Bivariate survival data with dependent event times and censored observations are common in medical research. Traditional survival analysis methods cannot effectively capture such dependence structures. In this paper, we propose bivariate Clayton Weibull (BCW) and bivariate Clayton exponential (BCE) models based on the Clayton copula under Type II censoring. Parameter estimation is performed using maximum likelihood estimation and Bayesian MCMC methods. Monte Carlo simulations evaluate point estimation accuracy, interval estimation, and dependence parameter estimation under various censoring levels. Results show that bias and mean squared error decrease as effective sample size increases. Under the same censoring level, Bayesian estimation outperforms maximum likelihood estimation. The models are applied to catheter infection data of kidney disease patients, demonstrating their validity and practicality on real medical data.
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