Motivated by an investigation of the relationship between blood pressure change and progression of microalbuminuria (MA) among individuals with type I diabetes, we propose a new semiparametric threshold model for censored longitudinal data analysis. We also study a new semiparametric Bayes information criterion-type criterion for identifying the parametric component of the proposed model. Cluster effects in the model are implemented as unknown fixed effects. Asymptotic properties are established for the proposed estimators. A quadratic approximation used to implement the estimation procedure makes the method very easy to implement by avoiding the computation of multiple integrals and the need for iterative algorithms. Simulation studies show that the proposed methods work well in practice. An illustration using the Wisconsin Diabetes Registry dataset suggests some interesting findings.