Multiple Sclerosis (MS) progresses at an unpredictable rate, but predictions on the disease course in each patient would be extremely useful to tailor therapy to the individual needs. We explore different machine learning (ML) approaches to predict whether a patient will shift from the initial Relapsing-Remitting (RR) to the Secondary Progressive (SP) form of the disease, using only "real world" data available in clinical routine. The clinical records of 1624 outpatients (207 in the SP phase) attending the MS service of Sant'Andrea hospital, Rome, Italy, were used. Predictions at 180, 360 or 720 days from the last visit were obtained considering either the data of the last available visit (Visit-Oriented setting), comparing four classical ML methods (Random Forest, Support Vector Machine, K-Nearest Neighbours and AdaBoost) or the whole clinical history of each patient (History-Oriented setting), using a Recurrent Neural Network model, specifically designed for historical data. Missing values were handled by removing either all clinical records presenting at least one missing parameter (Feature-saving approach) or the 3 clinical parameters which contained missing values (Record-saving approach). The performances of the classifiers were rated using common indicators, such as Recall (or Sensitivity) and Precision (or Positive predictive value). In the visit-oriented setting, the Record-saving approach yielded Recall values from 70% to 100%, but low Precision (5% to 10%), which however increased to 50% when considering only predictions for which the model returned a probability above a given "confidence threshold". For the History-oriented setting, both indicators increased as prediction time lengthened, reaching values of 67% (Recall) and 42% (Precision) at 720 days. We show how "real world" data can be effectively used to forecast the evolution of MS, leading to high Recall values and propose innovative approaches to improve Precision towards clinically useful values.

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The course of multiple sclerosis begins with a relapsing-remitting phase, which evolves into a secondarily progressive form over an extremely variable period, depending on many factors, each with a subtle influence. To date, no prognostic factors or risk score have been validated to predict disease course in single individuals. This is increasingly frustrating, since several treatments can prevent relapses and slow progression, even for a long time, although the possible adverse effects are relevant, in particular for the more effective drugs. An early prediction of disease course would allow differentiation of the treatment based on the expected aggressiveness of the disease, reserving high-impact therapies for patients at greater risk. To increase prognostic capacity, approaches based on machine learning (ML) algorithms are being attempted, given the failure of other approaches. Here we review recent studies that have used clinical data, alone or with other types of data, to derive prognostic models. Several algorithms that have been used and compared are described. Although no study has proposed a clinically usable model, knowledge is building up and in the future strong tools are likely to emerge.

We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. Providing the existence of an oracle to solve suitably defined single objective integer subproblems, the algorithm can handle biobjective nonlinear integer problems, in particular biobjective convex quadratic integer optimization problems. Our numerical experience on a benchmark of biobjective integer linear programming instances shows the efficiency of the approach in comparison with existing state-of-the-art methods. Further experiments on biobjective integer quadratic programming instances are reported.

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