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Stat Med. 2019 Sep 20;38(21):3961-3973. doi: 10.1002/sim.8213. Epub 2019 Jun 4.

Analysis of clustered failure time data with cure fraction using copula.

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Department of Mathematics and Statistics, McGill University, Montréal, Canada.
Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montréal, Canada.
Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina.


Clustered survival data in the presence of cure has received increasing attention. In this paper, we consider a semiparametric mixture cure model which incorporates a logistic regression model for the cure fraction and a semiparametric regression model for the failure time. We utilize Archimedean copula (AC) models to assess the strength of association for both susceptibility and failure times between susceptible individuals in the same cluster. Instead of using the full likelihood approach, we consider a composite likelihood function and a two-stage estimation procedure for both marginal and association parameters. A Jackknife procedure that takes out one cluster at a time is proposed for the variance estimation of the estimators. Akaike information criterion is applied to select the best model among ACs. Simulation studies are performed to validate our estimating procedures, and two real data sets are analyzed to demonstrate the practical use of our proposed method.


Archimedean copula; Cox proportional hazards model; accelerated failure time model; composite likelihood; two-stage estimation


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