IDEAS home Printed from https://ideas.repec.org/a/spr/aodasc/v7y2020i1d10.1007_s40745-019-00224-5.html
   My bibliography  Save this article

Illustration of the Flexibility of Generalized Gamma Distribution in Modeling Right Censored Survival Data: Analysis of Two Cancer Datasets

Author

Listed:
  • Suvra Pal

    (University of Texas at Arlington)

  • Hongbo Yu

    (University of Texas at Arlington)

  • Zachary D. Loucks

    (University of Texas at Arlington)

  • Ian M. Harris

    (University of Texas at Arlington)

Abstract

In this paper, our main objective is to illustrate the flexibility of the wider class of generalized gamma distribution to model right censored survival data. This distribution contains the commonly used gamma, Weibull, and lognormal distributions as particular cases and this flexibility allows us to carry out a model discrimination, within its class, to choose a lifetime distribution that provides the best fit to a given data. A detailed Monte Carlo simulation study is carried out to display the flexibility of the generalized distribution using likelihood ratio test and information-based criteria. The maximum likelihood estimates of the parameters are obtained by using inbuilt optimization techniques available in R statistical software. We also display the performance of the estimation technique by calculating the bias, mean square error, and coverage probabilities of the confidence intervals for different confidence levels. Finally, we illustrate the advantage of using the generalized gamma distribution using two real datasets and we motivate the use of an extended version of the generalized gamma distribution.

Suggested Citation

  • Suvra Pal & Hongbo Yu & Zachary D. Loucks & Ian M. Harris, 2020. "Illustration of the Flexibility of Generalized Gamma Distribution in Modeling Right Censored Survival Data: Analysis of Two Cancer Datasets," Annals of Data Science, Springer, vol. 7(1), pages 77-90, March.
    • Handle: RePEc:spr:aodasc:v:7:y:2020:i:1:d:10.1007_s40745-019-00224-5
    DOI: 10.1007/s40745-019-00224-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40745-019-00224-5
    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/s40745-019-00224-5?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. Hirose, Hideo, 2000. "Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 81-97.
    2. N. Balakrishnan & Suvra Pal, 2015. "An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetime and model discrimination using likelihood- and information-based methods," Computational Statistics, Springer, vol. 30(1), pages 151-189, March.
    3. W. Sauerbrei & P. Royston, 1999. "Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 71-94.
    4. Patrick Royston & Gareth Ambler, 1999. "Multivariable fractional polynomials," Stata Technical Bulletin, StataCorp LP, vol. 8(43).
    5. Jackson, Christopher, 2016. "flexsurv: A Platform for Parametric Survival Modeling in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i08).
    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. Combes, Catherine & Ng, Hon Keung Tony, 2022. "On parameter estimation for Amoroso family of distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 309-327.

    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. Marco Caliendo & Stefan Tübbicke, 2020. "New evidence on long-term effects of start-up subsidies: matching estimates and their robustness," Empirical Economics, Springer, vol. 59(4), pages 1605-1631, October.
    2. Annalisa Orenti & Patrizia Boracchi & Giuseppe Marano & Elia Biganzoli & Federico Ambrogi, 2022. "A pseudo-values regression model for non-fatal event free survival in the presence of semi-competing risks," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 709-727, September.
    3. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    4. Stefanie Hieke & Harald Binder & Alexandra Nieters & Martin Schumacher, 2014. "minPtest: a resampling based gene region-level testing procedure for genetic case-control studies," Computational Statistics, Springer, vol. 29(1), pages 51-63, February.
    5. Marisa Rifada & Vita Ratnasari & Purhadi Purhadi, 2023. "Parameter Estimation and Hypothesis Testing of The Bivariate Polynomial Ordinal Logistic Regression Model," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    6. Patrick Royston, 2012. "Tools to simulate realistic censored survival-time distributions," Stata Journal, StataCorp LP, vol. 12(4), pages 639-654, December.
    7. Schäfer, Dorothea & Werwatz, Axel & Zimmermann, Volker, 2004. "The Determinants of Debt and (Private) Equity Financing : The Case of Young, Innovative SMEs from Germany," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 11(3), pages 225-248.
    8. Sauerbrei, W. & Meier-Hirmer, C. & Benner, A. & Royston, P., 2006. "Multivariable regression model building by using fractional polynomials: Description of SAS, STATA and R programs," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3464-3485, August.
    9. Sauerbrei, Willi & Royston, Patrick & Zapien, Karina, 2007. "Detecting an interaction between treatment and a continuous covariate: A comparison of two approaches," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 4054-4063, May.
    10. William D. Dupont, 2010. "Review of Multivariable Model-building: A Pragmatic Approach to Regression Analysis Based on Fractional Polynomials for Modeling Continuous Variables, by Royston and Sauerbrei," Stata Journal, StataCorp LP, vol. 10(2), pages 297-302, June.
    11. Patrick Royston, 2007. "Profile likelihood for estimation and confidence intervals," Stata Journal, StataCorp LP, vol. 7(3), pages 376-387, September.
    12. Patrick Royston, 2004. "Multiple imputation of missing values," Stata Journal, StataCorp LP, vol. 4(3), pages 227-241, September.
    13. Stefanie Hieke & Axel Benner & Richard F Schlenk & Martin Schumacher & Lars Bullinger & Harald Binder, 2016. "Identifying Prognostic SNPs in Clinical Cohorts: Complementing Univariate Analyses by Resampling and Multivariable Modeling," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-18, May.
    14. Mike G. Tsionas, 2017. "“When, Where, and How” of Efficiency Estimation: Improved Procedures for Stochastic Frontier Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 948-965, July.
    15. Royston, P. & Sauerbrei, W., 2007. "Improving the robustness of fractional polynomial models by preliminary covariate transformation: A pragmatic approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4240-4253, May.
    16. Hoora Moradian & Denis Larocque & François Bellavance, 2017. "$$L_1$$ L 1 splitting rules in survival forests," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 671-691, October.
    17. Patrick Royston & Willi Sauerbrei, 2009. "Two techniques for investigating interactions between treatment and continuous covariates in clinical trials," Stata Journal, StataCorp LP, vol. 9(2), pages 230-251, June.
    18. Schäfer, Dorothea & Werwatz, Axel & Zimmermann, Volker, 2004. "The determinants of debt and (private-) equity financing in young innovative SMEs: Evidence from Germany," CFS Working Paper Series 2004/06, Center for Financial Studies (CFS).
    19. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Didier Maillard, 2019. "Computation of the corrected Cornish–Fisher expansion using the response surface methodology: application to VaR and CVaR," Annals of Operations Research, Springer, vol. 281(1), pages 423-453, October.
    20. Geweke, John & Petrella, Lea, 2014. "Likelihood-based inference for regular functions with fractional polynomial approximations," Journal of Econometrics, Elsevier, vol. 183(1), pages 22-30.

    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:aodasc:v:7:y:2020:i:1:d:10.1007_s40745-019-00224-5. 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.