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Joint Dispersion Model with a Flexible Link
The objective is to model longitudinal and survival data jointly taking into
account the dependence between the two responses in a real HIV/AIDS dataset
using a shared parameter approach inside a Bayesian framework. We propose a
linear mixed effects dispersion model to adjust the CD4 longitudinal biomarker
data with a between-individual heterogeneity in the mean and variance. In doing
so we are relaxing the usual assumption of a common variance for the
longitudinal residuals. A hazard regression model is considered in addition to
model the time since HIV/AIDS diagnostic until failure, being the coefficients,
accounting for the linking between the longitudinal and survival processes,
time-varying. This flexibility is specified using Penalized Splines and allows
the relationship to vary in time. Because heteroscedasticity may be related
with the survival, the standard deviation is considered as a covariate in the
hazard model, thus enabling to study the effect of the CD4 counts' stability on
the survival. The proposed framework outperforms the most used joint models,
highlighting the importance in correctly taking account the individual
heterogeneity for the measurement errors variance and the evolution of the
disease over time in bringing new insights to better understand this
biomarker-survival relation.Comment: 27 pages, 3 figures, 2 table
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