Semiparametric inference for longitudinal data with informative observation times and terminal event

In many longitudinal studies, irregularly repeated measures are often correlated with observation times. Also, there may exist a dependent terminal event such as death that stops the follow-up and is subject to right censoring. To deal with such complex data, we propose a class of flexible semiparametric marginal conditional mean models for longitudinal response processes. The new models include the interaction between the observation history and some covariates, and an unknown functional form of the length from the observation time to the terminal event time, while leaving the within-subject dependence structure of the response process and patterns of the observation process to be arbitrary. For estimation of both scalar and functional parameters in the proposed models, we develop a two-stage spline-based least squares estimation approach and establish the asymptotic properties of the proposed estimators. The performance of the proposed estimation procedure is examined by simulation studies, and a longitudinal data example is provided for illustration.