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 regressionbased 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.

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.

IMPORTANCE Quantitative assessment of bias from unmeasured confounding and missing data can help evaluate uncertainty in findings from indirect comparisons using real-world data (RWD).OBJECTIVE To compare the effectiveness of alectinib vs ceritinib in terms of overall survival (OS) in patients with ALK-positive, crizotinib-refractory, non-small cell lung cancer (NSCLC) and to assess the sensitivity of these findings to unmeasured confounding and missing data assumptions. DESIGN, SETTING, AND PARTICIPANTSThis comparative effectiveness research study compared patients from 2 phase 2 alectinib trials and real-world patients. Patients were monitored from June 2013 to March 2020. Comparisons of interest were between alectinib trial data vs ceritinib RWD and alectinib RWD vs ceritinib RWD. RWD treatment groups were selected from nationally representative cancer data from US cancer clinics, the majority from community centers. Participants were ALK-positive patients aged 18 years or older with advanced NSCLC, prior exposure to crizotinib, and Eastern Cooperative Oncology Group Performance Status (PS) of 0 to 2. Data analysis was performed from October 2020 to March 2021. EXPOSURES Initiation of alectinib or ceritinib therapy. MAIN OUTCOMES AND MEASURESThe main outcome was OS. RESULTSIn total, there were 355 patients: 183 (85 men [46.4%]) in the alectinib trial, 91 (43 men [47.3%]) in the ceritinib RWD group, and 81 (38 men [46.9%]) in the alectinib RWD group. Patients in the alectinib trial were younger (mean [SD] age, 52.53 [11.18] vs 57.97 [11.71] years), more heavily pretreated (mean [SD] number of prior therapy lines, 1.95 [0.72] vs 1.47 [0.81]), and had more favorable baseline ECOG PS (ECOG PS of 0 or 1, 165 patients [90.2%] vs 37 patients [77.1%]) than those in the ceritinib RWD group. The alectinib RWD group (mean [SD] age, 58.69 [11.26] years) had more patients with favorable ECOG PS (ECOG PS of 0 or 1, 49 patients [92.4%] vs 37 patients [77.1%])and more White patients (56 patients [72.7%] vs 53 patients [62.4%]) compared with the ceritinib group. Compared with ceritinib RWD, alectinib-exposed patients had significantly longer OS in alectinib trials (adjusted hazard ratio [HR], 0.59; 95% CI, 0.44-0.75; P < .001) and alectinib RWD (HR, 0.46; 95% CI, 0.29-0.63; P < .001) after adjustment for baseline confounders. For the worst-case HR estimate of 0.59, residual confounding by a hypothetical confounder associated with mortality and treatment by a risk ratio greater than 2.24 was required to reverse the findings. Conclusions were robust to plausible deviations from random missingness for missing ECOG PS and underrecorded comorbidities and central nervous system metastases in RWD. CONCLUSIONS AND RELEVANCEAlectinib exposure was associated with longer OS compared with ceritinib in patients with ALK-positive NSCLC, and only substantial levels of bias examined reversed (continued)

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