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Abstract This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze directional stationary solutions of the proposed formulation, obtaining a sufficient condition for a directional stationary solution to achieve optimality and establishing a bound of the distance from the solution to a reference point. We develop an efficient algorithm that adopts an alternating direction method of multiplier (ADMM), showing that the iterates converge to a directional stationary solution under certain conditions. In the numerical experiment, we implement the algorithm for generalized linear models with convex and nonconvex group regularizers to evaluate the model performance on various data types, noise levels, and sparsity settings. 

Background The United States has experienced high surge in COVID-19 cases since the dawn of 2020. Identifying the types of diagnoses that pose a risk in leading COVID-19 death casualties will enable our community to obtain a better perspective in identifying the most vulnerable populations and enable these populations to implement better precautionary measures. Objective To identify demographic factors and health diagnosis codes that pose a high or a low risk to COVID-19 death from individual health record data sourced from the United States. Methods We used logistic regression models to analyze the top 500 health diagnosis codes and demographics that have been identified as being associated with COVID-19 death. Results Among 223,286 patients tested positive at least once, 218,831 (98%) patients were alive and 4,455 (2%) patients died during the duration of the study period. Through our logistic regression analysis, four demographic characteristics of patients; age, gender, race and region, were deemed to be associated with COVID-19 mortality. Patients from the West region of the United States: Alaska, Arizona, California, Colorado, Hawaii, Idaho, Montana, Nevada, New Mexico, Oregon, Utah, Washington, and Wyoming had the highest odds ratio of COVID-19 mortality across the United States. In terms of diagnoses, Complications mainly related to pregnancy (Adjusted Odds Ratio, OR:2.95; 95% Confidence Interval, CI:1.4 - 6.23) hold the highest odds ratio in influencing COVID-19 death followed by Other diseases of the respiratory system (OR:2.0; CI:1.84 – 2.18), Renal failure (OR:1.76; CI:1.61 – 1.93), Influenza and pneumonia (OR:1.53; CI:1.41 – 1.67), Other bacterial diseases (OR:1.45; CI:1.31 – 1.61), Coagulation defects, purpura and other hemorrhagic conditions(OR:1.37; CI:1.22 – 1.54), Injuries to the head (OR:1.27; CI:1.1 - 1.46), Mood [affective] disorders (OR:1.24; CI:1.12 – 1.36), Aplastic and other anemias (OR:1.22; CI:1.12 – 1.34), Chronic obstructive pulmonary disease and allied conditions (OR:1.18; CI:1.06 – 1.32), Other forms of heart disease (OR:1.18; CI:1.09 – 1.28), Infections of the skin and subcutaneous tissue (OR: 1.15; CI:1.04 – 1.27), Diabetes mellitus (OR:1.14; CI:1.03 – 1.26), and Other diseases of the urinary system (OR:1.12; CI:1.03 – 1.21). Conclusion We found demographic factors and medical conditions, including some novel ones which are associated with COVID-19 death. These findings can be used for clinical and public awareness and for future research purposes.