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Joint models for a GLM-type longitudinal response and a time-to-event with smooth random effects

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Longitudinal studies often entail non-Gaussian primary responses. When dropout occurs, potential non-ignorability of the missingness process may occur, and a joint model for the primary response and a time-to-event may represent an appealing tool to account for dependence between the two processes. As an extension to the GLMJM, recently proposed, and based on Gaussian latent effects, we assume that the random effects follow a smooth, P-spline based density. To estimate model parameters, we adopt a two-step conditional Newton–Raphson algorithm. Since the maximization of the penalized log-likelihood requires numerical integration over the random effect, which is often cumbersome, we opt for a pseudo-adaptive Gaussian quadrature rule to approximate the model likelihood. We discuss the proposed model by analyzing an original dataset on dilated cardiomyopathies and through a simulation study.
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Keywords: 01A23; 45B67; Joint models; MDCM data; mixture of P-splines; smooth random effect distribution

Document Type: Research Article

Affiliations: Statistics Division, Food and Agriculture Organization (FAO) of the United Nations, Viale delle Terme di Caracalla, 00153, Roma, Italy

Publication date: November 18, 2019

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