A copula-based Markov chain model for serially dependent event times with a dependent terminal event

Xin Wei Huang, Weijing Wang, Takeshi Emura*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

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/).

Original languageEnglish
JournalJapanese Journal of Statistics and Data Science
DOIs
StateAccepted/In press - 2020

Keywords

  • Copulas
  • Dependent censoring
  • Markov chain
  • Serial dependence
  • Survival analysis
  • Time series

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