A semi-Markov model based on generalized Weibull distribution with an illustration for HIV disease.
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.
Foucher
Yohann
Y
Institut Universitaire de Recherche Clinique, Laboratoire de Biostatistique - 641, avenue du Doyen Gaston Giraud, 34093 Montpellier, France. Yohann.Foucher@iurc.montp.inserm.fr
Mathieu
Eve
E
Saint-Pierre
Philippe
P
Durand
Jean-François
JF
Daurès
Jean-Pierre
JP
D000328:Adult; D000367:Age Factors; D000368:Aged; D000369:Aged, 80 and over; D000465:Algorithms; D018450:Disease Progression; D018562:Disease Transmission, Infectious / Q000706:statistics & numerical data; D005260:Female; D015658:HIV Infections / Q000209:etiology* / Q000635:transmission; D006505:Hepatitis / Q000150:complications; D020010:Heterosexuality; D006716:Homosexuality; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D008297:Male; D008390:Markov Chains; D008875:Middle Aged; D015233:Models, Statistical; D015999:Multivariate Analysis; D011336:Probability; D016016:Proportional Hazards Models; D012737:Sex Factors; D016008:Statistical Distributions; D019966:Substance-Related Disorders