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A latent process model for joint modeling of events and marker
R Hashemi1, H Jacqmin-Gadda, D Commenges
1Razi University, Faculty of Science, Department of Statistics, Bagh-e-Ahrisham, Kermanshah, Iran.
Abstract:
The paper formulates joint modeling of a counting process and a sequence of longitudinal measurements, governed by a common latent stochastic process. The latent process is modeled as a function of explanatory variables and a Brownian motion process. The conditional likelihood given values of the latent process at the measurement times, has been drawn using Brownian bridge properties; then integrating over all possible values of the latent process at the measurement times leads to the desired joint likelihood. An estimation procedure using joint likelihood and a numerical optimization is described. The method is applied to the study of cognitive decline and Alzheimer's disease.