IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1461-d1100139.html
   My bibliography  Save this article

Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling

Author

Listed:
  • Ying Zhou

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Liang Wang

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251037, Taiwan)

  • Yogesh Mani Tripathi

    (Department of Mathematics, Indian Institute of Technology Patna, Bihta 801103, India)

Abstract

The ranked set sampling (RSS) is an efficient and flexible sampling method. Based on a modified RSS named minimum ranked set sampling samples (MinRSSU), inference of a dependent competing risks model is proposed in this paper. Then, Marshall–Olkin bivariate distribution model is used to describe the dependence of competing risks. When the competing risks data follow the proportional hazard rate distribution, a dependent competing risks model based on MinRSSU sampling is constructed. In addition, the model parameters and reliability indices were estimated by the classical and Bayesian method. Maximum likelihood estimators and corresponding asymptotic confidence intervals are constructed by using asymptotic theory. In addition, the Bayesian estimator and highest posterior density credible intervals are established under the general prior. Furthermore, according to E-Bayesian theory, the point and interval estimators of model parameters and reliability indices are obtained by a sampling algorithm. Finally, extensive simulation studies and a real-life example are presented for illustrations.

Suggested Citation

  • Ying Zhou & Liang Wang & Tzong-Ru Tsai & Yogesh Mani Tripathi, 2023. "Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling," Mathematics, MDPI, vol. 11(6), pages 1-30, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1461-:d:1100139
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1461/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1461/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Simon M. S. Lo & Ralf A. Wilke, 2010. "A copula model for dependent competing risks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 359-376, March.
    2. Malka Gorfine & Li Hsu, 2011. "Frailty-Based Competing Risks Model for Multivariate Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 415-426, June.
    3. Al-Saleh, M. Fraiwan & Al-Kadiri, M. Ali, 2000. "Double-ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 205-212, June.
    4. Guan, Qiang & Tang, Yincai & Xu, Ancha, 2013. "Objective Bayesian analysis for bivariate Marshall–Olkin exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 299-313.
    5. Ming Han, 2020. "E-Bayesian estimation and its E-posterior risk of the exponential distribution parameter based on complete and type I censored samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(8), pages 1858-1872, April.
    6. Hamid Rahmani & Mostafa Razmkhah, 2017. "Perfect ranking test in moving extreme ranked set sampling," Statistical Papers, Springer, vol. 58(3), pages 855-875, September.
    7. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    8. Sarhan, Ammar M. & Hamilton, David C. & Smith, B., 2010. "Statistical analysis of competing risks models," Reliability Engineering and System Safety, Elsevier, vol. 95(9), pages 953-962.
    9. Guoxin Qiu & Abbas Eftekharian, 2021. "Extropy information of maximum and minimum ranked set sampling with unequal samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(13), pages 2979-2995, July.
    10. Ehsan Zamanzade & M. Mahdizadeh & Hani M. Samawi, 2020. "Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 485-502, September.
    11. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhiyuan Zuo & Liang Wang & Yuhlong Lio, 2022. "Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations," Energies, MDPI, vol. 16(1), pages 1-25, December.
    2. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    3. Melanie Arntz & Simon Lo & Ralf Wilke, 2014. "Bounds analysis of competing risks: a non-parametric evaluation of the effect of unemployment benefits on migration," Empirical Economics, Springer, vol. 46(1), pages 199-228, February.
    4. Mhamed Mesfioui & Mohamed Kayid, 2021. "Residual Probability Function for Dependent Lifetimes," Mathematics, MDPI, vol. 9(15), pages 1-13, July.
    5. Lo Simon M.S. & Wilke Ralf A., 2014. "A Regression Model for the Copula-Graphic Estimator," Journal of Econometric Methods, De Gruyter, vol. 3(1), pages 21-46, January.
    6. Fei Jiang & Sebastien Haneuse, 2017. "A Semi-parametric Transformation Frailty Model for Semi-competing Risks Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 112-129, March.
    7. Coolen-Maturi, Tahani & Coolen, Frank P.A., 2014. "Nonparametric predictive inference for combined competing risks data," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 87-97.
    8. Alexander Begun & Anatoli Yashin, 2019. "Study of the bivariate survival data using frailty models based on Lévy processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 37-67, March.
    9. Coolen-Maturi, Tahani, 2014. "Nonparametric predictive pairwise comparison with competing risks," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 146-153.
    10. Herbert Hove & Frank Beichelt & Parmod K. Kapur, 2017. "Estimation of the Frank copula model for dependent competing risks in accelerated life testing," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 673-682, December.
    11. Kokol Bukovšek, Damjana & Košir, Tomaž & Mojškerc, Blaž & Omladič, Matjaž, 2022. "Extreme generators of shock induced copulas," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    12. Fang, Chen & Cui, Lirong, 2021. "Balanced Systems by Considering Multi-state Competing Risks Under Degradation Processes," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    13. Umberto Cherubini & Sabrina Mulinacci, 2021. "Hierarchical Archimedean Dependence in Common Shock Models," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 143-163, March.
    14. Manal M. Yousef & Amal S. Hassan & Abdullah H. Al-Nefaie & Ehab M. Almetwally & Hisham M. Almongy, 2022. "Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    15. Frank Eriksson & Thomas Scheike, 2015. "Additive gamma frailty models with applications to competing risks in related individuals," Biometrics, The International Biometric Society, vol. 71(3), pages 677-686, September.
    16. Mohammad Al-Saleh & Said Al-Hadhrami, 2003. "Estimation of the mean of the exponential distribution using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 44(3), pages 367-382, July.
    17. Jia-Han Shih & Takeshi Emura, 2019. "Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula," Statistical Papers, Springer, vol. 60(4), pages 1101-1118, August.
    18. Emanuel Krebs & Jeong E. Min & Elizabeth Evans & Libo Li & Lei Liu & David Huang & Darren Urada & Thomas Kerr & Yih-Ing Hser & Bohdan Nosyk, 2017. "Estimating State Transitions for Opioid Use Disorders," Medical Decision Making, , vol. 37(5), pages 483-497, July.
    19. Al-Saleh, Mohammad Fraiwan & Samuh, Monjed Hisham, 2008. "On multistage ranked set sampling for distribution and median estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2066-2078, January.
    20. Amer Ibrahim Al-Omari & Mohammad Fraiwan Al-Saleh, 2010. "Improvement in estimating the population mean using two-stage balanced groups ranked set sampling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 185-196.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1461-:d:1100139. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.