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Factor copula models for right-censored clustered survival data

Author

Listed:
  • Eleanderson Campos

    (Federal University of Lavras
    Universiteit Hasselt)

  • Roel Braekers

    (Universiteit Hasselt
    KU Leuven)

  • Devanil J. Souza

    (Federal University of Lavras)

  • Lucas M. Chaves

    (Federal University of Lavras)

Abstract

In this article we extend the factor copula model to deal with right-censored event time data grouped in clusters. The new methodology allows for clusters to have variable sizes ranging from small to large and intracluster dependence to be flexibly modeled by any parametric family of bivariate copulas, thus encompassing a wide range of dependence structures. Incorporation of covariates (possibly time dependent) in the margins is also supported. Three estimation procedures are proposed: both one- and two-stage parametric and a two-stage semiparametric method where marginal survival functions are estimated by using a Cox proportional hazards model. We prove that the estimators are consistent and asymptotically normally distributed, and assess their finite sample behavior with simulation studies. Furthermore, we illustrate the proposed methods on a data set containing the time to first insemination after calving in dairy cattle clustered in herds of different sizes.

Suggested Citation

  • Eleanderson Campos & Roel Braekers & Devanil J. Souza & Lucas M. Chaves, 2021. "Factor copula models for right-censored clustered survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 499-535, July.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:3:d:10.1007_s10985-021-09525-5
    DOI: 10.1007/s10985-021-09525-5
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    References listed on IDEAS

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    1. Jose S. Romeo & Renate Meyer & Diego I. Gallardo, 2018. "Bayesian bivariate survival analysis using the power variance function copula," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 355-383, April.
    2. Barthel, Nicole & Geerdens, Candida & Killiches, Matthias & Janssen, Paul & Czado, Claudia, 2018. "Vine copula based likelihood estimation of dependence patterns in multivariate event time data," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 109-127.
    3. Nicole Barthel & Candida Geerdens & Claudia Czado & Paul Janssen, 2019. "Dependence modeling for recurrent event times subject to right‐censoring with D‐vine copulas," Biometrics, The International Biometric Society, vol. 75(2), pages 439-451, June.
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    6. Luc Duchateau & Paul Janssen, 2004. "Penalized Partial Likelihood for Frailties and Smoothing Splines in Time to First Insemination Models for Dairy Cows," Biometrics, The International Biometric Society, vol. 60(3), pages 608-614, September.
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