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Estimation and testing for clustered interval-censored bivariate survival data with application using the semi-parametric version of the Clayton–Oakes model

Author

Listed:
  • Bernard Rosner

    (Harvard Medical School)

  • Camden Bay

    (Harvard Medical School)

  • Robert J. Glynn

    (Harvard Medical School)

  • Gui-shuang Ying

    (University of Pennsylvania)

  • Maureen G. Maguire

    (University of Pennsylvania)

  • Mei-Ling Ting Lee

    (University of Maryland at College Park)

Abstract

The Kaplan–Meier estimator is ubiquitously used to estimate survival probabilities for time-to-event data. It is nonparametric, and thus does not require specification of a survival distribution, but it does assume that the risk set at any time t consists of independent observations. This assumption does not hold for data from paired organ systems such as occur in ophthalmology (eyes) or otolaryngology (ears), or for other types of clustered data. In this article, we estimate marginal survival probabilities in the setting of clustered data, and provide confidence limits for these estimates with intra-cluster correlation accounted for by an interval-censored version of the Clayton–Oakes model. We develop a goodness-of-fit test for general bivariate interval-censored data and apply it to the proposed interval-censored version of the Clayton–Oakes model. We also propose a likelihood ratio test for the comparison of survival distributions between two groups in the setting of clustered data under the assumption of a constant between-group hazard ratio. This methodology can be used both for balanced and unbalanced cluster sizes, and also when the cluster size is informative. We compare our test to the ordinary log rank test and the Lin-Wei (LW) test based on the marginal Cox proportional Hazards model with robust standard errors obtained from the sandwich estimator. Simulation results indicate that the ordinary log rank test over-inflates type I error, while the proposed unconditional likelihood ratio test has appropriate type I error and higher power than the LW test. The method is demonstrated in real examples from the Sorbinil Retinopathy Trial, and the Age-Related Macular Degeneration Study. Raw data from these two trials are provided.

Suggested Citation

  • Bernard Rosner & Camden Bay & Robert J. Glynn & Gui-shuang Ying & Maureen G. Maguire & Mei-Ling Ting Lee, 2023. "Estimation and testing for clustered interval-censored bivariate survival data with application using the semi-parametric version of the Clayton–Oakes model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 854-887, October.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:4:d:10.1007_s10985-022-09588-y
    DOI: 10.1007/s10985-022-09588-y
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    References listed on IDEAS

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    1. Ying, Z. & Wei, L. J., 1994. "The Kaplan-Meier Estimate for Dependent Failure Time Observations," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 17-29, July.
    2. Liuquan Sun & Lianming Wang & Jianguo Sun, 2006. "Estimation of the Association for Bivariate Interval‐censored Failure Time Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 637-649, December.
    3. R. L. Prentice, 2016. "Higher dimensional Clayton–Oakes models for multivariate failure time data," Biometrika, Biometrika Trust, vol. 103(1), pages 231-236.
    4. Donglin Zeng & Fei Gao & D. Y. Lin, 2017. "Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data," Biometrika, Biometrika Trust, vol. 104(3), pages 505-525.
    5. Ross L. Prentice & Shanshan Zhao, 2018. "Nonparametric estimation of the multivariate survivor function: the multivariate Kaplan–Meier estimator," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 3-27, January.
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