design and optimize the performance of a scoring system for morbidity in intensive care units after heart surgery.
Methods
The bias-corrected and accelerated bootstrap method was used to estimate the 95% confidence intervals of outcome probabilities associated with a scoring system. These confidence intervals were calculated for each score and each step of the scoring-system design by means of one thousand bootstrapped samples. 1090 consecutive adult patients who underwent coronary artery bypass graft were assigned at random to two groups of equal size, so as to define random training and testing sets with equal percentage morbidities. A collection of 78 preoperative, intraoperative and postoperative variables were considered as likely morbidity predictors.
Results
Several competing scoring systems were compared on the basis of discrimination, generalization and uncertainty associated with the prognostic probabilities. The results showed that confidence intervals corresponding to different scores often overlapped, making it convenient to unite and thus reduce the score classes. After uniting two adjacent classes, a model with six score groups not only gave a satisfactory trade-off between discrimination and generalization, but also enabled patients to be allocated to classes, most of which were characterized by well separated confidence intervals of prognostic probabilities.
Conclusions
Scoring systems are often designed solely on the basis of discrimination and generalization characteristics, to the detriment of prediction of a trustworthy outcome probability. The present example demonstrates that using a bootstrap method for the estimation of outcome-probability confidence intervals provides useful additional information about score-class statistics, guiding physicians towards the most convenient model for predicting morbidity outcomes in their clinical context.
doi:10.1186/1472-6947-10-45
PMCID: PMC2940863  PMID: 20796275
4.  A comparative analysis of predictive models of morbidity in intensive care unit after cardiac surgery – Part II: an illustrative example 
Background
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.
Methods
Eight models were developed: Bayes linear and quadratic models, k-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.
Results
Scoring systems and the logistic regression model required the largest set of predictors, while Bayesian and k-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, k-nearest neighbour model and artificial neural networks, while Bayes (after recalibration) and logistic regression models gave adequate results.
Conclusion
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.
doi:10.1186/1472-6947-7-36
PMCID: PMC2222596  PMID: 18034873
5.  A comparative analysis of predictive models of morbidity in intensive care unit after cardiac surgery – Part I: model planning 
Background
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.
Methods
Models based on Bayes rule, k-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.
Results
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. k-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.
Conclusion
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.
doi:10.1186/1472-6947-7-35
PMCID: PMC2212627  PMID: 18034872

Results 1-5 (5)