Semiparametric regression analysis of multivariate longitudinal data with informative observation times

Multivariate longitudinal data arises when subjects under study may experience several possible related response outcomes. This article proposed a new class of flexible semiparametric models for multivariate longitudinal data with informative observation times through latent variables and completely unspecified link functions, which allows for any functional forms of covariate effects on the intensity functions for the observation processes. A novel estimating equation approach that does not rely on forms of link functions and distributions of frailties is developed. The asymptotic properties for the resulting estimators and the model checking technique for the overall fit of the proposed models are established. The simulation results show that the proposed approach works well. The analysis of skin cancer chemoprevention trial data is provided for illustration.