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Erning Li
Joint Models for a Primary Endpoint and Longitudinal Measurements

The relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest. A relevant framework is to assume the primary endpoint follows a generalized linear model with covariates that are subject-specific random effects in a linear mixed model for the longitudinal measurements. Normality of the random effects is a routine assumption in literature, which may be unrealistic. Under departure from normality, the methods depending on this parametric assumption can lead to biased inference or have poor coverage probability. We propose a full-likelihood approach which requires only that the random effects have a smooth density. EM algorithm is used for implementation and the random effects density is estimated along with other model parameters. To circumvent the numerical integration in the full-likelihood approach, a conditional estimation approach is proposed as an alternative where two unbiased estimating equations are derived and are straight forward and fast to implement. The proposed methods yield consistent inference across various true random effects distributions, and they are extended to accommodate multivariate longitudinal data. Their performances are illustrated by comparison to methods in literature, by an application to a study of osteopenia in peri-menopausal women, by an application to a study of hypertension, and via simulation.