The analysis of semi-competing risks data using Archimedean copula models

In this paper, we derive the copula-graphic estimator (Zheng and Klein) for marginal survival functions using Archimedean copula models based on competing risks data subject to univariate right censoring and prove its uniform consistency and asymptotic properties. We then propose a novel parameter estimation method based on the semi-competing risks data using Archimedean copula models. Based on our estimation strategy, we propose a new model selection procedure. We also describe an easy way to accommodate possible covariates in data analysis using our strategies. Simulation studies have shown that our parameter estimate outperforms the estimator proposed by Lakhal, Rivest and Abdous for the Hougaard model and the model selection procedure works quite well. We fit a leukemia dataset using our model and end our paper with some discussion.