In many situations, both longitudinal data and a primary endpoint in the form of a binary response, a count, or a continuous measurement may be collected. Such primary endpoints are usually represented by a generalized linear model. Here, we would like to model the primary endpoint as depending on the longitudinal data as covariates. Thus, for joint modeling of the longitudinal and such primary endpoint data, we consider generalized linear models with longitudinal covariates, which assume that the longitudinal data follow a linear mixed effects model and the primary endpoint depends on the longitudinal data through latent subject specific random effects. We discuss five estimation procedures, which include two stage, best linear unbiased prediction, quasilikelihood, conditional likelihood, and maximum likelihood. We study the large sample bias and relative efficiency of the methods. The proposed methods are illustrated through application to data from the Framingham study.
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