A more flexible joint latent model for longitudinal and survival time data

In this article, a more flexible and easily explained joint latent model with time-varying coefficients is used to characterize time-dependent responses and a failure time. The dependence within time-dependent responses and between time-dependent responses and a failure time, and the heterogeneity in both processes are established through partially non-parametric latent variables. Based on longitudinal and survival time data, an estimation procedure is proposed for the parameter functions of the joint latent model. In our estimation, the approximated likelihood is constructed via substituting the basis function expansions for parameter functions. The expectation and maximization (EM) algorithm is then implemented to obtain the maximizer of the approximated likelihood function, and, hence, the estimated parameter functions. The validity of the considered joint latent model enables us to derive the asymptotic properties of the estimated functions. Moreover, the corresponding finite sample properties and the usefulness of our methods are demonstrated through a Monte Carlo simulation and the AIDS Clinical Trials Group (ACTG) 175 data. A possible extension of our joint latent model and some additional topics of interest are also discussed herein.