Statistical inference on change points in generalized semiparametric segmented models.

This article focuses on developing a comprehensive semiparametric framework for detecting and estimating change points in generalized segmented models, which are widely used to model nonlinear effects with breakpoints (change points) in various scientific fields. The authors propose a semismooth estimating equation combined with a two-step semismooth Newton-Raphson (To-SNR) algorithm for efficient parameter estimation, and introduce an average score-type test to rigorously assess the existence of change points. Theoretical properties such as root-n consistency, asymptotic normality, and efficiency of the estimators are established, and extensive simulations demonstrate improved estimation accuracy and hypothesis testing performance compared to existing methods for binary and count outcomes. An application to cardiovascular data from the Blue Cross Blue Shield of Michigan Cardiovascular Consortium illustrates the method’s ability to identify clinically meaningful change points in body mass index and glomerular filtration rate affecting bleeding risk after intervention.