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Abstract:
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In biomedical research, a steep rise or decline in longitudinal biomarkers may indicate latent disease progression, which may subsequently cause patients to drop out of the study. Ignoring the informative drop-out can cause bias in estimation of the longitudinal model. For these types of longitudinal data, we develop a joint partially linear model, with an aim to find the longitudinal trajectory. Specifically, an arbitrary function of time along with linear fixed and random covariate effects is proposed in the model for the biomarker, while a flexible semiparametric transformation model is used to describe the drop-out mechanism. Advantages of this semiparametric joint modeling include an easier interpretation than nonparametric models and a natural way to control for common (observable and unobservable) prognostic factors that affect both the longitudinal trajectory and the drop-out process. We describe a sieve maximum likelihood estimation procedure using the EM algorithm, where AIC and BIC are considered to select the number of knots. Desirable properties of the method have been shown through empirical process theory, simulation studies, and prostate cancer data application.
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