ObjectiveLimited evidences are available on biomarkers to recognize Systemic Lupus erythematosus (SLE) patients at risk to develop erosive arthritis. Anti-citrullinated peptide antibodies (ACPA) have been widely investigated and identified in up to 50% of X-ray detected erosive arthritis; conversely, few studies evaluated anti-carbamylated proteins antibodies (anti-CarP). Here, we considered the application of machine learning models to identify relevant factors in the development of ultrasonography (US)-detected erosive damage in a large cohort of SLE patients with joint involvement.MethodsWe enrolled consecutive SLE patients with arthritis/arthralgia. All patients underwent joint (DAS28, STR) and laboratory assessment (detection of ACPA, anti-CarP, Rheumatoid Factor, SLE-related antibodies). The bone surfaces of metacarpophalangeal and proximal interphalangeal joints were assessed by US: the presence of erosions was registered with a dichotomous value (0/1), obtaining a total score (0–20). Concerning machine learning techniques, we applied and compared Logistic Regression and Decision Trees in conjunction with the feature selection Forward Wrapper method.ResultsWe enrolled 120 SLE patients [M/F 8/112, median age 47.0 years (IQR 15.0); median disease duration 120.0 months (IQR 156.0)], 73.3% of them referring at least one episode of arthritis. Erosive damage was identified in 25.8% of patients (mean±SD 0.7±1.6), all of them with clinically evident arthritis. We applied Logistic Regression in conjunction with the Forward Wrapper method, obtaining an AUC value of 0.806±0.02. As a result of the learning procedure, we evaluated the relevance of the different factors: this value was higher than 35% for ACPA and anti-CarP.ConclusionThe application of Machine Learning Models allowed to identify factors associated with US-detected erosive bone damage in a large SLE cohort and their relevance in determining this phenotype. Although the scope of this study is limited by the small sample size and its cross-sectional nature, the results suggest the relevance of ACPA and anti-CarP antibodies in the development of erosive damage as also pointed out in other studies.

In this manuscript, we consider the problem of minimizing a smooth function with cardinality constraint, i.e., the constraint requiring that the "Equation missing"-norm of the vector of variables cannot exceed a given threshold value. A well-known approach of the literature is represented by the class of penalty decomposition methods, where a sequence of penalty subproblems, depending on the original variables and new variables, are inexactly solved by a two-block decomposition method. The inner iterates of the decomposition method require to perform exact minimizations with respect to the two blocks of variables. The computation of the global minimum with respect to the original variables may be prohibitive in the case of nonconvex objective function. In order to overcome this nontrivial issue, we propose a modified penalty decomposition method, where the exact minimizations with respect to the original variables are replaced by suitable line searches along gradient-related directions. We also present a derivative-free penalty decomposition algorithm for black-box optimization. We state convergence results of the proposed methods, and we report the results of preliminary computational experiments.

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