Abstract
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.
Highlights
Survival analysis is concerned with the investigation of a particular event happening within a given duration of time
A two component survival mixture model of Weibull distributions was proposed; where the parameters of the models were estimated by graphical approach [6]
Two components survival mixture models of different distributions consisting of an Exponential-Gamma, an Exponential-Weibull and a Gamma-Weibull models were proposed for analysing heterogeneous survival data by employing Expectation Maximization Algorithm (EM) [12]
Summary
Survival analysis is concerned with the investigation of a particular event happening within a given duration of time. A two component mixture model of Weibull distributions was proposed to anlaysed survival data where the parameters of the model were estimated by the weighted least squares method [5]. Two components survival mixture models of different distributions consisting of an Exponential-Gamma, an Exponential-Weibull and a Gamma-Weibull models were proposed for analysing heterogeneous survival data by employing EM [12]. A parametric survival mixture model of the Exponential, Gamma and Weibull distributions was considered to fit heterogeneous survival data. A three component parametric survival mixture model of Weibull distributions was proposed to model survival data by applying Bayesian estimation method [18]. Real data were used to investigate the flexibility and appropriateness of a three component survival mixture of the Exponential, Gamma and Weibull distributions in modelling heterogeneous survival data. In section four the summary and conclusion were presented
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