IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v24y2018i2d10.1007_s10985-017-9394-3.html
   My bibliography  Save this article

Exponentiated Weibull regression for time-to-event data

Author

Listed:
  • Shahedul A. Khan

    (University of Saskatchewan)

Abstract

The Weibull, log-logistic and log-normal distributions are extensively used to model time-to-event data. The Weibull family accommodates only monotone hazard rates, whereas the log-logistic and log-normal are widely used to model unimodal hazard functions. The increasing availability of lifetime data with a wide range of characteristics motivate us to develop more flexible models that accommodate both monotone and nonmonotone hazard functions. One such model is the exponentiated Weibull distribution which not only accommodates monotone hazard functions but also allows for unimodal and bathtub shape hazard rates. This distribution has demonstrated considerable potential in univariate analysis of time-to-event data. However, the primary focus of many studies is rather on understanding the relationship between the time to the occurrence of an event and one or more covariates. This leads to a consideration of regression models that can be formulated in different ways in survival analysis. One such strategy involves formulating models for the accelerated failure time family of distributions. The most commonly used distributions serving this purpose are the Weibull, log-logistic and log-normal distributions. In this study, we show that the exponentiated Weibull distribution is closed under the accelerated failure time family. We then formulate a regression model based on the exponentiated Weibull distribution, and develop large sample theory for statistical inference. We also describe a Bayesian approach for inference. Two comparative studies based on real and simulated data sets reveal that the exponentiated Weibull regression can be valuable in adequately describing different types of time-to-event data.

Suggested Citation

  • Shahedul A. Khan, 2018. "Exponentiated Weibull regression for time-to-event data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 328-354, April.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:2:d:10.1007_s10985-017-9394-3
    DOI: 10.1007/s10985-017-9394-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-017-9394-3
    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/s10985-017-9394-3?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. Nash, John C., 2014. "On Best Practice Optimization Methods in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i02).
    2. McElroy, Tucker & Wildi, Marc, 2013. "Multi-step-ahead estimation of time series models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 378-394.
    3. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, 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. Shakhawat Hossain & Shahedul A. Khan, 2020. "Shrinkage estimation of the exponentiated Weibull regression model for time‐to‐event data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 592-610, November.
    2. Adam Braima S. Mastor & Abdulaziz S. Alghamdi & Oscar Ngesa & Joseph Mung’atu & Christophe Chesneau & Ahmed Z. Afify, 2023. "The Extended Exponential-Weibull Accelerated Failure Time Model with Application to Sudan COVID-19 Data," Mathematics, MDPI, vol. 11(2), pages 1-26, January.

    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. D.-C. Jhwueng & V. Maroulas, 2016. "Adaptive trait evolution in random environment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2310-2324, September.
    2. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    3. Roger Tovar-Falón & Guillermo Martínez-Flórez & Heleno Bolfarine, 2022. "Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    4. Tiandong Wang & Panpan Zhang, 2022. "Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 957-986, October.
    5. Wei Chen & Yixin Lu & Liangfei Qiu & Subodha Kumar, 2021. "Designing Personalized Treatment Plans for Breast Cancer," Information Systems Research, INFORMS, vol. 32(3), pages 932-949, September.
    6. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 154-183.
    7. Di Piazza, A. & Di Piazza, M.C. & La Tona, G. & Luna, M., 2021. "An artificial neural network-based forecasting model of energy-related time series for electrical grid management," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 184(C), pages 294-305.
    8. Guillermo Martínez-Flórez & Diego I. Gallardo & Osvaldo Venegas & Heleno Bolfarine & Héctor W. Gómez, 2021. "Flexible Power-Normal Models with Applications," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    9. Guillermo Martínez-Flórez & Roger Tovar-Falón & Heleno Bolfarine, 2023. "The Log-Bimodal Asymmetric Generalized Gaussian Model with Application to Positive Data," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    10. Sameh Abdulah & Yuxiao Li & Jian Cao & Hatem Ltaief & David E. Keyes & Marc G. Genton & Ying Sun, 2023. "Large‐scale environmental data science with ExaGeoStatR," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    11. Stavrakoudis, Athanassios & Panagiotou, Dimitrios, 2016. "Price dependence and asymmetric responses between coffee varieties," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 17(2), June.
    12. R. N. Rattihalli, 2023. "A Class of Multivariate Power Skew Symmetric Distributions: Properties and Inference for the Power-Parameter," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1356-1393, August.
    13. Wang, Sheng & Zimmerman, Dale L. & Breheny, Patrick, 2020. "Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    14. Wildi, Marc, 2010. "Real-Time Signal Extraction: a Shift of Perspective/Extracción de señal en tiempo real: un cambio de perspectiva," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 28, pages 497-518, Diciembre.
    15. Ghysels, Eric & Kvedaras, Virmantas & Zemlys, Vaidotas, 2016. "Mixed Frequency Data Sampling Regression Models: The R Package midasr," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 72(i04).
    16. Christos Katris & Manolis G. Kavussanos, 2021. "Time series forecasting methods for the Baltic dry index," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1540-1565, December.
    17. Nicholas J. Rockwood, 2020. "Maximum Likelihood Estimation of Multilevel Structural Equation Models with Random Slopes for Latent Covariates," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 275-300, June.
    18. Aurél Galántai, 2023. "A Stochastic Convergence Result for the Nelder–Mead Simplex Method," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    19. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor Gómez, 2015. "Doubly censored power-normal regression models with inflation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 265-286, June.
    20. Kovalchik, Stephanie, 2020. "Extension of the Elo rating system to margin of victory," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1329-1341.

    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:24:y:2018:i:2:d:10.1007_s10985-017-9394-3. 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.