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**A copula-based Markov chain model for serially dependent event times with a dependent terminal event.**
*(English)*
Zbl 1478.62257

Jpn. J. Stat. Data Sci. 4, No. 2, 917-951 (2021); correction ibid. 4, No. 1, 475 (2021).

Summary: Copula modeling for serial dependence has been extensively discussed in a time series context. However, fitting copula-based Markov models for serially dependent survival data is challenging due to the complex censoring mechanisms. The purpose of this paper is to develop likelihood-based methods for fitting a copula-based Markov chain model to serially dependent event times that are dependently censored by a terminal event, such as death. We propose a novel copula-based Markov chain model for describing serial dependence in recurrent event times. We also apply another copula model for handling dependent censoring. Due to the complex likelihood function with the two copulas, we propose a two-stage estimation method under Weibull distributions for fitting the survival data. The asymptotic normality of the proposed estimator is established through the theory of estimating functions. We propose a jackknife method for interval estimates, which is shown to be asymptotically consistent. To select suitable copulas for a given dataset, we propose a model selection method according to the 2nd stage likelihood. We conduct simulation studies to assess the performance of the proposed methods. For illustration, we analyze survival data from colorectal cancer patients. We implement the proposed methods in our original R package “Copula.Markov.survival” that is made available in CRAN (https://cran.r-project.org/).

### MSC:

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62H05 | Characterization and structure theory for multivariate probability distributions; copulas |

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

62G05 | Nonparametric estimation |

62H12 | Estimation in multivariate analysis |

62E20 | Asymptotic distribution theory in statistics |

62N01 | Censored data models |

62N05 | Reliability and life testing |

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

### Keywords:

copulas; Markov chain; serial dependence; dependent censoring; survival analysis; time series
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\textit{X.-W. Huang} et al., Jpn. J. Stat. Data Sci. 4, No. 2, 917--951 (2021; Zbl 1478.62257)

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