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A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data

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  • Qingning Zhou
  • Tao Hu
  • Jianguo Sun

Abstract

Interval-censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis. However, most of the existing methods are for univariate data and there exists only limited research on bivariate data, especially on regression analysis of bivariate interval-censored data. We present a class of semiparametric transformation models for the problem and for inference, a sieve maximum likelihood approach is developed. The model provides a great flexibility, in particular including the commonly used proportional hazards model as a special case, and in the approach, Bernstein polynomials are employed. The strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore, the estimators are shown to be asymptotically efficient. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. Supplementary materials for this article are available online.

Suggested Citation

  • Qingning Zhou & Tao Hu & Jianguo Sun, 2017. "A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 664-672, April.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:664-672
    DOI: 10.1080/01621459.2016.1158113
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    References listed on IDEAS

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    1. Donglin Zeng & Qingxia Chen & Joseph G. Ibrahim, 2009. "Gamma frailty transformation models for multivariate survival times," Biometrika, Biometrika Trust, vol. 96(2), pages 277-291.
    2. Richard J. Cook & Leilei Zeng & Ker-Ai Lee, 2008. "A Multistate Model for Bivariate Interval-Censored Failure Time Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1100-1109, December.
    3. Wen, Chi-Chung & Chen, Yi-Hau, 2011. "Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1053-1060, February.
    4. William B. Goggins & Dianne M. Finkelstein, 2000. "A Proportional Hazards Model for Multivariate Interval-Censored Failure Time Data," Biometrics, The International Biometric Society, vol. 56(3), pages 940-943, September.
    5. Wang, Naichen & Wang, Lianming & McMahan, Christopher S., 2015. "Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 140-150.
    6. Debajyoti Sinha & Ming-Hui Chen & Sujit K. Ghosh, 1999. "Bayesian Analysis and Model Selection for Interval-Censored Survival Data," Biometrics, The International Biometric Society, vol. 55(2), pages 585-590, June.
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    Cited by:

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    3. 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.
    4. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2018. "Outcome†dependent sampling with interval†censored failure time data," Biometrics, The International Biometric Society, vol. 74(1), pages 58-67, March.
    5. Mengzhu Yu & Mingyue Du, 2022. "Regression Analysis of Multivariate Interval-Censored Failure Time Data under Transformation Model with Informative Censoring," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    6. Yudong Wang & Zhi‐Sheng Ye & Hongyuan Cao, 2021. "On computation of semiparametric maximum likelihood estimators with shape constraints," Biometrics, The International Biometric Society, vol. 77(1), pages 113-124, March.
    7. Kin Yau Wong & Qingning Zhou & Tao Hu, 2023. "Semiparametric regression analysis of doubly-censored data with applications to incubation period estimation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 87-114, January.
    8. Baihua He & Yanyan Liu & Yuanshan Wu & Xingqiu Zhao, 2020. "Semiparametric efficient estimation for additive hazards regression with case II interval-censored survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 708-730, October.
    9. Peijie Wang & Danning Li & Jianguo Sun, 2021. "A pairwise pseudo‐likelihood approach for left‐truncated and interval‐censored data under the Cox model," Biometrics, The International Biometric Society, vol. 77(4), pages 1303-1314, December.
    10. Chi‐Chung Wen & Yi‐Hau Chen, 2018. "Pseudo and conditional score approach to joint analysis of current count and current status data," Biometrics, The International Biometric Society, vol. 74(4), pages 1223-1231, December.
    11. Liu, Xiaoyu & Xiang, Liming, 2021. "Generalized accelerated hazards mixture cure models with interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    12. Botosaru, Irene, 2020. "Nonparametric analysis of a duration model with stochastic unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 217(1), pages 112-139.
    13. Petti, Danilo & Eletti, Alessia & Marra, Giampiero & Radice, Rosalba, 2022. "Copula link-based additive models for bivariate time-to-event outcomes with general censoring scheme," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    14. Tao Sun & Ying Ding, 2023. "Neural network on interval‐censored data with application to the prediction of Alzheimer's disease," Biometrics, The International Biometric Society, vol. 79(3), pages 2677-2690, September.
    15. Yuxiang Wu & Hui Zhao & Jianguo Sun, 2023. "Group variable selection for the Cox model with interval‐censored failure time data," Biometrics, The International Biometric Society, vol. 79(4), pages 3082-3095, December.
    16. Chun Yin Lee & Kin Yau Wong & K. F. Lam & Jinfeng Xu, 2022. "Analysis of clustered interval‐censored data using a class of semiparametric partly linear frailty transformation models," Biometrics, The International Biometric Society, vol. 78(1), pages 165-178, March.

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