@article{wang_martin_2020, title={Model-free posterior inference on the area under the receiver operating characteristic curve}, volume={209}, ISSN={["1873-1171"]}, DOI={10.1016/j.jspi.2020.03.008}, abstractNote={The area under the receiver operating characteristic curve (AUC) serves as a summary of a binary classifier's performance. Methods for estimating the AUC have been developed under a binormality assumption which restricts the distribution of the score produced by the classifier. However, this assumption introduces an infinite-dimensional nuisance parameter and can be inappropriate, especially in the context of machine learning. This motivates us to adopt a model-free Gibbs posterior distribution for the AUC. We present the asymptotic Gibbs posterior concentration rate, and a strategy for tuning the learning rate so that the corresponding credible intervals achieve the nominal frequentist coverage probability. Simulation experiments and a real data analysis demonstrate the Gibbs posterior's strong performance compared to existing methods based on a rank likelihood.}, journal={JOURNAL OF STATISTICAL PLANNING AND INFERENCE}, author={Wang, Zhe and Martin, Ryan}, year={2020}, month={Dec}, pages={174–186} }
 @article{zura_watson_einhorn_mehta_della rocca_xiong_wang_jones_steen_2017, title={An inception cohort analysis to predict nonunion in tibia and 17 other fracture locations}, volume={48}, ISSN={["1879-0267"]}, DOI={10.1016/j.injury.2017.03.036}, abstractNote={The epidemiology of fracture nonunion has been characterized so it is potentially possible to predict nonunion using patient-related risk factors. However, prediction models are currently too cumbersome to be useful. We test a hypothesis that nonunion can be predicted with ≤10 variables, retaining the predictive accuracy of a full model with 42 variables.We sought to predict nonunion with prospectively-acquired inception cohort data for 18 different bones, using the smallest possible number of variables that did not substantially decrease prediction accuracy. An American nationwide claims database of ∼90.1 million participants was used, which included medical and drug expenses for 2011-2012. Continuous enrollment was required for 12 months after fracture, to allow sufficient time to capture a nonunion diagnosis. Health claims were evaluated for 309,330 fractures. A training dataset used a random subset of 2/3 of these fractures, while the remaining fractures formed a validation dataset. Multivariate logistic regression and stepwise logistic regression were used to identify variables predictive of nonunion. P value and the Akaike Information Criterion (AIC) were used to select variables for reduced models. Area-under-the-curve (AUC) was calculated to characterize the success of prediction.Nonunion rate in 18 fracture locations averaged 4.93%. Algorithms to predict nonunion in 18 locations in the full-model validation set had average AUC=0.680 (±0.034). In the reduced models, average validation set AUC=0.680 (±0.033) and the average number of risk factors required for prediction was 7.6. There was agreement across training set, validation set, and reduced set; in tibia, reduced model validation AUC=0.703, while the full-model validation AUC=0.709. Certain risk factors were important for predicting nonunion in ≥10 bones, including open fracture, multiple fracture, osteoarthritis, surgical treatment, and use of certain medications, including anticoagulants, anticonvulsants, or analgesics.Nonunion can be predicted in 18 fracture locations using parsimonious models with <10 patient demography-related risk factors. The model reduction approach used results in simplified models that have nearly the same AUC as the full model. Reduced algorithms can predict nonunion because risk factors important in the full models remain important in the reduced models. This prognostic inception cohort study provides Level I evidence.}, number={6}, journal={INJURY-INTERNATIONAL JOURNAL OF THE CARE OF THE INJURED}, author={Zura, Robert and Watson, J. Tracy and Einhorn, Thomas and Mehta, Samir and Della Rocca, Gregory J. and Xiong, Ze and Wang, Zhe and Jones, John and Steen, R. Grant}, year={2017}, month={Jun}, pages={1194–1203} }
 @article{zura_xiong_einhorn_watson_ostrum_prayson_della rocca_mehta_mckinley_wang_et al._2016, title={Epidemiology of fracture nonunion in 18 human bones}, volume={151}, number={11}, journal={JAMA Surgery}, author={Zura, R. and Xiong, Z. and Einhorn, T. and Watson, J. T. and Ostrum, R. F. and Prayson, M. J. and Della Rocca, G. J. and Mehta, S. and McKinley, T. and Wang, Z. and et al.}, year={2016} }