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In survival studies it is important to record the values of key longitudinalcovariates until the occurrence of event of a subject. For this reason, it isessential to study the association between longitudinal and time-to-eventoutcomes using the joint model. In this paper, profile likelihood approach hasbeen used to estimate the cumulative hazard and regression parameters from thejoint model of survival and longitudinal data. Moreover, we show the asymptoticnormality of the profile likelihood estimator via asymptotic expansion of theprofile likelihood and obtain the explicit form of the variance estimator. Theestimators of the regression parameters from the joint model are shown to besemi-parametric efficient.

Efficient Estimation For The Joint Model of Survival and Longitudinal Data