Open AccessA Mixture of Gamma-Gamma, Loglogistic-Gamma Distributions for the Analysis of Heterogenous Survival Data
Author(s) -
Othman Musa Yakubu,
Yusuf Abbakar Mohammed,
Imam Akeyede
Publication year - 2022
Publication title -
international journal of mathematical research
Language(s) - English
Resource type - Journals
eISSN - 2311-7427
pISSN - 2306-2223
DOI - 10.18488/24.v11i1.2924
Subject(s) - mixture model , censoring (clinical trials) , statistics , mathematics , gamma distribution , mean squared error , parametric statistics , nonparametric statistics , consistency (knowledge bases) , parametric model , expectation–maximization algorithm , maximum likelihood , geometry
Survival analysis deals with failure time data. The presence of censoring makes the application of the classical parametric and nonparametric methods of survival analysis inadequate and as such need’s modifications. Parametric mixture models are applied where a single classical model may not suffice. The parametric mixture needs to be made more robust to address the heterogeneity of survival data. This paper proposed a mixture of two distributions for the analysis of survival data, the models consist of Gamma-Gamma, and Loglogistic-Gamma distributions. Data was simulated to investigate the performance of the models, and used to estimate the maximum likelihood parameters of the models by employing Expectation Maximization (EM). Parameters of the models were estimated and were all close the postulated values. Simulations were repeated to test the consistency and stability of the models through mean square error (MSE) and root mean square error (RMSE), and were all found to be stable and consistent. Real data was applied to determine the best fit among the mixture models and classical distributions using information criteria. Mixture models were found to model the data and the mixture of two different distributions gives the best fit.