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 analysis 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 involving 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.