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Abstract In statistical literature, joint modeling survival data and longitudinal covariates has been studied, but almost all existing methods rely on parametric or semiparametric assumptions on longitudinal covariate process, and the resulting inferences critically depend on the validity of these assumptions that are unjustifiable or difficult to verify in practice. Without these parametric/semiparametric assumptions, this article proposes a generalized latent proportional hazards (GLPH) model for right censored survival time with longitudinal covariates, which treats longitudinal covariate process as unknown stochastic process with unknown hidden random variable and takes into account the within-subject historic change patterns of longitudinal covariates. The asymptotic properties of empirical likelihood MLE for GLPH model are established here for intensive longitudinal covariates, which lead to a statistical analysis of a very intensive longitudinal dataset. Moreover, the established asymptotic results give the construction of a novel method for joint modeling survival time and sparse longitudinal covariates via GLPH model.
Ren et al. (Fri,) studied this question.