IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v144y2020ics0167947319302348.html
   My bibliography  Save this article

A multivariate normal regression model for survival data subject to different types of dependent censoring

Author

Listed:
  • Deresa, Negera Wakgari
  • Van Keilegom, Ingrid

Abstract

In survival analysis observations are often right censored and this complicates considerably the analysis of these data. Right censoring can have several underlying causes: administrative censoring, loss to follow up, competing risks, etc. The (latent) censoring times corresponding to the latter two types of censoring are possibly related to the survival time of interest, and in that case this should be taken into account in the model. A unifying model is presented that allows these censoring mechanisms in one single model, and that is also able to incorporate the effect of covariates on these times. Each time variable is modeled by means of a transformed linear model, with the particularity that the error terms of the transformed times follow a multivariate normal distribution allowing for non-zero correlations. It is shown that the model is identified and the model parameters are estimated through a maximum likelihood approach. The performance of the proposed method is compared with methods that assume independent censoring using finite sample simulations. The results show that the proposed method exhibits major advantages in terms of reducing the bias of the parameter estimates. However, a strong deviation from normality and/or a strong violation of the homogeneous variance assumption may lead to biased estimates. Finally, the model and the estimation method are illustrated using the analysis of data coming from a prostate cancer clinical trial.

Suggested Citation

  • Deresa, Negera Wakgari & Van Keilegom, Ingrid, 2020. "A multivariate normal regression model for survival data subject to different types of dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302348
    DOI: 10.1016/j.csda.2019.106879
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319302348
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.106879?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Yi‐Hau Chen, 2010. "Semiparametric marginal regression analysis for dependent competing risks under an assumed copula," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 235-251, March.
    2. Basu, A. P. & Ghosh, J. K., 1978. "Identifiability of the multinormal and other distributions under competing risks model," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 413-429, September.
    3. John P. Klein & Per Kragh Andersen, 2005. "Regression Modeling of Competing Risks Data Based on Pseudovalues of the Cumulative Incidence Function," Biometrics, The International Biometric Society, vol. 61(1), pages 223-229, March.
    4. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 138-155, October.
    7. Ronald B. Geskus, 2011. "Cause-Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring," Biometrics, The International Biometric Society, vol. 67(1), pages 39-49, March.
    8. White, Halbert, 1983. "Corrigendum [Maximum Likelihood Estimation of Misspecified Models]," Econometrica, Econometric Society, vol. 51(2), pages 513-513, March.
    9. Per Kragh Andersen, 2003. "Generalised linear models for correlated pseudo-observations, with applications to multi-state models," Biometrika, Biometrika Trust, vol. 90(1), pages 15-27, March.
    10. Xuelin Huang & Nan Zhang, 2008. "Regression Survival Analysis with an Assumed Copula for Dependent Censoring: A Sensitivity Analysis Approach," Biometrics, The International Biometric Society, vol. 64(4), pages 1090-1099, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Emura, Takeshi & Hsu, Jiun-Huang, 2020. "Estimation of the Mann–Whitney effect in the two-sample problem under dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    2. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    3. Janette Larney & James Samuel Allison & Gerrit Lodewicus Grobler & Marius Smuts, 2023. "Modelling the Time to Write-Off of Non-Performing Loans Using a Promotion Time Cure Model with Parametric Frailty," Mathematics, MDPI, vol. 11(10), pages 1-17, May.
    4. Gilles Crommen & Jad Beyhum & Ingrid Van Keilegom, 2024. "An instrumental variable approach under dependent censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 473-495, June.
    5. Gilles Crommen & Jad Beyhum & Ingrid Van Keilegom, 2025. "Estimation of the complier causal hazard ratio under dependent censoring," Papers 2504.02096, arXiv.org.
    6. Kosuke Nakazono & Yu-Cheng Lin & Gen-Yih Liao & Ryuji Uozumi & Takeshi Emura, 2024. "Computation of the Mann–Whitney Effect under Parametric Survival Copula Models," Mathematics, MDPI, vol. 12(10), pages 1-22, May.

    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. Sangbum Choi & Xuelin Huang, 2014. "Maximum likelihood estimation of semiparametric mixture component models for competing risks data," Biometrics, The International Biometric Society, vol. 70(3), pages 588-598, September.
    2. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    3. Myrthe D’Haen & Ingrid Van Keilegom & Anneleen Verhasselt, 2025. "Quantile regression under dependent censoring with unknown association," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(2), pages 253-299, April.
    4. 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.
    5. Lo, Simon M.S. & Wilke, Ralf A. & Emura, Takeshi, 2024. "A semiparametric model for the cause-specific hazard under risk proportionality," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
    6. Kim, Dongwoo, 2023. "Partially identifying competing risks models: An application to the war on cancer," Journal of Econometrics, Elsevier, vol. 234(2), pages 536-564.
    7. Jia-Han Shih & Takeshi Emura, 2018. "Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula," Computational Statistics, Springer, vol. 33(3), pages 1293-1323, September.
    8. Negera Wakgari Deresa & Ingrid Van Keilegom, 2025. "Semiparametric transformation models for survival data with dependent censoring," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(3), pages 425-457, June.
    9. Yi‐Hau Chen, 2010. "Semiparametric marginal regression analysis for dependent competing risks under an assumed copula," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 235-251, March.
    10. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    11. Das, Debojyoti & Bhatia, Vaneet & Kumar, Surya Bhushan & Basu, Sankarshan, 2022. "Do precious metals hedge crude oil volatility jumps?," International Review of Financial Analysis, Elsevier, vol. 83(C).
    12. P.A.V.B. Swamy & I-Lok Chang & Jatinder S. Mehta & William H. Greene & Stephen G. Hall & George S. Tavlas, 2016. "Removing Specification Errors from the Usual Formulation of Binary Choice Models," Econometrics, MDPI, vol. 4(2), pages 1-21, June.
    13. Carlo Altavilla & Raffaella Giacomini & Giuseppe Ragusa, 2017. "Anchoring the yield curve using survey expectations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1055-1068, September.
    14. Fernando Rios-Avila & Gustavo J. Canavire-Bacarreza, 2017. "Standard Error Correction in Two-Stage Optimization Models: A Quasi-Maximum Likelihood Estimation Approach," Documentos de Trabajo de Valor Público 15659, Universidad EAFIT.
    15. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    16. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    17. Ayouz, Mourad K. & Remaud, Herve, 2003. "The Internationalization Determinants Of The Small Agro-Food Firms: Hypotheses And Statistical Tests," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association, vol. 5(2), pages 1-27.
    18. Broze, Laurence & Gourieroux, Christian, 1998. "Pseudo-maximum likelihood method, adjusted pseudo-maximum likelihood method and covariance estimators," Journal of Econometrics, Elsevier, vol. 85(1), pages 75-98, July.
    19. Sridhar, Shrihari & Naik, Prasad A. & Kelkar, Ajay, 2017. "Metrics unreliability and marketing overspending," International Journal of Research in Marketing, Elsevier, vol. 34(4), pages 761-779.
    20. Yen, Steven T. & Chern, Wen S. & Lee, Hwang-Jaw, 1991. "Effects Of Income Sources On Household Food Expenditures," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271167, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:csdana:v:144:y:2020:i:c:s0167947319302348. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.