A latent process model for joint modeling of events and marker.
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.
Hashemi
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R
Razi University, Faculty of Science, Department of Statistics, Bagh-e-Ahrisham, Kermanshah, Iran.
Jacqmin-Gadda
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H
Commenges
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D
D000368:Aged; D000465:Algorithms; D003072:Cognition Disorders; D003627:Data Interpretation, Statistical; D005602:France; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D008875:Middle Aged; D011594:Psychometrics; D013269:Stochastic Processes; D013997:Time Factors