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The log-exponentiated Weibull regression model for interval-censored data

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  • Hashimoto, Elizabeth M.
  • Ortega, Edwin M.M.
  • Cancho, Vicente G.
  • Cordeiro, Gauss M.

Abstract

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data.

Suggested Citation

  • Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Cancho, Vicente G. & Cordeiro, Gauss M., 2010. "The log-exponentiated Weibull regression model for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1017-1035, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:1017-1035
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    References listed on IDEAS

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    1. Juliana Fachini & Edwin Ortega & Francisco Louzada-Neto, 2008. "Influence diagnostics for polyhazard models in the presence of covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(4), pages 413-433, October.
    2. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Paula, Gilberto A., 2008. "Log-modified Weibull regression models with censored data: Sensitivity and residual analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4021-4039, April.
    3. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
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    6. Xie, Feng-Chang & Wei, Bo-Cheng, 2007. "Diagnostics analysis for log-Birnbaum-Saunders regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4692-4706, May.
    7. C. P. Farrington, 2000. "Residuals for Proportional Hazards Models with Interval-Censored Survival Data," Biometrics, The International Biometric Society, vol. 56(2), pages 473-482, June.
    8. Silva, Giovana Oliveira & Ortega, Edwin M.M. & Cancho, Vicente G. & Barreto, Mauricio Lima, 2008. "Log-Burr XII regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3820-3842, March.
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    1. 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.
    2. Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Paula, Gilberto A. & Barreto, Mauricio L., 2011. "Regression models for grouped survival data: Estimation and sensitivity analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 993-1007, February.
    3. Elizabeth Hashimoto & Gauss Cordeiro & Edwin Ortega, 2013. "The new Neyman type A beta Weibull model with long-term survivors," Computational Statistics, Springer, vol. 28(3), pages 933-954, June.
    4. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
    5. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    6. Fábio Prataviera & Elizabeth M. Hashimoto & Edwin M. M. Ortega & Taciana V. Savian & Gauss M. Cordeiro, 2023. "Interval-Censored Regression with Non-Proportional Hazards with Applications," Stats, MDPI, vol. 6(2), pages 1-14, May.
    7. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.

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