A large and diverse set of measurements are regularly collected during a patient's hospital stay to monitor their health status. Tools for integrating these measurements into severity scores, that accurately track changes in illness severity, can improve clinicians ability to provide timely interventions. Existing approaches for creating such scores either 1) rely on experts to fully specify the severity score, 2) infer a score using detailed models of disease progression, or 3) train a predictive score, using supervised learning, by regressing against a surrogate marker of severity such as the presence of downstream adverse events. The first approach does not extend to diseases where an accurate score cannot be elicited from experts. The second assumes that the progression of disease can be accurately modeled, limiting its application to populations with simple, well-understood disease dynamics. The third approach, also most commonly used, often produces scores that suffer from bias due to treatment-related censoring (Paxton et al, 2013). Specifically, since the downstream outcomes used for their training are observed only noisily and are influenced by treatment administration patterns, these scores do not generalize well when treatment administration patterns change. We propose a novel ranking based framework for disease severity score learning (DSSL). DSSL exploits the following key observation: while it is challenging for experts to quantify the disease severity at any given time, it is often easy to compare the disease severity at two different times. Extending existing ranking algorithms, DSSL learns a function that maps a vector of patient's measurements to a scalar severity score subject to two constraints. First, the resulting score should be consistent with the expert's ranking of the disease severity state. Second, changes in score between consecutive periods should be smooth. We apply DSSL to the problem of learning a sepsis severity score using a large, real-

We study the problem of optimal leader selection in consensus networks under two performance measures (1) formation coherence when subject to additive perturbations, as quantified by the steady-state variance of the deviation from the desired trajectory, and (2) convergence rate to a consensus value. The objective is to identify the set of k leaders that optimizes the chosen performance measure. In both cases, an optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the k-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the k-leader selection problem can be solved in polynomial time (in both k and the network size n). We give an O(n 3 ) solution for optimal k-leader selection in path graphs and an O(kn 3 ) solution for optimal k-leader selection in ring graphs.

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BackgroundThis study estimated the extent and predictors of primary nonadherence (i.e., prescriptions made by physicians but not initiated by patients) to methotrexate and to biologics or tofacitinib in rheumatoid arthritis (RA) patients who were newly prescribed these medications.MethodsUsing administrative claims linked with electronic health records (EHRs) from multiple healthcare provider organizations in the USA, RA patients who received a new prescription for methotrexate or biologics/tofacitinib were identified from EHRs. Claims data were used to ascertain filling or administration status. A logistic regression model for predicting primary nonadherence was developed and tested in training and test samples. Predictors were selected based on clinical judgment and LASSO logistic regression.ResultsA total of 36.8% of patients newly prescribed methotrexate failed to initiate methotrexate within 2 months; 40.6% of patients newly prescribed biologics/tofacitinib failed to initiate within 3 months. Factors associated with methotrexate primary nonadherence included age, race, region, body mass index, count of active drug ingredients, and certain previously diagnosed and treated conditions at baseline. Factors associated with biologics/tofacitinib primary nonadherence included age, insurance, and certain previously treated conditions at baseline. The area under the receiver operating characteristic curve of the logistic regression model estimated in the training sample and applied to the independent test sample was 0.86 and 0.78 for predicting primary nonadherence to methotrexate and to biologics/tofacitinib, respectively.ConclusionsThis study confirmed that failure to initiate new prescriptions for methotrexate and biologics/tofacitinib was common in RA patients. It is feasible to predict patients at high risk of primary nonadherence to methotrexate and to biologics/tofacitinib and to target such patients for early interventions to promote adherence.