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Copula-based score test for bivariate time-to-event data, with application to a genetic study of AMD progression

Author

Listed:
  • Tao Sun

    (University of Pittsburgh)

  • Yi Liu

    (University of Pittsburgh)

  • Richard J. Cook

    (University of Waterloo)

  • Wei Chen

    (Children’s Hospital of Pittsburgh)

  • Ying Ding

    (University of Pittsburgh)

Abstract

Motivated by a genome-wide association study to discover risk variants for the progression of Age-related Macular Degeneration (AMD), we develop a computationally efficient copula-based score test, in which the dependence between bivariate progression times is taken into account. Specifically, a two-step estimation approach with numerical derivatives to approximate the score function and observed information matrix is proposed. Both parametric and weakly parametric marginal distributions under the proportional hazards assumption are considered. Extensive simulation studies are conducted to evaluate the Type I error control and power performance of the proposed method. Finally, we apply our method to a large randomized trial data, the Age-related Eye Disease Study, to identify susceptible risk variants for AMD progression. The top variants identified on Chromosome 10 show significantly differential progression profiles for different genetic groups, which are critical in characterizing and predicting the risk of progression-to-late-AMD for patients with mild to moderate AMD.

Suggested Citation

  • Tao Sun & Yi Liu & Richard J. Cook & Wei Chen & Ying Ding, 2019. "Copula-based score test for bivariate time-to-event data, with application to a genetic study of AMD progression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 546-568, July.
    • Handle: RePEc:spr:lifeda:v:25:y:2019:i:3:d:10.1007_s10985-018-09459-5
    DOI: 10.1007/s10985-018-09459-5
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    References listed on IDEAS

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    1. Wenqing He & Jerald F. Lawless, 2003. "Flexible Maximum Likelihood Methods for Bivariate Proportional Hazards Models," Biometrics, The International Biometric Society, vol. 59(4), pages 837-848, December.
    2. Chen, Xiaohong & Fan, Yanqin & Pouzo, Demian & Ying, Zhiliang, 2010. "Estimation and model selection of semiparametric multivariate survival functions under general censorship," Journal of Econometrics, Elsevier, vol. 157(1), pages 129-142, July.
    3. Klara Goethals & Paul Janssen & Luc Duchateau, 2008. "Frailty models and copulas: similarities and differences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1071-1079.
    4. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    5. Johanna M Seddon & Robyn Reynolds & Yi Yu & Bernard Rosner, 2014. "Three New Genetic Loci (R1210C in CFH, Variants in COL8A1 and RAD51B) Are Independently Related to Progression to Advanced Macular Degeneration," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-11, January.
    6. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
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    Cited by:

    1. Yue Wei & Yi Liu & Tao Sun & Wei Chen & Ying Ding, 2020. "Gene‐based association analysis for bivariate time‐to‐event data through functional regression with copula models," Biometrics, The International Biometric Society, vol. 76(2), pages 619-629, June.
    2. Yichen Lou & Peijie Wang & Jianguo Sun, 2023. "A semi-parametric weighted likelihood approach for regression analysis of bivariate interval-censored outcomes from case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 628-653, July.
    3. Shu Jiang & Richard J. Cook, 2020. "A Mixture Model for Bivariate Interval-Censored Failure Times with Dependent Susceptibility," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(1), pages 37-62, April.

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