Joint analysis of longitudinal data with dependent observation times

This article discusses regression analysis of longitudinal data that often occur in medical follow-up studies and observational investigations. For the analy- sis of these data, most of the existing methods assume that observation times are independent of recurrent events completely, or given covariates, which may not be true in practice. We propose a joint modeling approach that uses a latent variable and a completely unspecified link function to characterize the correlations between the longitudinal response variable and the observation times. For inference about regression parameters, estimating equation approaches are developed without in- volving estimation for latent variables and the asymptotic properties of the resulting estimators are established. Methods for model checking are also presented. The performance of the proposed estimation procedures are evaluated through Monte Carlo simulations, and a data set from a bladder tumor study is analyzed as an illustrative example. The analysis of longitudinal data has recently attracted considerable atten- tion. These data frequently occur in medical follow-up studies and observational investigations. For the analysis of longitudinal data, a number of methods have been developed, mostly under the assumption that the longitudinal response pro- cess and the observation process are independent completely, or given covariates. For example, Diggle, Liang, and Zeger (1994) presented an excellent summary about such commonly used methods as estimating equation and random-effect model approaches, and Lin and Ying (2001) and Welsh, Lin, and Carroll (2002) discussed general semiparametric regression analysis of longitudinal data when both observation times and the censoring times may depend on covariates. A common situation where informative observation times occur is that these times are subject or response variable-dependent. For example, they may be hospitalization times of subjects in the study (Wang, Qin and Chiang (2001)). In a bladder cancer study, Sun and Wei (2000) and Zhang (2002) discussed a