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Regression models for grouped survival data: Estimation and sensitivity analysis

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  • Hashimoto, Elizabeth M.
  • Ortega, Edwin M.M.
  • Paula, Gilberto A.
  • Barreto, Mauricio L.

Abstract

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:993-1007
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    References listed on IDEAS

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    1. 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.
    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. Enrico A. Colosimo & Liciana V. A. S. Chalita & Clarice G. B. Demétrio, 2000. "Tests of Proportional Hazards and Proportional Odds Models for Grouped Survival Data," Biometrics, The International Biometric Society, vol. 56(4), pages 1233-1240, December.
    4. 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.
    5. 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.
    6. 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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    Cited by:

    1. Jóźwiak, Katarzyna & Moerbeek, Mirjam, 2012. "Cost-effective designs for trials with discrete-time survival endpoints," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2086-2096.
    2. 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.
    3. Elton G. Aráujo & Julio C. S. Vasconcelos & Denize P. Santos & Edwin M. M. Ortega & Dalton Souza & João P. F. Zanetoni, 2023. "The Zero-Inflated Negative Binomial Semiparametric Regression Model: Application to Number of Failing Grades Data," Annals of Data Science, Springer, vol. 10(4), pages 991-1006, August.
    4. Blanco-Fernández, Angela & Corral, Norberto & González-Rodríguez, Gil, 2011. "Estimation of a flexible simple linear model for interval data based on set arithmetic," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2568-2578, September.

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