Parametric mixture model of three components for modelling heterogeneos survival data

Previous studies showed that two components of survival mixture model performed better than pure classical parametric survival model. However there are crucial needs for three components of survival mixture model due to the behaviour of heterogeneous survival data which commonly comprises of more than two distributions. Therefore in this study two models of three components of survival mixture model were developed. Model 1 is three components of parametric survival mixture model of Gamma distributions and Model 2 is three components of parametric survival mixture model of Exponential, Gamma and Weibull distributions. Both models were estimated using the Expectation Maximization (EM) and validated via simulation and empirical studies. The simulation was repeated 300 times by incorporating three different sample sizes: 100, 200, 500; three different censoring percentages: 10%, 20%, 40%; and two different sets of mixing probabilities: ascending (10%, 40%, 50%) and descending (50%, 30%, 20%). Several sets of real data were used in the empirical study and models comparisons were implemented. Model 1 was compared with pure classical parametric survival model, two and four components parametric survival mixture models of Gamma distribution, respectively. Model 2 was compared with pure classical parametric survival models and three components parametric survival mixture models of the same distribution. Graphical presentations, log likelihood (LL), Akaike Information Criterion (AIC), Mean Square Error (MSE) and Root Mean Square Error (RMSE) were used to evaluate the performance. Simulation findings revealed that both models performed well at large sample size, small percentage of censoring and ascending mixing probabilities. Both models also produced smaller errors compared to other type of survival models in the empirical study. These indicate that both of the developed models are more accurate and provide better option to analyse heterogeneous survival data

A simulation study of a parametric mixture model of three different distributions to analyze heterogeneous survival data

In this paper a simulation study of a parametric mixture model of three different distributions is considered to model heterogeneous survival data.Some properties of the proposed parametric mixture of Exponential, Gamma and Weibull are investigated.The Expectation Maximization Algorithm (EM) is implemented to estimate the maximum likelihood estimators of three different postulated parametric mixture model parameters.The simulations are performed by simulating data sampled from a population of three component parametric mixture of three different distributions, and the simulations are repeated 10, 30, 50, 100 and 500 times to investigate the consistency and stability of the EM scheme.The EM Algorithm scheme developed is able to estimate the parameters of the mixture which are very close to the parameters of the postulated model.The repetitions of the simulation give parameters closer and closer to the postulated models, as the number of repetitions increases, with relatively small standard errors

Mixture model of the Exponential, Gamma and Weibull distributions to analyse heterogeneous survival data

Aims: In this study a survival mixture model of three components is considered to analyse survival data of heterogeneous nature.The survival mixture model is of the Exponential, Gamma and Weibull distributions.Methodology: The proposed model was investigated and the Maximum Likelihood (ML) estimators of the parameters of the model were evaluated by the application of the Expectation Maximization Algorithm (EM).Graphs, log likelihood (LL) and the Akaike Information Criterion (AIC) were used to compare the proposed model with the pure classical parametric survival models corresponding to each component using real survival data.The model was compared with the survival mixture models corresponding to each component.Results: The graphs, LL and AIC values showed that the proposed model fits the real data better than the pure classical survival models corresponding to each component.Also the proposed model fits the real data better than the survival mixture models corresponding to each component. Conclusion: The proposed model showed that survival mixture models are flexible and maintain the features of the pure classical survival model and are better option for modelling heterogeneous survival data

A parametric mixture model of three different distributions: An approach to analyse heterogeneous survival data

A parametric mixture model of three different distributions is proposed to analyse heterogeneous survival data.The maximum likelihood estimators of the postulated parametric mixture model are estimated by applying an Expectation Maximization Algorithm (EM) scheme.The simulations are performed by generating data, sampled from a population of three component parametric mixture of three different distributions. The parameters estimated by the proposed EM Algorithm scheme are close to the parameters of the postulated model.To investigate the consistency and stability of the EM scheme, the simulations are repeated several times. The repetitions of the simulation gave parameters closer to the values of postulated models, with relatively small standard errors.Log likelihood, AIC and BIC are computed to compare the proposed mixture model with parametric mixture models of one distribution.The calculated values of Log likelihood, AIC and BIC are all infavour of the proposed parametric mixture model of different distributions

A Mixture of Gamma-Gamma, Loglogistic-Gamma Distributions for the Analysis of Heterogenous Survival Data

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.</jats:p