Bayesian approach to cox regression model with covariate subject to measurement error

The Cox regression model with the measurement error covariate can cause an important bias when estimating coefficients by maximizing the known partial likelihood function. In this case, alternative estimation methods have been proposed and the effectiveness of these methods has been discussed. The measurement error occurs when the actual values of the covariates measured on a continuous scale cannot be obtained. Biological measurements such as systolic blood pressure and CD4 count, which are frequently used in survival analysis, are mostly variables with measurement error. The Bayesian approach is one of the methods used to reduce the bias arising from measurement error in the Cox regression model. In this thesis, the corrected Bayesian Cox regression model with polygonal prior to measurement error was proposed as an alternative to the partial likelihood function method, its Bayesian approach and the corrected Bayesian Cox regression model with Gamma prior to measurement error and its effectiveness was investigated. The results of the Cox regression model obtained from the partial likelihood function, its Bayesian analysis, the corrected Bayesian Cox regression model with Gamma prior to measurement error, and the corrected Bayesian Cox regression model with polygonal prior to measurement error were compared. Simulation studies were performed with different scenarios to evaluate the performance of the estimators obtained with these methods. It is concluded that as a result of the analysis, in cases where the risk is high, the corrected Bayesian Cox regression model with Gamma prior to measurement error gives the best results in all scenarios, and in the case of low risk, not a suitable alternative in almost all scenarios. It is also shown that if the risk is low, the corrected Bayesian Cox regression model with polygonal prior to measurement error gives better results in low and medium reliability situations except for low censoring and large sample size, and at least one of the corrected models is an alternative method to Cox regression model and its Bayesian analysis in high reliability scenarios. However, if the model has the explanatory variable subject to measurement error, as the sample size increases, the coverage possibilities for the coefficients obtained by the classical method and its Bayesian analysis decrease well below the normal level especially in low and medium reliability cases. To demonstrate the applicability of the methods in real data, the results of the primary biliary cirrhosis data from the Mayo Clinic study in R were obtained, compared, and interpreted. As a second application, model results were obtained for different samples randomly selected from AIDS data used by Goldman et al. (1996) in R. Based on the information obtained as a result of the simulation study, considering that the Cox and Bayesian Cox regression models are not suitable in the presence of measurement error covariate, the best model for both applications was obtained with the corrected Bayesian Cox regression model with polygonal prior to measurement error.