Far East Journal of Theoretical Statistics
Volume 19, Issue 2, Pages 185 - 201
(July 2006)
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A SEMI-MARKOV FRAILTY MODEL FOR MULTISTATE AND CLUSTERED
SURVIVAL DATA
Yohann Foucher (France), Philippe Saint-Pierre (France), Jean-Pierre Daures (France) and Jean-Francois Durand (France)
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Abstract: In the longitudinal analysis of
chronic diseases, investigators are often interested in studying multiple
transitions between various states of disease progression. Semi-Markov models
may be used for modeling this type of process. We propose a novel semi-Markov
model with random effects. This allows for the dependence of transition times
within subgroups. Another originality consists in the introduction of a
generalized Weibull distribution for the hazard functions, offering a more
global parametric method than those frequently used. Laplace transform is used
to define a marginal likelihood function in order to estimate the regression
parameters. A real dataset for HIV is analyzed to illustrate the methodology.
Correlation subgroups are defined according to the subjects, because a same
transition can be observed several times for a given subject. Based on our
model, we estimate individual effects and test the independence of observed
transition times. The results demonstrate that all the observations are
independent whoever the subject and that traditional semi-Markov models may thus
be used in our application. |
Keywords and phrases: semi-Markov process, gamma frailty, generalized Weibull, Laplace transform, HIV. |
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