A Functional Early Warning Model for Sparse Binary Monitoring Data Using Penalized Logistic Splines

Abstract

Early warning systems aim to detect increasing risk in dynamic processes before critical events occur. In many applications, observations are sparse binary measurements collected at irregular time points, creating challenges for traditional longitudinal and functional data methods. This paper proposes a functional early warning model based on penalized logistic spline estimation within an RKHS induced by a composite kernel. The proposed kernel combines Sobolev, squared exponential, and rational quadratic components to capture global smoothness and local temporal variation. The estimator is obtained by penalized likelihood maximization and computed through a representer theorem based on finite-dimensional formulation with penalized iteratively reweighted least squares. Simulation studies and a longitudinal clinical application demonstrate the effectiveness of the proposed approach for dynamic risk assessment.