Sparse Generalized Functional Linear Model for Predicting Remission Status of Depression Patients

Complex diseases such as major depression affect people over time in complicated patterns. Longitudinal data analysis is thus crucial for understanding and prognosis of such diseases and has received considerable attention in the biomedical research community. Traditional classification and regression methods have been commonly applied in a simple (controlled) clinical setting with a small number of time points. However, these methods cannot be easily extended to the more general setting for longitudinal analysis, as they are not inherently built for time-dependent data. Functional regression, in contrast, is capable of identifying the relationship between features and outcomes along with time information by assuming features and/or outcomes as random functions over time rather than independent random variables. In this paper, we propose a novel sparse generalized functional linear model for the prediction of treatment remission status of the depression participants with longitudinal features. Compared to traditional functional regression models, our model enables high-dimensional learning, smoothness of functional coefficients, longitudinal feature selection and interpretable estimation of functional coefficients. Extensive experiments have been conducted on the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) data set and the results show that the proposed sparse functional regression method achieves significantly higher prediction power than existing approaches.