Joint analysis of longitudinal data with additive mixed effect model for informative observation times

• We propose a new joint modeling of longitudinal data with informative observation times via two random effects.
• A class of semiparametric mixed effects models is used for the longitudinal process, and an additive mixed effect model is used for the observation process.
• The proposed joint model is flexible and robust in that the distributions of the random effects and the dependence structure between two random effects are left unspecified.

Longitudinal data occur in many clinical and observational studies, and in many situations, longitudinal responses are often correlated with observation times. In this article, we propose a new joint model for the analysis of longitudinal data with informative observation times via two random effects. In particular, an additive mixed effect model is used for observation times. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are provided for model checking. The finite-sample behavior of the proposed method is evaluated through simulation studies, and an application to a bladder cancer study is illustrated.