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. 2012 Sep;3(9):644-51.

Breast Cancer Survival Analysis: Applying the Generalized Gamma Distribution under Different Conditions of the Proportional Hazards and Accelerated Failure Time Assumptions

Alireza Abadi  1 , Farzaneh Amanpour, Chris Bajdik, Parvin Yavari
Affiliations

Breast Cancer Survival Analysis: Applying the Generalized Gamma Distribution under Different Conditions of the Proportional Hazards and Accelerated Failure Time Assumptions

Alireza Abadi et al. Int J Prev Med. 2012 Sep.

Abstract

Background: The goal of this study is to extend the applications of parametric survival models so that they include cases in which accelerated failure time (AFT) assumption is not satisfied, and examine parametric and semiparametric models under different proportional hazards (PH) and AFT assumptions.

Methods: The data for 12,531 women diagnosed with breast cancer in British Columbia, Canada, during 1990-1999 were divided into eight groups according to patients' ages and stage of disease, and each group was assumed to have different AFT and PH assumptions. For parametric models, we fitted the saturated generalized gamma (GG) distribution, and compared this with the conventional AFT model. Using a likelihood ratio statistic, both models were compared to the simpler forms including the Weibull and lognormal. For semiparametric models, either Cox's PH model or stratified Cox model was fitted according to the PH assumption and tested using Schoenfeld residuals. The GG family was compared to the log-logistic model using Akaike information criterion (AIC) and Baysian information criterion (BIC).

Results: When PH and AFT assumptions were satisfied, semiparametric and parametric models both provided valid descriptions of breast cancer patient survival. When PH assumption was not satisfied but AFT condition held, the parametric models performed better than the stratified Cox model. When neither the PH nor the AFT assumptions were met, the log normal distribution provided a reasonable fit.

Conclusions: When both the PH and AFT assumptions are satisfied, the parametric and semiparametric models provide complementary information. When PH assumption is not satisfied, the parametric models should be considered, whether the AFT assumption is met or not.

Keywords: Breast cancer; generalized gamma distribution; parametric regression; stratified Cox model; survival analysis.

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Conflict of interest statement

Conflict of Interest: None declared

Figures

Figure 1
Figure 1
Cox-Snell residual plot for fitted conventional lognormal model for patients under age 50 years with stage IV cancer
Figure 2
Figure 2
Cox-Snell residual plot for fitted conventional log-logistic model for patients under age 50 years with stage IV cancer
Figure 3
Figure 3
Cox-Snell residual plot for proportional Cox model for patients under age 50 years with stage IV cancer
See this image and copyright information in PMC

References

    1. Hosmer D, Lemeshow S. Applied Survival Analysis. New York: Wiley; 1989.
    1. Kleinbaum D, Klein M. Survival Analysis. New York: Springer; 2005.
    1. Cox C, Chu H, Schneider MF, Muñoz A. parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat Med. 2007;26:4352–74. - PubMed
    1. Nardi A, Schemper M. Comparing Cox and parametric models in clinical studies. Stat Med. 2003;22:3597–610. - PubMed
    1. Lee E, Wang J. Statistical Methods for Survival Data Analysis. New Jersey: Wiley; 2003.

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