A penalized likelihood approach for a progressive three-state model with censored and truncated data: application to AIDS.

*(English)*Zbl 1059.62664Summary: We consider the estimation of the intensity and survival functions for a continuous time progressive three-state semi-Markov model with intermittently observed data. The estimator of the intensity function is defined nonparametrically as the maximum of a penalized likelihood. We thus obtain smooth estimates of the intensity and survival functions. This approach can accommodate complex observation schemes such as truncation and interval censoring. The method is illustrated with a study of hemophiliacs infected by HIV. The intensity functions and the cumulative distribution functions for the time to infection and for the time to AIDS are estimated. Covariates can easily be incorporated into the model.

##### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62N02 | Estimation in survival analysis and censored data |

62G05 | Nonparametric estimation |

60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |

##### Keywords:

intensity function; interval-censoring; penalized likelihood; splines; three-state semi-Markov model; truncation
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\textit{P. Joly} and \textit{D. Commenges}, Biometrics 55, No. 3, 887--890 (1999; Zbl 1059.62664)

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