ABSTRACT
• We study the problem of estimating smooth curves which verify structural properties. • We propose a mathematical optimization formulation to build constrained P-splines. • An open-source Python library is developed: cpsplines. • We estimate constrained curves in simulated, COVID-19 and demographic data. Decision-making is often based on the analysis of complex and evolving data. Thus, having systems which allow to incorporate human knowledge and provide valuable support to the decider becomes crucial. In this work, statistical modelling and mathematical optimization paradigms merge to address the problem of estimating smooth curves which verify structural properties, both in the observed domain in which data have been gathered and outwards. We assume that the curve to be estimated is defined through a reduced-rank basis (B -splines) and fitted via a penalized splines approach (P -splines). To incorporate requirements about the sign, monotonicity and curvature in the fitting procedure, a conic programming approach is developed which, for the first time, successfully conveys out-of-range constrained prediction. In summary, the contributions of this paper are fourfold: first, a mathematical optimization formulation for the estimation of non-negative P-splines is proposed;second, previous results are generalized to the out-of-range prediction framework;third, these approaches are extended to other shape constraints and to multiple curves fitting;and fourth, an open source Python library is developed: cpsplines. We use simulated instances, data of the evolution of the COVID-19 pandemic and of mortality rates for different age groups to test our approaches. [ FROM AUTHOR]
ABSTRACT
Background and Objectives: Aspirin (ASA) is a commonly used antithrombotic drug that has been demonstrated to reduce venous thromboembolism. The aim was to analyze if geriatric COVID-19 patients undergoing a 100 mg/day Aspirin (ASA) treatment prior to hospitalization differ in hospital outcome compared to patients without previous ASA therapy. Materials and Methods: An observational retrospective study was carried out using an anonymized database including geriatric COVID-19 patients (March to April 2020) admitted to Madrid Hospitals Group. A group of COVID-19 patients were treated with low ASA (100 mg/day) prior to COVID-19 infection. Results: Geriatric ASA-treated patients were older (mean age over 70 years; n = 41), had higher frequency of hypertension and hyperlipidemia, and upon admission had higher D-dimer levels than non-ASA-treated patients (mean age over 73 years; n = 160). However, patients under ASA treatment did not show more frequent pulmonary thromboembolism (PE) than non-ASA-treated patients. ASA-treated geriatric COVID-19-infected patients in-hospital < 30 days all-cause mortality was more frequent than in non-ASA-treated COVID-19 patients. In ASA-treated COVID-19-infected geriatric patients, anticoagulant therapy with low molecular weight heparin (LMWH) significantly reduced need of ICU care, but tended to increase in-hospital < 30 days all-cause mortality. Conclusions: Prior treatment with a low dose of ASA in COVID-19-infected geriatric patients increased frequency of in-hospital < 30 days all-cause mortality, although it seemed to not increase PE frequency despite D-dimer levels upon admission being higher than in non-ASA users. In ASA-treated geriatric COVID-19-infected patients, addition of LMWH therapy reduced frequency of ICU care, but tended to increase in-hospital < 30 days all-cause mortality.