Bayesian network models with decision tree analysis for management of childhood malaria in Malawi.

BACKGROUND: Malaria is a major cause of death in children under five years old in low- and middle-income countries such as Malawi. Accurate diagnosis and management of malaria can help reduce the global burden of childhood morbidity and mortality. Trained healthcare workers in rural health centers manage malaria with limited supplies of malarial diagnostic tests and drugs for treatment. A clinical decision support system that integrates predictive models to provide an accurate prediction of malaria based on clinical features could aid healthcare workers in the judicious use of testing and treatment. We developed Bayesian network (BN) models to predict the probability of malaria from clinical features and an illustrative decision tree to model the decision to use or not use a malaria rapid diagnostic test (mRDT). METHODS: We developed two BN models to predict malaria from a dataset of outpatient encounters of children in Malawi. The first BN model was created manually with expert knowledge, and the second model was derived using an automated method. The performance of the BN models was compared to other statistical models on a range of performance metrics at multiple thresholds. We developed a decision tree that integrates predictions with the costs of mRDT and a course of recommended treatment. RESULTS: The manually created BN model achieved an area under the ROC curve (AUC) equal to 0.60 which was statistically significantly higher than the other models. At the optimal threshold for classification, the manual BN model had sensitivity and specificity of 0.74 and 0.42 respectively, and the automated BN model had sensitivity and specificity of 0.45 and 0.68 respectively. The balanced accuracy values were similar across all the models. Sensitivity analysis of the decision tree showed that for values of probability of malaria below 0.04 and above 0.40, the preferred decision that minimizes expected costs is not to perform mRDT. CONCLUSION: In resource-constrained settings, judicious use of mRDT is important. Predictive models in combination with decision analysis can provide personalized guidance on when to use mRDT in the management of childhood malaria. BN models can be efficiently derived from data to support clinical decision making.

Risk stratification in pulmonary arterial hypertension using Bayesian analysis.

BACKGROUND: Current risk stratification tools in pulmonary arterial hypertension (PAH) are limited in their discriminatory abilities, partly due to the assumption that prognostic clinical variables have an independent and linear relationship to clinical outcomes. We sought to demonstrate the utility of Bayesian network-based machine learning in enhancing the predictive ability of an existing state-of-the-art risk stratification tool, REVEAL 2.0. METHODS: We derived a tree-augmented naïve Bayes model (titled PHORA) to predict 1-year survival in PAH patients included in the REVEAL registry, using the same variables and cut-points found in REVEAL 2.0. PHORA models were validated internally (within the REVEAL registry) and externally (in the COMPERA and PHSANZ registries). Patients were classified as low-, intermediate- and high-risk (<5%, 5-20% and >10% 12-month mortality, respectively) based on the 2015 European Society of Cardiology/European Respiratory Society guidelines. RESULTS: PHORA had an area under the curve (AUC) of 0.80 for predicting 1-year survival, which was an improvement over REVEAL 2.0 (AUC 0.76). When validated in the COMPERA and PHSANZ registries, PHORA demonstrated an AUC of 0.74 and 0.80, respectively. 1-year survival rates predicted by PHORA were greater for patients with lower risk scores and poorer for those with higher risk scores (p<0.001), with excellent separation between low-, intermediate- and high-risk groups in all three registries. CONCLUSION: Our Bayesian network-derived risk prediction model, PHORA, demonstrated an improvement in discrimination over existing models. This is reflective of the ability of Bayesian network-based models to account for the interrelationships between clinical variables on outcome, and tolerance to missing data elements when calculating predictions.

Probabilistic Graphical Modeling for Estimating Risk of Coronary Artery Disease: Applications of a Flexible Machine-Learning Method.

Objectives. Coronary artery disease (CAD) is the leading cause of death and disease burden worldwide, causing 1 in 7 deaths in the United States alone. Risk prediction models that can learn the complex causal relationships that give rise to CAD from data, instead of merely predicting the risk of disease, have the potential to improve transparency and efficacy of personalized CAD diagnosis and therapy selection for physicians, patients, and other decision makers. Methods. We use Bayesian networks (BNs) to model the risk of CAD using the Z-Alizadehsani data set-a published real-world observational data set of 303 Iranian patients at risk for CAD. We also describe how BNs can be used for incorporation of background knowledge, individual risk prediction, handling missing observations, and adaptive decision making under uncertainty. Results. BNs performed on par with machine-learning classifiers at predicting CAD and showed better probability calibration. They achieved a mean 10-fold area under the receiver-operating characteristic curve (AUC) of 0.93 ± 0.04, which was comparable with the performance of logistic regression with L1 or L2 regularization (AUC: 0.92 ± 0.06), support vector machine (AUC: 0.92 ± 0.06), and artificial neural network (AUC: 0.91 ± 0.05). We describe the use of BNs to predict with missing data and to adaptively calculate prognostic values of individual variables under uncertainty. Conclusion. BNs are powerful and versatile tools for risk prediction and health outcomes research that can complement traditional statistical techniques and are particularly useful in domains in which information is uncertain or incomplete and in which interpretability is important, such as medicine.

Bayesian Networks for Risk Prediction Using Real-World Data: A Tool for Precision Medicine.

OBJECTIVE: The fields of medicine and public health are undergoing a data revolution. An increasing availability of data has brought about a growing interest in machine-learning algorithms. Our objective is to present the reader with an introduction to a knowledge representation and machine-learning tool for risk estimation in medical science known as Bayesian networks (BNs). STUDY DESIGN: In this article we review how BNs are compact and intuitive graphical representations of joint probability distributions (JPDs) that can be used to conduct causal reasoning and risk estimation analysis and offer several advantages over regression-based methods. We discuss how BNs represent a different approach to risk estimation in that they are graphical representations of JPDs that take the form of a network representing model random variables and the influences between them, respectively. METHODS: We explore some of the challenges associated with traditional risk prediction methods and then describe BNs, their construction, application, and advantages in risk prediction based on examples in cancer and heart disease. RESULTS: Risk modeling with BNs has advantages over regression-based approaches, and in this article we focus on three that are relevant to health outcomes research: (1) the generation of network structures in which relationships between variables can be easily communicated; (2) their ability to apply Bayes's theorem to conduct individual-level risk estimation; and (3) their easy transformation into decision models. CONCLUSIONS: Bayesian networks represent a powerful and flexible tool for the analysis of health economics and outcomes research data in the era of precision medicine.

Bayesian network-based framework for exposure-response study design and interpretation.

Conventional environmental-health risk-assessment methods are often limited in their ability to account for uncertainty in contaminant exposure, chemical toxicity and resulting human health risk. Exposure levels and toxicity are both subject to significant measurement errors, and many predicted risks are well below those distinguishable from background incident rates in target populations. To address these issues methods are needed to characterize uncertainties in observations and inferences, including the ability to interpret the influence of improved measurements and larger datasets. Here we develop a Bayesian network (BN) model to quantify the joint effects of measurement errors and different sample sizes on an illustrative exposure-response system. Categorical variables are included in the network to describe measurement accuracies, actual and measured exposures, actual and measured response, and the true strength of the exposure-response relationship. Network scenarios are developed by fixing combinations of the exposure-response strength of relationship (none, medium or strong) and the accuracy of exposure and response measurements (low, high, perfect). Multiple cases are simulated for each scenario, corresponding to a synthetic exposure response study sampled from the known scenario population. A learn-from-cases algorithm is then used to assimilate the synthetic observations into an uninformed prior network, yielding updated probabilities for the strength of relationship. Ten replicate studies are simulated for each scenario and sample size, and results are presented for individual trials and their mean prediction. The model as parameterized yields little-to-no convergence when low accuracy measurements are used, though progressively faster convergence when employing high accuracy or perfect measurements. The inferences from the model are particularly efficient when the true strength of relationship is none or strong with smaller sample sizes. The tool developed in this study can help in the screening and design of exposure-response studies to better anticipate where such outcomes can occur under different levels of measurement error. It may also serve to inform methods of analysis for other network models that consider multiple streams of evidence from multiple studies of cumulative exposure and effects.

Application of Bayesian network modeling to pathology informatics.

BACKGROUND: In the era of extensive data collection, there is a growing need for a large scale data analysis with tools that can handle many variables in one modeling framework. In this article, we present our recent applications of Bayesian network modeling to pathology informatics. METHODS: Bayesian networks (BNs) are probabilistic graphical models that represent domain knowledge and allow investigators to process this knowledge following sound rules of probability theory. BNs can be built based on expert opinion as well as learned from accumulating data sets. BN modeling is now recognized as a suitable approach for knowledge representation and reasoning under uncertainty. Over the last two decades BN have been successfully applied to many studies on medical prognosis and diagnosis. RESULTS: Based on data and expert knowledge, we have constructed several BN models to assess patient risk for subsequent specific histopathologic diagnoses and their related prognosis in gynecological cytopathology and breast pathology. These models include the Pittsburgh Cervical Cancer Screening Model assessing risk for histopathologic diagnoses of cervical precancer and cervical cancer, modeling of the significance of benign-appearing endometrial cells in Pap tests, diagnostic modeling to determine whether adenocarcinoma in tissue specimens is of endometrial or endocervical origin, and models to assess risk for recurrence of invasive breast carcinoma and ductal carcinoma in situ. CONCLUSIONS: Bayesian network models can be used as powerful and flexible risk assessment tools on large clinical datasets and can quantitatively identify variables that are of greatest significance in predicting specific histopathologic diagnoses and their related prognosis. Resulting BN models are able to provide individualized quantitative risk assessments and prognostication for specific abnormal findings commonly reported in gynecological cytopathology and breast pathology.

Development and Preliminary Feasibility Testing of a Decision Support Tool for Childhood Anxiety Treatment.

In this practical application, we describe the steps to build a decision-support tool using GeNIe 2.1 software. The method incorporates principles of decision analyses and allows for a systematic strategy to balance treatment efficacy data with patient preferences. We illustrate the utility for helping clinicians and patients choose between two or more efficacious treatment options (CBT, medication, or their combination). Preliminary pilot data from families (n = 5) seeking services at a specialty clinic for childhood anxiety disorders support the usability of the tool and high patient satisfaction. We use case examples and sample graphical output to illustrate how the decision-support system can be used to integrate data on, 1) baseline symptom severity 2) the relative effectiveness of two or more treatment options, and 3) patient preferences and values, to arrive at a personalized treatment recommendation. The decision-support tool enabled child and parent preferences to be explicitly stated and facilitated discussions about how best to incorporate their preferences into an evidenced-based treatment strategy.

Performance Budget Planning: The Case of a Research University.

We describe a performance budget planning model developed for a research university, comprised of a set of 88 key variables and 38 non-linear structural equations that describe interactions among them. These equations, based on the knowledge of research university's financial working and theoretical considerations, relate expenditures and revenues to teaching and research operations. We demonstrate the value of this model for developing insight into the financial structure of the university. In particular, we show how the model aids in (1) comparing the effect of various policy alternatives on the performance of the university, (2) performing comparative statics analysis of any subset of variables of interest, (3) choice of policy variables and policy alternatives, and (4) gaining insight into the structure of the interactions for a given policy alternative in terms of the causal chain between policy variables and outcome variables. We also describe a computer implementation of the model and discuss a class of mathematical tools for policy planning analysis that facilitate the use and manipulation of models based on sets of nonlinear constraints.

A Bayesian Network Interpretation of the Cox's Proportional Hazard Model.

Cox's proportional hazards (CPH) model is quite likely the most popular modeling technique in survival analysis. While the CPH model is able to represent a relationship between a collection of risks and their common effect, Bayesian networks have become an attractive alternative with an increased modeling power and far broader applications. Our paper focuses on a Bayesian network interpretation of the CPH model (BN-Cox). We provide a method of encoding knowledge from existing CPH models in the process of knowledge engineering for Bayesian networks. This is important because in practice we often have CPH models available in the literature and no access to the original data from which they have been derived. We compare the accuracy of the resulting BN-Cox model to the original CPH model, Kaplan-Meier estimate, and Bayesian networks learned from data, including Naive Bayes, Tree Augmented Naive Bayes, Noisy-Max, and parameter learning by means of the EM algorithm. BN-Cox model came out as the most accurate of all BN approaches and very close to the original CPH model. We study two approaches for simplifying the BN-Cox model for the sake of representational and computational efficiency: (1) parent divorcing and (2) removing less important risk factors. We show that removing less important risk factors leads to smaller loss of accuracy.

Validation workflow for a clinical Bayesian network model in multidisciplinary decision making in head and neck oncology treatment.

PURPOSE: Oncological treatment is being increasingly complex, and therefore, decision making in multidisciplinary teams is becoming the key activity in the clinical pathways. The increased complexity is related to the number and variability of possible treatment decisions that may be relevant to a patient. In this paper, we describe validation of a multidisciplinary cancer treatment decision in the clinical domain of head and neck oncology. METHOD: Probabilistic graphical models and corresponding inference algorithms, in the form of Bayesian networks, can support complex decision-making processes by providing a mathematically reproducible and transparent advice. The quality of BN-based advice depends on the quality of the model. Therefore, it is vital to validate the model before it is applied in practice. RESULTS: For an example BN subnetwork of laryngeal cancer with 303 variables, we evaluated 66 patient records. To validate the model on this dataset, a validation workflow was applied in combination with quantitative and qualitative analyses. In the subsequent analyses, we observed four sources of imprecise predictions: incorrect data, incomplete patient data, outvoting relevant observations, and incorrect model. Finally, the four problems were solved by modifying the data and the model. CONCLUSION: The presented validation effort is related to the model complexity. For simpler models, the validation workflow is the same, although it may require fewer validation methods. The validation success is related to the model's well-founded knowledge base. The remaining laryngeal cancer model may disclose additional sources of imprecise predictions.

Modeling Women's Menstrual Cycles using PICI Gates in Bayesian Network.

A major difficulty in building Bayesian network (BN) models is the size of conditional probability tables, which grow exponentially in the number of parents. One way of dealing with this problem is through parametric conditional probability distributions that usually require only a number of parameters that is linear in the number of parents. In this paper, we introduce a new class of parametric models, the Probabilistic Independence of Causal Influences (PICI) models, that aim at lowering the number of parameters required to specify local probability distributions, but are still capable of efficiently modeling a variety of interactions. A subset of PICI models is decomposable and this leads to significantly faster inference as compared to models that cannot be decomposed. We present an application of the proposed method to learning dynamic BNs for modeling a woman's menstrual cycle. We show that PICI models are especially useful for parameter learning from small data sets and lead to higher parameter accuracy than when learning CPTs.

How to interpret the results of medical time series data analysis: Classical statistical approaches versus dynamic Bayesian network modeling.

BACKGROUND: Classical statistics is a well-established approach in the analysis of medical data. While the medical community seems to be familiar with the concept of a statistical analysis and its interpretation, the Bayesian approach, argued by many of its proponents to be superior to the classical frequentist approach, is still not well-recognized in the analysis of medical data. AIM: The goal of this study is to encourage data analysts to use the Bayesian approach, such as modeling with graphical probabilistic networks, as an insightful alternative to classical statistical analysis of medical data. MATERIALS AND METHODS: This paper offers a comparison of two approaches to analysis of medical time series data: (1) classical statistical approach, such as the Kaplan-Meier estimator and the Cox proportional hazards regression model, and (2) dynamic Bayesian network modeling. Our comparison is based on time series cervical cancer screening data collected at Magee-Womens Hospital, University of Pittsburgh Medical Center over 10 years. RESULTS: The main outcomes of our comparison are cervical cancer risk assessments produced by the three approaches. However, our analysis discusses also several aspects of the comparison, such as modeling assumptions, model building, dealing with incomplete data, individualized risk assessment, results interpretation, and model validation. CONCLUSION: Our study shows that the Bayesian approach is (1) much more flexible in terms of modeling effort, and (2) it offers an individualized risk assessment, which is more cumbersome for classical statistical approaches.

A new Bayesian network-based risk stratification model for prediction of short-term and long-term LVAD mortality.

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.

Cardiac Health Risk Stratification System (CHRiSS): a Bayesian-based decision support system for left ventricular assist device (LVAD) therapy.

This study investigated the use of Bayesian Networks (BNs) for left ventricular assist device (LVAD) therapy; a treatment for end-stage heart failure that has been steadily growing in popularity over the past decade. Despite this growth, the number of LVAD implants performed annually remains a small fraction of the estimated population of patients who might benefit from this treatment. We believe that this demonstrates a need for an accurate stratification tool that can help identify LVAD candidates at the most appropriate point in the course of their disease. We derived BNs to predict mortality at five endpoints utilizing the Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS) database: containing over 12,000 total enrolled patients from 153 hospital sites, collected since 2006 to the present day, and consisting of approximately 230 pre-implant clinical variables. Synthetic minority oversampling technique (SMOTE) was employed to address the uneven proportion of patients with negative outcomes and to improve the performance of the models. The resulting accuracy and area under the ROC curve (%) for predicted mortality were 30 day: 94.9 and 92.5; 90 day: 84.2 and 73.9; 6 month: 78.2 and 70.6; 1 year: 73.1 and 70.6; and 2 years: 71.4 and 70.8. To foster the translation of these models to clinical practice, they have been incorporated into a web-based application, the Cardiac Health Risk Stratification System (CHRiSS). As clinical experience with LVAD therapy continues to grow, and additional data is collected, we aim to continually update these BN models to improve their accuracy and maintain their relevance. Ongoing work also aims to extend the BN models to predict the risk of adverse events post-LVAD implant as additional factors for consideration in decision making.

Impact of precision of Bayesian network parameters on accuracy of medical diagnostic systems.

OBJECTIVE: One of the hardest technical tasks in employing Bayesian network models in practice is obtaining their numerical parameters. In the light of this difficulty, a pressing question, one that has immediate implications on the knowledge engineering effort, is whether precision of these parameters is important. In this paper, we address experimentally the question whether medical diagnostic systems based on Bayesian networks are sensitive to precision of their parameters. METHODS AND MATERIALS: The test networks include Hepar II, a sizeable Bayesian network model for diagnosis of liver disorders and six other medical diagnostic networks constructed from medical data sets available through the Irvine Machine Learning Repository. Assuming that the original model parameters are perfectly accurate, we lower systematically their precision by rounding them to progressively courser scales and check the impact of this rounding on the models' accuracy. RESULTS: Our main result, consistent across all tested networks, is that imprecision in numerical parameters has minimal impact on the diagnostic accuracy of models, as long as we avoid zeroes among parameters. CONCLUSION: The experiments' results provide evidence that as long as we avoid zeroes among model parameters, diagnostic accuracy of Bayesian network models does not suffer from decreased precision of their parameters.

Development of a hybrid decision support model for optimal ventricular assist device weaning.

BACKGROUND: Despite the small but promising body of evidence for cardiac recovery in patients that have received ventricular assist device (VAD) support, the criteria for identifying and selecting candidates who might be weaned from a VAD have not been established. METHODS: A clinical decision support system was developed based on a Bayesian Belief Network that combined expert knowledge with multivariate statistical analysis. Expert knowledge was derived from interviews of 11 members of the Artificial Heart Program at the University of Pittsburgh Medical Center. This was supplemented by retrospective clinical data from the 19 VAD patients considered for weaning between 1996 and 2004. Artificial Neural Networks and Natural Language Processing were used to mine these data and extract sensitive variables. RESULTS: Three decision support models were compared. The model exclusively based on expert-derived knowledge was the least accurate and most conservative. It underestimated the incidence of heart recovery, incorrectly identifying 4 of the successfully weaned patients as transplant candidates. The model derived exclusively from clinical data performed better but misidentified 2 patients: 1 weaned successfully, and 1 that needed a cardiac transplant ultimately. An expert-data hybrid model performed best, with 94.74% accuracy and 75.37% to 99.07% confidence interval, misidentifying only 1 patient weaned from support. CONCLUSIONS: A clinical decision support system may facilitate and improve the identification of VAD patients who are candidates for cardiac recovery and may benefit from VAD removal. It could be potentially used to translate success of active centers to those less established and thereby expand use of VAD therapy.

The Pittsburgh Cervical Cancer Screening Model: a risk assessment tool.

CONTEXT: Evaluation of cervical cancer screening has grown increasingly complex with the introduction of human papillomavirus (HPV) vaccination and newer screening technologies approved by the US Food and Drug Administration. OBJECTIVE: To create a unique Pittsburgh Cervical Cancer Screening Model (PCCSM) that quantifies risk for histopathologic cervical precancer (cervical intraepithelial neoplasia [CIN] 2, CIN3, and adenocarcinoma in situ) and cervical cancer in an environment predominantly using newer screening technologies. DESIGN: The PCCSM is a dynamic Bayesian network consisting of 19 variables available in the laboratory information system, including patient history data (most recent HPV vaccination data), Papanicolaou test results, high-risk HPV results, procedure data, and histopathologic results. The model's graphic structure was based on the published literature. Results from 375 441 patient records from 2005 through 2008 were used to build and train the model. Additional data from 45 930 patients were used to test the model. RESULTS: The PCCSM compares risk quantitatively over time for histopathologically verifiable CIN2, CIN3, adenocarcinoma in situ, and cervical cancer in screened patients for each current cytology result category and for each HPV result. For each current cytology result, HPV test results affect risk; however, the degree of cytologic abnormality remains the largest positive predictor of risk. Prior history also alters the CIN2, CIN3, adenocarcinoma in situ, and cervical cancer risk for patients with common current cytology and HPV test results. The PCCSM can also generate negative risk projections, estimating the likelihood of the absence of histopathologic CIN2, CIN3, adenocarcinoma in situ, and cervical cancer in screened patients. CONCLUSIONS: The PCCSM is a dynamic Bayesian network that computes quantitative cervical disease risk estimates for patients undergoing cervical screening. Continuously updatable with current system data, the PCCSM provides a new tool to monitor cervical disease risk in the evolving postvaccination era.