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A New Bayesian Network-Based Risk Stratification Model for Prediction of Short-Term and Long-Term LVAD Mortality

Loghmanpour, Natasha A.*; Kanwar, Manreet K.; Druzdzel, Marek J.‡§; Benza, Raymond L.; Murali, Srinivas; Antaki, James F.*

doi: 10.1097/MAT.0000000000000209
Adult Circulatory Support

Existing risk assessment tools for patient selection for left ventricular assist devices (LVADs) such as the Destination Therapy Risk Score and HeartMate II Risk Score (HMRS) have limited predictive ability. This study aims to overcome the limitations of traditional statistical methods by performing the first application of Bayesian analysis to the comprehensive Interagency Registry for Mechanically Assisted Circulatory Support dataset and comparing it to HMRS. We retrospectively analyzed 8,050 continuous flow LVAD patients and 226 preimplant variables. We then derived Bayesian models for mortality at each of five time end-points postimplant (30 days, 90 days, 6 month, 1 year, and 2 years), achieving accuracies of 95%, 90%, 90%, 83%, and 78%, Kappa values of 0.43, 0.37, 0.37, 0.45, and 0.43, and area under the receiver operator characteristic (ROC) of 91%, 82%, 82%, 80%, and 81%, respectively. This was in comparison to the HMRS with an ROC of 57% and 60% at 90 days and 1 year, respectively. Preimplant interventions, such as dialysis, ECMO, and ventilators were major contributing risk markers. Bayesian models have the ability to reliably represent the complex causal relations of multiple variables on clinical outcomes. Their potential to develop a reliable risk stratification tool for use in clinical decision making on LVAD patients encourages further investigation.

From the *Department of Biomedical Engineering, Carnegie Mellon Engineering, Pittsburgh, Pennsylvania; Cardiovascular Institute, Allegheny General Hospital, Allegheny Health Network, Pittsburgh, Pennsylvania; Decision Systems Laboratory, School of Information Sciences, University of Pittsburgh, Pittsburgh, Pennsylvania; and §Faculty of Computer Science, Bialystok University of Technology, Bialystok, Poland.

Submitted for consideration November 2014; accepted for publication in revised form January 2015.

Disclosure: The authors have no conflict of interest to report.

Funding was provided by the 1R41 HL120428-01, 1R01HL086918, and U01HL101066-01 NIH Grants.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text, and links to the digital files are provided in the HTML and PDF versions of this article on the journal’s Web site (

Correspondence: James F. Antaki, Department of Biomedical Engineering, 700 Technology Drive, Carnegie Mellon University, Pittsburgh, Pennsylvania 15219. Email:

As the prevalence of advanced heart failure (HF) steadily increases,1 the number of patients requiring consideration for mechanical circulatory support is also on the rise. Left ventricular assist devices (LVADs) have been used for nearly 25 years to support patients with advanced HF and improve mortality.2,3 In fact, LVADs are now considered standard of care for end-stage HF patients, providing alternatives for patients awaiting transplant (bridge-to-transplant—BTT listed), for those ineligible for transplant (destination therapy—DT), or for those patients whose eventual transplant candidacy is unknown (BTT—likely).

Given the complexity of medical comorbidities ailing end-stage HF patients, careful selection is critical in predicting outcomes. The main goal of this selection is to derive the maximum benefit from this expensive and evolving technology, and keeping the cost per patient life year optimal. Therefore, we need a simple, reliable risk tool that can predict optimal clinical outcomes, quality of life, and functional benefit with LVAD therapy in individual HF patients.

Several risk scores and risk factors for both postop morbidity4–6 and mortality2,7 have been derived from LVAD population and are currently being used in the clinical setting. Unfortunately, all published risk assessment scores to date are limited by having a narrow scope and inability to generalize across a rather heterogeneous HF population. For example, the commonly cited Destination Therapy Risk Score (DTRS) derived from first generation pulsatile flow pumps demonstrated less than satisfactory performance8 in estimating mortality when applied to continuous flow LVAD (CF LVAD) populations.2 The more recent risk score derived exclusively for patients receiving the most widely used CF LVAD, HeartMate II, demonstrated only marginal improvement over the DTRS. This HeartMate II Risk Score (HMRS) was able to predict 90 day survival based on five variables with an area under the curve (AUC) of 70%, but only when applied to the same data from which it was derived. Furthermore, the predictors of long-term survival (1 year) were limited to only two variables: age and implant center experience.7 A recent study to test the validity of the HMRS to a single site demonstrated minimal statistical differences among the survival of the low-, medium-, and high-risk cohorts.9

We hypothesize that the prevailing conventional scores are limited in scope because of their assumption of linear relations between significant clinical variables and that these limitations can be overcome by using modern machine learning algorithms. The purpose of this study was to evaluate the efficacy of one such algorithm, the Bayesian network (BN) classifier, for predicting mortality at multiple postimplant timepoints (30 day, 90 day, 6 months, 1 year, and 2 years). Although the final web-based application of the risk model is a work in progress, this study presents the performance of the predictive Bayesian models, introduced here as the Cardiac Outcomes Risk Assessment (CORA) models, along with its comparison to the HMRS.

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Patient Cohort

The retrospective data for this study was provided by the Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS) database, which in turn was collected under IRB approval by over 150 participating hospitals. Patients or designated surrogates provided written informed consent for their information to be recorded in the registry before the device implant. We excluded data from patients not receiving a CF LVAD as the primary implant, pediatric patients (defined by INTERMACS as age < 19), or those records for which no preimplant data (within 60 days before implant) was available. Patients who also received a right ventricular assist device were included as long as the primary or initial implant was an LVAD. Data were obtained for 8,050 patients from July 2006 to June 2013. Data from patients whose LVAD was electively removed (e.g., because of transplantation or recovery) were included for postop outcomes but eventually censored at the time of explant (Table 1). Medical comorbidities, such as events or other surgeries during hospitalization and interventions before 48 hours of implant, as well as complications were defined using the INTERMACS definitions.

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The initial dataset consisted of 226 preimplant clinical variables. These were initially screened on the basis of sparseness, wherein variables with greater than 20%, 50%, and 80% missing entries were excluded, leaving for analysis 96, 111, and 184 variables, respectively. Missing values were replaced with either the mean or the mode (for continuous and discrete variables, respectively). Supplemental Table 1 (Supplemental Digital Content, provides the list of variables with their respective formats and input values.

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Bayesian Network Models

Bayesian networks10 are classification algorithms in which nodes represent variables and directed edges (depicted as arrows between nodes) represent influences between those variables. The absence of an arrow between a pair of nodes implies independence between those variables. This allows for significant savings in the number of parameters necessary to represent the complete probability distribution of predictive factors in this complex patient population, making BNs highly practical. In addition to the graph structure, a BN is equipped with conditional probability tables associated with each node, which not only describe the direction of influence amongst variables but also allows for representation of the degree of influence.

Consider a simple BN model in Supplemental Figure 1 (Supplemental Digital Content,, containing risk factors related to LVAD survival. The percentages in Supplemental Figure 1a (Supplemental Digital Content, correspond to the prevalence of each factor in this example population. The network represents the joint probability distribution of the four clinical factors on survival: age, center experience, albumin, and creatinine contributing to a predicted 2 year mortality of 27%. Now considering a specific patient (see Figure 1b, Supplemental Digital Content, greater than 70 years of age at an inexperienced center for which albumin and creatinine values are unavailable, the model predicts a 58% chance of survival. If albumin and creatinine values were made available for this patient, Supplemental Figure 1c ( demonstrates a reduction in the chance of survival to 41%. By contrast, Supplemental Figure 1d ( illustrates a much more favorable prognosis (94% chance of survival) using the same BN for a different patient, age 51–60 years at an experienced center and normal albumin and creatinine values. This example illustrates the ability of BN models to accommodate incomplete datasets.11,12

The methods used for the present study evolved from our prior experience with machine learning for decision support of optimal VAD weaning,13 the need for right ventricular support due to right ventricular failure in LVAD recipients14–16 a two-center study to predict 90-day survival for continuous flow LVADs17–19 and previous mortality studies using INTERMACS.20,21 For this study, we investigated three BN classification algorithms: the Naïve Bayes, Tree-Augmented Naïve Bayes (TAN), and Hill Climber Bayes Net for their unique features, each based on a subset of clinical variables. Naïve Bayes assume that all clinical variables affect the outcome (mortality), but are independent of each other. TAN allows representation of correlations/dependence between the variables, as well as their impact on outcome, represented as multiple arrows. For example, Naïve Bayes could link preop international normalized ratio (INR) and albumin to mortality and TAN would take this initial Naïve Bayes structure and then add an arrow between INR and albumin. Hill Chamber Bayes Net22 adds, deletes, and reverses edges (arrows) as it searches through the feature space and terminates when an optimal model structure is achieved.

The subsets of clinical variables were derived using a process called feature selection, which reduces the total number of variables to avoid over-fitting the model to the data. In this study, this was performed by three different evaluators including χ2 correlation analysis and information gain.23 These processes allow for variables to be ranked based on their predictive power. All BN classifiers were evaluated on an independent dataset comprised of a training set of approximately 90% of the data records and a testing set from the remaining approximate 10%, also known as tenfold cross validation. Multiple timepoints were chosen for mortality postop to demonstrate the ability of BN risk scores to be consistently reproducible and clinically relevant. The final step was to re-rank variables at each mortality end-point by sequentially removing those that were least predictive, to obtain a subset that was most accurate and relevant for that particular mortality end-point.

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Comparison to HeartMate II Risk Score

The HMRS, which is the only predictive score derived and validated on a cohort of CF LVADs, was derived initially for 90 day survival, but also applied and validated for the 1 year mortality end-point. In this study, we calculated the 90 day and 1 year mortality stratified by the HMRS for comparison with the Bayesian (CORA) models. The HMRS variables are: center experience (0 if ≥15 VADs/year, 1 if ≤15 VADs/year), age (per 10 years), albumin, creatinine, and INR. The HMRS equation = (0.0274 × [age in years]) - (0.723 × [albumin]) + (0.74 × [creatinine]) + (1.13× [INR]) + (0.807 × [center LVAD volume < 15]).7

As the INTEMACS data for age were recorded by decade (e.g., 40–49 or 50–59 years), it was coded by the median value (e.g., 55 for 50–59). The site of LVAD implant for each patient was also not provided, so we assumed that all centers were considered experienced, which ultimately neutralized the variable. Missing values were replaced by the mean of the associated feature: albumin (844 missing, mean = 3.39), INR (434 missing, mean = 1.34), and creatinine (35 missing, mean = 1.43). There were no missing entries for the age variable. The performance of the HMRS was assessed by the AUC of the receiver operator characteristic (ROC) curve, the Kaplan–Meier curves, and the general distribution of predicted low-, medium-, and high-risk patients.

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Performance Metrics

The BN (CORA) models were assessed by their accuracy, Kappa statistic, area under the ROC curve (AUC %) and Kaplan–Meier curve. Accuracy was defined as the sum of true positive and true negative instances divided by the total number of instances. Standard ROC curves were constructed to capture the relation between overall sensitivity (true positive rate) and specificity (true negative rate). The area under the ROC curve (AUC %) provided a measure of overall performance. The Kappa statistic measured the agreement of the prediction with the true class (actual outcome), where 1.0 signifies complete agreement and 0 is agreement based on chance.

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Comparison of Feature Selection Methods

Univariate statistical analysis was performed to corroborate the statistical significance of the variables that were identified by the BN feature selection. Cox proportional hazards regression model was used to identify statistically significant variables (defined as p ≤ 0.05) using MedCalc Statistical Software (version 13.0.6, Ostend, Belgium, 2014) and SAS (version 9.4, Cary, NC).

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Survival Analysis

Patient survival estimated by each of the predictive models (BN and HMRS) was plotted as Kaplan–Meier curves for 90 days and 1 year. The latter plots were stratified according to HMRS classification: low-, medium-, high-risk. Bayesian network plots were stratified according to the prediction of survival at the associated end-point. Differences between stratified groups were compared using log-rank statistics.24 The log-rank test was used to compare the survival curves, with statistical significance defined as p ≤ 0.05. Survival was calculated from the day of implant.

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The most predictive variables (according to information gain) for each CORA Bayesian models are provided in Table 2. Variables that were common among all five models across the different timepoints were: 1) intervention within the last 48 hours, 2) creatinine, 3) events experienced during the hospitalization closest to LVAD implantation, 4) previous cardiac operations, 5) IV inotrope therapy agent, 6) primary diagnosis, 7) hemoglobin, 8) LVAD device strategy, and 9) INTERMACS profile. The specific interventions and events found to be most predictive of mortality were: cardiac arrest, intubation, dialysis, ECMO, feeding tube, and IABP. However, it is noteworthy that the relative importance of predictive variables differed among survival end-points given their varying influence on outcomes with passing time. The significant univariate correlations with 90 day and 1 year mortality are reported in Supplemental Tables 2 and 3, respectively (Supplemental Digital Content, In general, the predictive variables in the CORA Bayesian models were also found to be significant (p < 0.05) by the univariate Cox proportional hazard model.

Resulting from model optimization, the best performance resulted from using the information gain evaluator, the ranker method for ordering the predicting variables, the TAN model structure (maximum of two arrows directed at each node), and varying variable subset sizes depending on the end-point (30 days: n = 60; 90 days: n = 68; 6 months: n = 80; 1 year: n = 89; 2 years: n = 65). The models were derived using the cutoff point for inclusion of at least 50% completion for each variable, as opposed to the 20% or 80% thresholds. Although the model performances of all three cutoffs for data completeness were comparable, we chose 50% for the final model derivation to preserve the maximal number of clinically relevant variables. A summary of the performance of each model is provided in Table 3, which reports accuracies as large as 96%, AUC of the ROC as large as 89%, and Kappa values as large as 0.47. Figure 1 shows the CORA Bayesian models for 1) 90 days and 2) 1 year. These networks indicate the predicted mortality for an individual exemplary patient, which are 78% at 90 days and 76% at 1 year. The shade of red indicates the sensitivity of a given variable for that particular patient; the thickness of the arrows indicates the strength of influence between two variables. These results predict that the majority of the risk is within the initial 3 months postimplant and the risk remains relatively constant for the remainder of the year. The exact clinical variable entries are listed in the figure caption.

Supplemental Table 4 (Supplemental Digital Content, summarizes the HMRS risk profile distributions for 90 day and 1 year mortality, with the majority of patients predicted as low risk (93% for both). This overwhelming skew is also depicted in the Figure 2 frequency charts.

The ROC in Figure 3 illustrates a consistent superiority of the CORA Bayesian model predictions for five mortality time end-points over the two HMRS time intervals, which were close to the line of unity (ROC curve if solely based on chance). The 90 day and 1 year HMRS stratifications had AUC of 60% and 57%, respectively, whereas the Bayesian 90 day and 1 year predictions exhibited AUC of 81% and 79%, respectively.

Figures 4 and 5 show the Kaplan–Meier survival curves stratified by the 1) HMRS and 2) CORA Bayesian models at the 90 day and 1 year end-points, respectively. Whereas the differences between HMRS risk groups are barely discernable, the CORA BN models provide clear distinctions in the survival curves.

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Appropriate patient selection is vital to optimal postsurgical outcomes and cost–effectiveness of LVAD therapy. There is a critical need for accurate, flexible, and improved predictive model to account for the heterogeneity of end-stage HF patients and BN analyses can provide the necessary tools to achieve that as demonstrated in the aforementioned analysis. In contradistinction to the traditional statistical methods, which are comprised of weighted combinations of independent variables, BNs provide the advantages of a rigorous probabilistic framework in which to perform inference of multiple variables and a visual representation that is easy to interpret by clinicians. These qualities provide a more accurate depiction of human decision-making process and improved performance than the “black box” type risk scores, which can only take into account restricted number of variables that fail to represent the complexity of an end-stage HF patient.

The utility of the Bayesian approach was only recognized within the past 25 years,25 with the more recent application of BN-based decision support being published in a wide variety of medical disciplines.26–31 In 2010, the FDA released a guidance for the use of Bayesian statistics in medical device clinical trials.32 In 2013, United Network for Organ Sharing proposed the adoption of a new Bayesian methodology to better identify those transplant programs that may be underperforming in the area of patient and graft survival.33

To the best of our knowledge, this is the first application of Bayesian analysis to any LVAD cohort and the first study to report the findings of predictive models derived from both Bayesian and traditional statistical methods (HMRS). The final BN models included both nonmodifiable/historical variables (such as implant year) and modifiable variables (such as nutritional assessment, renal function etc.). The former are useful in extrapolating future predictions based on the current trajectory and the latter provide a meaningful way of applying this model prospectively. In this analysis, there were several variables found to have significant impact on the predicted mortality. These included clinical and nonclinical variables, both of which play a vital role in decision-making that occurs on a day-to-day basis with these often critically ill patients. An example of a nonclinical variable would be an inability to perform a quality of life questionnaire, because of patient-related reasons as opposed to administrative reasons (as defined by INTERMACS) suggesting poor prognosis and correlating with increased mortality. Not only were certain preoperative variables associated with higher mortality, having several of these risk factors compounded their impact in an incremental fashion. For example, a patient on dialysis had a predicted 28% risk of death at 90 days postimplant (baseline risk of 10%), which increased to 44% if they were also intubated, and further increased to 66% if they also experienced cardiac arrest. In another example, a patient on ECMO within 48 hours of implant had a 20% risk of death at 90 days, which increased to 31% if they were also on a ventilator and increased even further to 61% if they were additionally on IABP and feeding tube. Bayesian network analyses can not only show how clinical variables (e.g., low cardiac output and renal dysfunction) impact the predicted class value (mortality) independently but also analyze how they impact each other (e.g., low cardiac output contributes to renal dysfunction, and thereby mortality). This allows a user to input these various scenarios and calculate the changes in predicted chance of mortality. Traditional risk scores are only able to show how each clinical variable relates to the outcome and not to each other.

To provide a real-life comparison of the BN and HMRS performances, consider the following two real-life, representative case studies. Patient A is a 60 year old Caucasian male, who is INTERMACS level 1 with New York Heart Association functional class (NYHA) class IV symptoms, on ventilator and IABP, with a creatinine level of 2.0 mg/dl. Patient B is a 70 year old Caucasian female who is INTERMACS level 3, with NYHA class IV symptoms, chronic renal disease, with creatinine level of 3.3 mg/dl. Appling the HMRS, patient A is predicted to be at low risk (8% risk of 90 day mortality), whereas CORA predicted this patient to have a 44% chance of survival at 90 days. In case B, HMRS this patient to have a medium risk of mortality (11% at 90 days), whereas CORA predicted the same patient to have a 96% chance of survival at 90 days. In reality, patient A died during their initial hospitalization of multiorgan failure, whereas patient B continued to thrive on pump support after 2 years. These examples demonstrate the improved utility of CORA over HMRS and highlight the already noted shortcomings of HMRS. Also noted in Figure 2, the HMRS exhibited an inherent bias toward identifying patients as low risk. This may stem from the conservative stratification using five variables used to calculate the HMRS. This is in comparison to the 60–89 variables included in the CORA models, which comprehensively include: demographics, comorbidities, hemodynamics, laboratory values, medications, and quality of life metrics.

We acknowledge that this study has several important limitations, including extensive missing data pertaining to the independent variables. Although the INTERMACS database is large and representative, it suffers from sparsity of many of the data elements. This prompted us to exclude a large quantity of variables, and compelled us to impute missing values. We elected to use the arithmetic mean, which we understand is more likely to introduce bias than multiple imputation. However, it is more appropriate for data which is not missing at random.34 Our ongoing objective is to continually update the database with prospectively collected data specifically for the prognostic model.

Additional limitations include: uneven distribution of classes, which may impact the accuracy of learning; uneven distribution of many continuous variables and skew of categorical variables; inherent retrospective bias (all patients were already chosen to receive a VAD); and finally, only FDA-approved VADs were included in registry. Furthermore, the preponderance of the INTERMACS data set is derived from HeartMate II, and therefore might not accurately reflect outcomes of competitive devices. However, despite these limitations, our study does not suffer from other, more common limitations (e.g., single centered) as we utilized the most comprehensive and robust registry currently available for LVAD recipients.

In the current model, we chose five discrete end-points, although it is possible to include more specificity with respect to time (e.g., 30 days, 45 days, and 60 days) the resulting accuracy would degrade. It is ostensibly possible to provide a prediction of mortality as a continuous variable but at the expense of accuracy.

The CORA Bayesian models demonstrated a remarkable improvement over the HMRS with respect to accuracy, sensitivity, specificity, and more realistic Kaplan–Meier survival distinctions comparisons. The CORA models consistently outperformed HMRS because of their ability to 1) learn from prior probability, 2) account for relations between variables, and 3) tolerate missing data elements and allow for blank data entries without loss of continuity. In addition, BNs are able to more closely reflect the natural clinical decision-making process as compared with traditional risk scores and therefore provide greater confidence as a tool for those making medical decisions. These results encourage continued validation and expansion of the models with a prospective, multicenter study.

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Translation to Clinical Practice

Now that the validity of Bayesian analysis in predicting clinical outcomes has been established, the next step is the translation of CORA to clinical practice. This will entail its incorporation into an easily interpretable online application that is accessible at key decision points along the continuum of a patient’s clinical course. For this reason, we are currently in the process of programming a demonstration model available to clinicians to solicit feedback to improve both the aesthetics and usability of the interface. The application is intended to integrate with the electronic health record to compute the prognosis (risk of death or adverse events) for an LVAD patient, based on the most current clinical data available. An additional feature will allow LVAD centers to customize the decision support tool according to the unique protocols in their individual programs.

We acknowledge that HF is a continuum of diseases, and that a computer decision support system is not necessary to identify the extreme cases for whom LVAD therapy is obviously not appropriate. Hence, the potential utility of the CORA models is to assist the clinical team in decision making with patients for whom the merits or contraindications to an LVAD are not immediately apparent. Accordingly, we hope that CORA may promote more judicious use of LVAD therapy: by sparing the questionable patients who would do poorly, and by providing supporting evidence for those patients who are likely to benefit, but might otherwise be denied LVAD therapy.

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The authors thank the Data Access, Analysis, and Publications Committee of INTERMACS for allowing us to use their registry for the study. Models described in this paper have been constructed using GeNIe, a modeling environment for graphical probabilistic models available at

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LVAD; mortality; Bayesian; risk assessment; decision support system

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