A copula-based Markov chain model for serially dependent event times with a dependent terminal event
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Recent Statistical Methods for Survival Analysis
A copula‑based Markov chain model for serially dependent event times with a dependent terminal event Xin‑Wei Huang1 · Weijing Wang1 · Takeshi Emura2 Received: 10 March 2020 / Accepted: 6 August 2020 © Japanese Federation of Statistical Science Associations 2020
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/). Keywords Copulas · Markov chain · Serial dependence · Dependent censoring · Survival analysis · Time series
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s4208 1-020-00087-8) contains supplementary material, which is available to authorized users. * Takeshi Emura [email protected] Extended author information available on the last page of the article
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Japanese Journal of Statistics and Data Science
1 Introduction Modeling serial correlations in time series data plays a fundamental role in a variety of statistical problems. For example, time series data arising from daily manufacturing processes, stock prices, and health check-ups, are often not independent since today’s conditions may depend on the past. Accordingly, statistical models accounting for serial dependence have been extensively studied in the literature. Most existing literature focuses on the conditional linear models, such as the first-order autoregressive model [i.e., the AR(1) model]. However, the assumption of the conditional linear dependence can be restrictive for some real life data Since the pioneering work of Darsow et al. (1992), copula-based Markov chain models have been successfully applied to a number of different statistical problems. The appl
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