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Joint Likelihood Estimation for Joint Modeling Survival and Multiple Longitudinal Processes

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Motivated from an empirical analysis of data collected by a smoking cession study, we propose a joint model
(JM) of  survival data and multiple longitudinal covariate processes, develop an estimation procedure for
this model using likelihood-based approach, and further establish the consistency and asymptotic normality of
the resulting estimate. Computation for the proposed likelihood-based approach in the joint modeling is
particularly challenging since the estimation procedure involves numerical integration over multi-dimensional
space for the random effects in the JM. Existing numerical integration methods become ineffective or
infeasible for the JM. We introduce a numerical integration method based on computer experimental designs for
the JM. We conduct Monte Carlo simulation to examine the finite sample performance of the procedure and
compare the new numerical integration method with existing ones. We further illustrate the proposed procedure
via an empirical study of smoking cession data.