On testing the fit of accelerated failure time and proportional hazard Weibull extension models
Characterized by three parameters, the Weibull extension distribution is introduced by Xie et al. as a generalization of the classical Weibull distribution. In this article, we are interested in the construction of modified chi-squared goodness-of-fit tests for both an accelerated failure time and Cox proportional hazards models with the Weibull extension distribution as the baseline distribution. We use the technique introduced by Bagdonavicius and Nikulin for right-censored samples. Besides an important simulation study, the obtained results are applied to illustrative examples from real data sets.
KeywordsAccelerated failure time models censored data chi-squared test Cox proportional hazards model maximum likelihood estimation
AMS Subject Classification60E15 62F03 62F12 62G05
Unable to display preview. Download preview PDF.
- Cox, D. R., and D. Oakes. 1984. Analysis of survival data. Monographs on Statistics and Applied Probabilities. New York, NY: Chapman & Hall/CRC.Google Scholar
- Freireich, E. J., E. Gehan, E. Frei, L. R. Schroeder, I. J. Wolman, R. Anbari, E. O. Burgert, S. D. Mills, D. Pinkel, and O. S. Selawry. 1963. The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: A model for evaluation of other potentially useful therapy. Blood 21 (6):699–716.Google Scholar
- Nikulin, N. S., and X. Q. Tran. 2014. On chi-squared testing in accelerated trials. International Journal of Performability Engineering 10 (1):53–62.Google Scholar
- Ravi, V., and P. D. Gilbert. 2009. BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. Journal Statist Software 32 (4):1–26.Google Scholar
- Treidi, W., and N. Seddik-Ameur. 2016. NRR statistic for the extension Weibull distribution. Global Journal of Pure and Applied Mathematics 12 (4):2809–18.Google Scholar