Regression analysis of longitudinal data with random change point

A great deal of literature has been established for regression analysis of longitudinal data and in particular, many methods have been proposed for the situation where there exist some change points. However, most of these methods only apply to continuous response and focus on the situations where the change point only occurs on the response or the trend of the individual trajectory. In this article, we propose a new joint modeling approach that allows not only the change point to vary for different subjects or be subject-specific but also the effect heterogeneity of the covariates before and after the change point. The method combines a generalized linear mixed effect model with a random change point for the longitudinal response and a log-linear regression model for the random change point. For inference, a maximum likelihood estimation procedure is developed and the asymptotic properties of the resulting estimators, which differ from the standard asymptotic results, are established. A simulation study is conducted and suggests that the proposed method works well for practical situations. An application to a set of real data on COVID-19 is provided.