Illustration of the Flexibility of Generalized Gamma Distribution in Modeling Right Censored Survival Data: Analysis of Two Cancer Datasets

Annals of Data Science - Tập 7 - Trang 77-90 - 2019
Suvra Pal1, Hongbo Yu1, Zachary D. Loucks1, Ian M. Harris1
1Department of Mathematics, University of Texas at Arlington, Arlington, USA

Tóm tắt

In this paper, our main objective is to illustrate the flexibility of the wider class of generalized gamma distribution to model right censored survival data. This distribution contains the commonly used gamma, Weibull, and lognormal distributions as particular cases and this flexibility allows us to carry out a model discrimination, within its class, to choose a lifetime distribution that provides the best fit to a given data. A detailed Monte Carlo simulation study is carried out to display the flexibility of the generalized distribution using likelihood ratio test and information-based criteria. The maximum likelihood estimates of the parameters are obtained by using inbuilt optimization techniques available in R statistical software. We also display the performance of the estimation technique by calculating the bias, mean square error, and coverage probabilities of the confidence intervals for different confidence levels. Finally, we illustrate the advantage of using the generalized gamma distribution using two real datasets and we motivate the use of an extended version of the generalized gamma distribution.

Tài liệu tham khảo

Agarwal SK, Al-Saleh JA (2001) Generalized gamma type distribution and its hazard rate function. Commun Stat Theory Methods 30:309–318

Huang PH, Hwang TY (2006) On new moment estimation of parameters of the generalized gamma distribution using it’s characterization. Taiwan J Math 10:1083–1093

Jackson C (2016) flexsurv: a platform for parametric survival modeling in R. J Stat Softw 70:1–33

Loprinzi CL, Laurie JA, Wieand HS et al (1994) Prospective evaluation of prognostic variables from patient-completed questionnaires. J Clin Oncol 12:601–607