Failure time data are used in survival analysis. The traditional parametric and nonparametric methods of survival analysis must be modified since the existence of censoring renders them inadequate. When one classical model may not be enough, parametric mixture models are used. To handle the heterogeneity of survival data, a more robust parametric mixture is required. For the study of survival data, this paper proposed a mixture of two distributions; the models are the Loglogistic-Loglogistic and Loglogistic-Gamma distributions. The models' performance was investigated using simulated data, and several iterations were run to test consistency. Expectation Maximization (EM) was employed to calculate the models' maximum likelihood parameters. The computed model parameters all fell within a narrow range of the postulated values. The models' consistency and stability were tested repeatedly through simulations using mean square error (MSE) and root mean square error (RMSE), and all were found to be stable and consistent. Real data were used to compare the fit of mixture models and classical distributions using information criteria (AIC). The best fit for the data was found using mixture models, which combine two different distributions. i.e., Loglogistic-Gamma distribution.
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.
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