Utilization of a Mixture Cure Rate Model based on the Generalized Modified Weibull Distribution for the Analysis of Leukemia Patients

Document Type : Research Articles


1 Department of Mathematics, College of Science, Sudan University of Science and Technology, Khartoum, Sudan.

2 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia.

3 Institute of Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia.


Objective: Cure rate models are survival models, commonly applied to model survival data with a cured fraction. In the existence of a cure rate, if the distribution of survival times for susceptible patients is specified, researchers usually prefer cure models to parametric models. Different distributions can be assumed for the survival times, for instance, generalized modified Weibull (GMW), exponentiated Weibull (EW), and log-beta Weibull. The purpose of this study is to select the best distribution for uncured patients’ survival times by comparing the mixture cure models based on the GMW distribution and its particular cases. Materials and Methods: A data set of 91 patients with high-risk acute lymphoblastic leukemia (ALL) followed for five years from 1982 to 1987 was chosen for fitting the mixture cure model. We used the maximum likelihood estimation technique via R software 3.6.2 to obtain the estimates for parameters of the proposed model in the existence of cure rate, censored data, and covariates. For the best model choice, the Akaike information criterion (AIC) was implemented. Results: After comparing different parametric models fitted to the data, including or excluding cure fraction, without covariates, the smallest AIC values were obtained by the EW and the GMW distributions, (953.31/969.35) and (955.84/975.99), respectively. Besides, assuming a mixture cure model based on GMW with covariates, an estimated ratio between cure fractions for allogeneic and autologous bone marrow transplant groups (and its 95% confidence intervals) were 1.42972 (95% CI: 1.18614 - 1.72955). Conclusion: The results of this study reveal that the EW and the GMW distributions are the best choices for the survival times of Leukemia patients.


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