Statistical Modelling 8 (2008), 169198
Bayesian semiparametric multi-state models
Thomas Kneib
Department of Statistics,
Luwigs-Maximilian University,
D80539 München
Germany
eMail:
thomas.kneib@stat.uni-muenchen.de
Andrea Hennerfeind
Department of Statistics,
Luwigs-Maximilian University
Germany
Abstract:
Multi-state models provide a unified framework for the description of
the evolution of discrete phenomena in continuous time. One particular
example is Markov processes which can be characterised by a set of
time-constant transition intensities between the states. In this paper,
we will extend such parametric approaches to semiparametric models with
flexible transition intensities based on Bayesian versions of penalised
splines. The transition intensities will be modelled as smooth functions
of time and can further be related to parametric as well as nonparametric
covariate effects. Covariates with time-varying effects and frailty terms
can be included in addition. Inference will be conducted either fully
Bayesian (using Markov chain Monte Carlo simulation techniques) or
empirically Bayesian (based on a mixed model representation). A counting
process representation of semiparametric multi-state models provides the
likelihood formula and also forms the basis for model validation via
martingale residual processes. As an application, we will consider human
sleep data with a discrete set of sleep states such as REM and non-REM
phases. In this case, simple parametric approaches are inappropriate
since the dynamics underlying human sleep are strongly varying throughout
the night and individual-specific variation has to be accounted for using
covariate information and frailty terms.
Keywords:
frailties; martingale residuals; multi-state models; penalised splines;
time-varying effects; transition intensities
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