Factor copula models for right-censored clustered survival data.
Eleanderson Campos, Roel Braekers, Devanil J de Souza, Lucas M Chaves
Author Information
Eleanderson Campos: Department of Statistics, Federal University of Lavras, Lavras, Minas Gerais, Brazil. eleandersoncampos@estudante.ufla.br. ORCID
Roel Braekers: Data Science Institute, Interuniversity Institute for Biostatistics and statistical Bioinformatics - I-BioStat, Universiteit Hasselt, Diepenbeek, Belgium.
Devanil J de Souza: Department of Statistics, Federal University of Lavras, Lavras, Minas Gerais, Brazil.
Lucas M Chaves: Department of Statistics, Federal University of Lavras, Lavras, Minas Gerais, Brazil.
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.
Andersen EW (2005) Two-stage estimation in copula models used in family studies. Lifetime Data Anal 11(3):333–350
[DOI: 10.1007/s10985-005-2966-7]
Barthel N, Geerdens C, Killiches M, Janssen P, Czado C (2018) Vine copula based likelihood estimation of dependence patterns in multivariate event time data. Comput Stat Data Anal 117:109–127
[DOI: 10.1016/j.csda.2017.07.010]
Barthel N, Geerdens C, Czado C, Janssen P (2019) Dependence modeling for recurrent event times subject to right-censoring with d-vine copulas. Biometrics 75(2):439–451
[DOI: 10.1111/biom.13014]
Cox DR (1972) Regression models and life-tables. J Roy Stat Soc: Ser B (Methodol) 34(2):187–202
Cox DR, Hinkley D (1974) Theoretical statistics. Chapman and Hall, London
[DOI: 10.1007/978-1-4899-2887-0]
Duchateau L, Janssen P (2004) Penalized partial likelihood for frailties and smoothing splines in time to first insemination models for dairy cows. Biometrics 60(3):608–614
[DOI: 10.1111/j.0006-341X.2004.00209.x]
Duchateau L, Janssen P (2008) The frailty model. Springer, Berlin
Emura T, Nakatochi M, Murotani K, Rondeau V (2017) A joint frailty-copula model between tumour progression and death for meta-analysis. Stat Methods Med Res 26(6):2649–2666
[DOI: 10.1177/0962280215604510]
Glidden DV (2000) A two-stage estimator of the dependence parameter for the clayton-oakes model. Lifetime Data Anal 6(2):141–156
[DOI: 10.1023/A]
Goethals K, Janssen P, Duchateau L (2008) Frailty models and copulas: similarities and differences. J Appl Stat 35(9):1071–1079
[DOI: 10.1080/02664760802271389]
Hougaard P (2000) Analysis of multivariate survival data. Springer, New York
[DOI: 10.1007/978-1-4612-1304-8]
Joe H (2005) Asymptotic efficiency of the two-stage estimation method for copula-based models. J Multiv Anal 94(2):401–419
[DOI: 10.1016/j.jmva.2004.06.003]
Joe H (2014) Dependence modeling with copulas. Chapman & Hall/CRC, Boca Raton
[DOI: 10.1201/b17116]
Krupskii P, Joe H (2013) Factor copula models for multivariate data. J Multiv Anal 120:85–101
[DOI: 10.1016/j.jmva.2013.05.001]
Lehmann EL, Casella G (1998) Theory of point estimation. Springer, New York
Massonnet G, Janssen P, Duchateau L (2009) Modelling udder infection data using copula models for quadruples. J Stat Plan Inference 139(11):3865–3877
[DOI: 10.1016/j.jspi.2009.05.025]
Nelsen RB (2007) An introduction to copulas. Springer Science & Business Media, New York
Othus M, Li Y (2010) A gaussian copula model for multivariate survival data. Stat Biosci 2(2):154–179
[DOI: 10.1007/s12561-010-9026-x]
Prenen L, Braekers R, Duchateau L (2017a) Extending the archimedean copula methodology to model multivariate survival data grouped in clusters of variable size. J R Stat Soc Ser B 79(2):483–505
[DOI: 10.1111/rssb.12174]
Prenen L, Braekers R, Duchateau L, De Troyer E (2017b) Sunclarco: survival analysis using copulas. R package version 1
R Core Team (2018) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria
Romeo JS, Meyer R, Gallardo DI (2018) Bayesian bivariate survival analysis using the power variance function copula. Lifetime Data Anal 24(2):355–383
[DOI: 10.1007/s10985-017-9396-1]
Schneider S, Demarqui FN, Colosimo EA, Mayrink VD (2020) An approach to model clustered survival data with dependent censoring. Biom J 62(1):157–174
[DOI: 10.1002/bimj.201800391]
Shih JH, Louis TA (1995) Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51:1384–1399
[DOI: 10.2307/2533269]
Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publ Inst Statist Univ Par 8:229–231
Spiekerman CF, Lin D (1998) Marginal regression models for multivariate failure time data. J Am Stat Assoc 93(443):1164–1175
[DOI: 10.1080/01621459.1998.10473777]
Therneau TM (2015) A Package for Survival Analysis in S. R package version 2:38
Van der Vaart AW (2000) Asymptotic statistics, vol 3. Cambridge University Press, Cambridge
Wienke A (2011) Frailty models in survival analysis. Chapman and Hall, Boca Raton
Xu JJ (1996) Statistical modelling and inference for multivariate and longitudinal discrete response data. PhD thesis, University of British Columbia
Yan J et al (2007) Enjoy the joy of copulas: with a package copula. J Stat Softw 21(4):1–21
[DOI: 10.18637/jss.v021.i04]
