Functional Multivariable Logistic Regression With an Application to HIV Viral Suppression Prediction

Motivated by improving the prediction of the human immunodeficiency virus (HIV) suppression status using electronic health records (EHR) data, we propose a functional multivariable logistic regression model, which accounts for the longitudinal binary process and continuous process simultaneously. Specifically, the longitudinal measurements for either binary or continuous variables are modeled by functional principal components analysis, and their corresponding functional principal component scores are used to build a logistic regression model for prediction. The longitudinal binary data are linked to underlying Gaussian processes. The estimation is done using penalized spline for the longitudinal continuous and binary data. Group-lasso is used to select longitudinal processes, and the multivariate functional principal components analysis is proposed to revise functional principal component scores with the correlation. The method is evaluated via comprehensive simulation studies and then applied to predict viral suppression using EHR data for people living with HIV in South Carolina.