Statistical Inference Of Accelerated Failure Time Model Under Bivariate Censored Data Based On Copula Method

Bivariate censored data often appears in interdisciplinary disciplines such as biomedicine,demography,industrial engineering and economics.The development of analysis methods of bivariate data is one of the main work of current data analysis researchers.In this paper,we assume the accelerated failure time model as the marginal model,introduce the Copula function to characterize the dependence between the marginal models,establish the Copula model under two different bivariate dependent censored data,and give a two-step maximum likelihood estimation method.The first part considers the Copula method based on the AFT model under the bivariate right-censored data.Under the right censored data,the accelerated failure time model(AFT model)with normal distributed error terms is established for two marginal distributions,and the Copula function is used to obtain the joint survival function.Furthermore,using a two-step maximum likelihood estimation method constrained the maximum likelihood for parameter estimation,followed by extensive numerical simulation studies,verifying the excellent performance of the proposed method under a limited sample.Finally,applying the proposed model and method to the failure time of retinopathy in diabetic patients has yielded some meaningful clinical analysis results.The second part considers the Copula statistical method based on the AFT model under the bivariate interval censored data.Under the bivariate interval censored data,the accelerated failure time model with error terms is normally established,and a new bivariate model is constructed by Copula method to show the correlation between two marginal models.The estimation method is similar to that of the first part.In the likelihood estimation of the parameters,the two-step maximum likelihood estimation method is adopted.Finally,the estimation effect is evaluated by some simulated and real data examples at different Copula functions.