The segmented model has significant applications in scientific research when the change-point effect exists. In this article, we propose a comprehensive semiparametric framework in segmented models to test the existence and estimate the location of change points in the generalized outcome setting. The proposed framework is based on a semismooth estimating equation for the change-point estimation and an average score-type test for hypothesis testing. The root-n consistency, asymptotic normality, and asymptotic efficiency of estimators for all parameters in the segmented model are rigorously studied. The distribution of the average score-type test statistics under the null hypothesis is rigorously derived. Extensive simulation studies are conducted to assess the numerical performance of the proposed change-point estimation method and the average score-type test. We investigate change-point effects of baseline glomerular filtration rate and body mass index on bleeding after intervention using data from Blue Cross Blue Shield. This application study successfully identifies statistically significant change-point effects, with the estimated values providing clinically meaningful insights.