Sieve estimation in semiparametric modeling of longitudinal data with informative observation times

Analyzing irregularly spaced longitudinal data often involves modeling possibly correlated response and observation processes. In this article, we propose a new class of semiparametric mean models that allows for the interaction between the observation history and covariates, leaving patterns of the observation process to be arbitrary. For inference on the regression parameters and the baseline mean function, a spline-based least squares estimation approach is proposed. The consistency, rate of convergence, and asymptotic normality of the proposed estimators are established. Our new approach is different from the usual approaches relying on the model specification of the observation scheme, and it can be easily used for predicting the longitudinal response. Simulation studies demonstrate that the proposed inference procedure performs well and is more robust. The analyses of bladder tumor data and medical cost data are presented to illustrate the proposed method.