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A Semi‐Markov Model Based on Generalized Weibull Distribution with an Illustration for HIV Disease
Author(s) -
Foucher Yohann,
Mathieu Eve,
SaintPierre Philippe,
Durand JeanFrançois,
Daurès JeanPierre
Publication year - 2005
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200410170
Subject(s) - covariate , mathematics , weibull distribution , markov chain , exponential distribution , markov model , gamma distribution , parametric statistics , statistics , markov process , econometrics , statistical physics , physics
Multi‐state stochastic models are useful tools for studying complex dynamics such as chronic diseases. Semi‐Markov models explicitly define distributions of waiting times, giving an extension of continuous time and homogeneous Markov models based implicitly on exponential distributions. This paper develops a parametric model adapted to complex medical processes. (i) We introduced a hazard function of waiting times with a U or inverse U shape. (ii) These distributions were specifically selected for each transition. (iii) The vector of covariates was also selected for each transition. We applied this method to the evolution of HIV infected patients. We used a sample of 1244 patients followed up at the hospital in Nice, France. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)