Objective: Blood pressure (BP) is inherently variable. White-coat (WC) and masked hypertension are manifestations of this variability making office BP (OBP) unreliable with direct implications on diagnosis and management. Whilst the causes for this phenomenon are not fully known, predicting whether an individual's BP has WC or masked pattern will improve efficiencies in overall BP management. In this study, we used machine learning (ML) methods which are powerful in finding generalisable predictive patterns to develop models for accurate prediction of different BP patterns. Design and method: Data from patients referred from primary care to the specialist Glasgow BP clinic, all of whom underwent ambulatory blood pressure monitoring (ABPM) were analysed. The independent variables included a range of conventional clinical parameters included in the referral letter along with OBP. Missing data were imputed using K nearest neighbours, an ML algorithm that approximates a point value based on the nearest available point values. Following this, four ML algorithms (support vector machine, decision tree, random forest (RF) and extreme gradient boosting (XGBoost)) were applied to the dataset, split into 70% training and 30% validation subsets. Performance of models was reported using area under the curve, accuracy, precision (fraction of relevant instances among the retrieved instances) and recall (fraction of the total amount of relevant instances that were actually retrieved) measures. Results: There were 926 patients – average age 51 ± 16 years, 43%-female, 49% were new presentation for investigation of hypertension, 38% were not on any BP lowering therapy, 1.1% had type 2 diabetes and 5.2% had eGFR < 60. The proportion of different BP patterns were – Normal BP:8.1%, Normal BP-masked:3.7%, Normal BP-whitecoat: 30.7%, Hypertension-whitecoat:23.3% and Hypertension:34%. Of the four predictor models, the highest classification accuracies were obtained for the XGBoost algorithm (accuracy:85%, precision:85%) followed by the RF classifier (accuracy:84%, precision:84%). Figure-1 demonstrates the multiclass AUC and leading predictors using the XGBoost model. Conclusions: ML models are able to predict WC and masked patterns in hypertensive patients and those suspected of having hypertension with relatively high accuracy and this warrants validation in larger cohorts.

In this paper, we explore model-based approach to training robust and interpretable binarized regression models for multiclass classification tasks using Mixed-Integer Programming (MIP). Our MIP model balances the optimization of prediction margin and model size by using a weighted objective that: minimizes the total margin of incorrectly classified training instances, maximizes the total margin of correctly classified training instances, and maximizes the overall model regularization. We conduct two sets of experiments to test the classification accuracy of our MIP model over standard and corrupted versions of multiple classification datasets, respectively. In the first set of experiments, we show that our MIP model outperforms an equivalent Pseudo-Boolean Optimization (PBO) model and achieves competitive results to Logistic Regression (LR) and Gradient Descent (GD) in terms of classification accuracy over the standard datasets. In the second set of experiments, we show that our MIP model outperforms the other models (i.e., GD and LR) in terms of classification accuracy over majority of the corrupted datasets. Finally, we visually demonstrate the interpretability of our MIP model in terms of its learned parameters over the MNIST dataset. Overall, we show the effectiveness of training robust and interpretable binarized regression models using MIP.

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