A Multi-way Multi-task Learning Approach for Multinomial Logistic Regression An Application in Joint Prediction of Appointment Miss-opportunities across Multiple Clinics

Objectives: Whether they have been engineered for it or not, most healthcare systems experience a variety of unexpected events such as appointment miss-opportunities that can have significant impact on their revenue, cost and resource utilization. In this paper, a multi-way multi-task learning model based on multinomial logistic regression is proposed to jointly predict the occurrence of different types of miss-opportunities at multiple clinics. Methods: An extension of L-1/L-2 regularization is proposed to enable transfer of information among various types of miss-opportunities as well as different clinics. A proximal algorithm is developed to transform the convex but non-smooth likelihood function of the multi-way multi-task learning model into a convex and smooth optimization problem solvable using gradient descent algorithm. Results: A dataset of real attendance records of patients at four different clinics of a VA medical center is used to verify the perform ance of the proposed multi-task learning approach. Additionally, a simulation study, investigating more general data situations is provided to highlight the specific aspects of the proposed approach. Various individual and integrated multinomial logistic regression models with/without LASSO penalty along with a number of other common classification algorithms are fitted and compared against the proposed multi-way multi-task learning approach. Fivefold cross validation is used to estimate comparing models parameters and their predictive accuracy. The multi-way multi-task learning framework enables the proposed approach to achieve a considerable rate of parameter shrinkage and superior prediction accuracy across various types of miss-opportunities and clinics. Conclusions: The proposed approach provides an integrated structure to effectively transfer knowledge among different miss-opportunities and clinics to reduce model size, increase estimation efficacy, and more importantly improve predictions results. The proposed framework can be effectively applied to medical centers with multiple clinics, especially those suffering from information scarcity on some type of disruptions and/or clinics.