IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v23y2017i2d10.1007_s10985-015-9346-8.html
   My bibliography  Save this article

Jointly modeling longitudinal proportional data and survival times with an application to the quality of life data in a breast cancer trial

Author

Listed:
  • Hui Song

    (Dalian University of Technology)

  • Yingwei Peng

    (Queen’s University)

  • Dongsheng Tu

    (Queen’s University)

Abstract

Motivated by the joint analysis of longitudinal quality of life data and recurrence free survival times from a cancer clinical trial, we present in this paper two approaches to jointly model the longitudinal proportional measurements, which are confined in a finite interval, and survival data. Both approaches assume a proportional hazards model for the survival times. For the longitudinal component, the first approach applies the classical linear mixed model to logit transformed responses, while the second approach directly models the responses using a simplex distribution. A semiparametric method based on a penalized joint likelihood generated by the Laplace approximation is derived to fit the joint model defined by the second approach. The proposed procedures are evaluated in a simulation study and applied to the analysis of breast cancer data motivated this research.

Suggested Citation

  • Hui Song & Yingwei Peng & Dongsheng Tu, 2017. "Jointly modeling longitudinal proportional data and survival times with an application to the quality of life data in a breast cancer trial," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 183-206, April.
    • Handle: RePEc:spr:lifeda:v:23:y:2017:i:2:d:10.1007_s10985-015-9346-8
    DOI: 10.1007/s10985-015-9346-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-015-9346-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10985-015-9346-8?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Samuli Ripatti & Juni Palmgren, 2000. "Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood," Biometrics, The International Biometric Society, vol. 56(4), pages 1016-1022, December.
    2. Zhenguo Qiu & Peter X.‐K. Song & Ming Tan, 2008. "Simplex Mixed‐Effects Models for Longitudinal Proportional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 577-596, December.
    3. Peter Xue-Kun Song & Ming Tan, 2000. "Marginal Models for Longitudinal Continuous Proportional Data," Biometrics, The International Biometric Society, vol. 56(2), pages 496-502, June.
    4. Barndorff-Nielsen, O. E. & Jørgensen, B., 1991. "Some parametric models on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 106-116, October.
    5. Dimitris Rizopoulos & Geert Verbeke & Emmanuel Lesaffre, 2009. "Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 637-654, June.
    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. Wenting Liu & Huiqiong Li & Anmin Tang & Zixin Cui, 2023. "Bayesian Joint Modeling Analysis of Longitudinal Proportional and Survival Data," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    2. An-Min Tang & Nian-Sheng Tang & Dalei Yu, 2023. "Bayesian semiparametric joint model of multivariate longitudinal and survival data with dependent censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 888-918, October.

    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. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    2. Ricardo Rasmussen Petterle & Wagner Hugo Bonat & Cassius Tadeu Scarpin, 2019. "Quasi-beta Longitudinal Regression Model Applied to Water Quality Index Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 346-368, June.
    3. Wenting Liu & Huiqiong Li & Anmin Tang & Zixin Cui, 2023. "Bayesian Joint Modeling Analysis of Longitudinal Proportional and Survival Data," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    4. Jay Verkuilen & Michael Smithson, 2012. "Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 82-113, February.
    5. Rosineide Fernando da Paz & Jorge Luis Bazán & Luis Aparecido Milan, 2017. "Bayesian estimation for a mixture of simplex distributions with an unknown number of components: HDI analysis in Brazil," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1630-1643, July.
    6. Josmar Mazucheli & Bruna Alves & Mustafa Ç. Korkmaz & Víctor Leiva, 2022. "Vasicek Quantile and Mean Regression Models for Bounded Data: New Formulation, Mathematical Derivations, and Numerical Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    7. Jaeun Choi & Jianwen Cai & Donglin Zeng, 2017. "Penalized Likelihood Approach for Simultaneous Analysis of Survival Time and Binary Longitudinal Outcome," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 190-216, November.
    8. Zhenguo Qiu & Peter X.‐K. Song & Ming Tan, 2008. "Simplex Mixed‐Effects Models for Longitudinal Proportional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 577-596, December.
    9. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    10. Shilan Li & Jianxin Shi & Paul Albert & Hong-Bin Fang, 2022. "Dependence Structure Analysis and Its Application in Human Microbiome," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    11. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    12. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    13. Guillaume Horny & Dragana Djurdjevic & Bernhard Boockmann & François Laisney, 2008. "Bayesian Estimation of Cox Models with Non-nested Random Effects: an Application to the Ratification Of ILO Conventions by Developing Countries," Annals of Economics and Statistics, GENES, issue 89, pages 193-214.
    14. Bernardi, Mauro & Costola, Michele, 2019. "High-dimensional sparse financial networks through a regularised regression model," SAFE Working Paper Series 244, Leibniz Institute for Financial Research SAFE.
    15. Zhang, Zili & Charalambous, Christiana & Foster, Peter, 2023. "A Gaussian copula joint model for longitudinal and time-to-event data with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    16. Goele Massonnet & Paul Janssen & Tomasz Burzykowski, 2008. "Fitting Conditional Survival Models to Meta‐Analytic Data by Using a Transformation Toward Mixed‐Effects Models," Biometrics, The International Biometric Society, vol. 64(3), pages 834-842, September.
    17. Tang, Nian-Sheng & Tang, An-Min & Pan, Dong-Dong, 2014. "Semiparametric Bayesian joint models of multivariate longitudinal and survival data," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 113-129.
    18. Dimitris Rizopoulos, 2011. "Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 67(3), pages 819-829, September.
    19. Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2014. "Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 146-162.
    20. Jing Wang, 2019. "Weighted estimation for multivariate shared frailty models for complex surveys," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 469-479, July.

    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:spr:lifeda:v:23:y:2017:i:2:d:10.1007_s10985-015-9346-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.