The prediction of posttraumatic stress disorder (PTSD) has gained a lot of interest in clinical studies. Identifying patients with a high risk of PTSD can guide mental healthcare workers when making treatment decisions. The main goal of this paper is to propose several Bayesian network (BN) models to assess the probability that a veteran has PTSD when first visiting a U.S. Department of Veteran Affairs (VA) facility seeking medical care. The current practice is to use a five-question test called PC-PTSD-5. We aim to use the PC-PTSD-5 test, which is currently administered to most incoming new patients, and demographic information, military service history, and medical history. We construct a Bayes information criterion score-based BN, a group L2-regularized BN (GL2-regularized BN), and a naïve Bayes BN to assess the probability that a patient has PTSD. The GL2-regularized BN is a new method for constructing a BN motivated by some of the challenges of analyzing this data set. A secondary goal is to identify which features are important in predicting PTSD. We discover that the following features help compute the probability of PTSD: PC-PTSD-5, service-connected flag, combat flag, agent orange flag, military sexual trauma flag, traumatic brain injury, and age. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0174 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0174 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We propose a method for simultaneous estimation and variable selection of an additive quantile regression model that can be used with high dimensional data. Quantile regression is an appealing method for analyzing high dimensional data because it can correctly model heteroscedastic relationships, is robust to outliers in the response, sparsity levels can change with quantiles, and it provides a thorough analysis of the conditional distribution of the response. An additive nonlinear model can capture more complex relationships, while avoiding the curse of dimensionality. The additive nonlinear model is fit using B-splines and a nonconvex group penalty is used for simultaneous estimation and variable selection. We derive the asymptotic properties of the estimator, including an oracle property, under general conditions that allow for the number of covariates, $p_n$, and the number of true covariates, $q_n$, to increase with the sample size, $n$. In addition, we propose a coordinate descent algorithm that reduces the computational cost compared to the linear programming approach typically used for solving quantile regression problems. The performance of the method is tested using Monte Carlo simulations, an analysis of fat content of meat conditional on a 100 channel spectrum of absorbances and predicting TRIM32 expression using gene expression data from the eyes of rats.