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Residual Analysis for Poisson-Exponentiated Weibull Regression Models with Cure Fraction

Author

Listed:
  • Cleanderson R. Fidelis

    (Department of Exact Sciences, “Luiz de Queiroz” School of Agriculture, University of São Paulo—ESALQ/USP, Piracicaba 13418-900, Brazil)

  • Edwin M. M. Ortega

    (Department of Exact Sciences, “Luiz de Queiroz” School of Agriculture, University of São Paulo—ESALQ/USP, Piracicaba 13418-900, Brazil)

  • Gauss M. Cordeiro

    (Department of Statistics, Centro de Ciências Exatas e da Natureza, Universidade Federal de Pernambuco, Recife 50670-901, Brazil)

Abstract

The use of cure-rate survival models has grown in recent years. Even so, proposals to perform the goodness of fit of these models have not been so frequent. However, residual analysis can be used to check the adequacy of a fitted regression model. In this context, we provide Cox–Snell residuals for Poisson-exponentiated Weibull regression with cure fraction. We developed several simulations under different scenarios for studying the distributions of these residuals. They were applied to a melanoma dataset for illustrative purposes.

Suggested Citation

  • Cleanderson R. Fidelis & Edwin M. M. Ortega & Gauss M. Cordeiro, 2024. "Residual Analysis for Poisson-Exponentiated Weibull Regression Models with Cure Fraction," Stats, MDPI, vol. 7(2), pages 1-16, May.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:2:p:30-507:d:1398230
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    References listed on IDEAS

    as
    1. Thiago G. Ramires & Niel Hens & Gauss M. Cordeiro & Edwin M. M. Ortega, 2018. "Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model," Computational Statistics, Springer, vol. 33(2), pages 709-730, June.
    2. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    3. Edwin Ortega & Gauss Cordeiro & Michael Kattan, 2013. "The log-beta Weibull regression model with application to predict recurrence of prostate cancer," Statistical Papers, Springer, vol. 54(1), pages 113-132, February.
    4. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    5. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    6. Yingwei Peng & Jeremy M. G. Taylor, 2017. "Residual-based model diagnosis methods for mixture cure models," Biometrics, The International Biometric Society, vol. 73(2), pages 495-505, June.
    7. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
    8. Rodrigues, Josemar & Cancho, Vicente G. & de Castro, Mrio & Louzada-Neto, Francisco, 2009. "On the unification of long-term survival models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 753-759, March.
    9. Vicente G. Cancho & Gladys D. C. Barriga & Gauss M. Cordeiro & Edwin M. M. Ortega & Adriano K. Suzuki, 2021. "Bayesian survival model induced by frailty for lifetime with long‐term survivors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 299-323, August.
    10. Rodrigo R. Pescim & Edwin M. M. Ortega & Adriano K. Suzuki & Vicente G. Cancho & Gauss M. Cordeiro, 2019. "A new destructive Poisson odd log-logistic generalized half-normal cure rate model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2113-2128, May.
    11. Scolas, Sylvie & Legrand, Catherine & Oulhaj, Abderrahim & El Ghouch, Anouar, 2018. "Diagnostic checks in mixture cure models with interval-censoring," LIDAM Reprints ISBA 2018038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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