Parameter estimation for a frailty semi-competing model with measurement errors in covariates

In this paper, we consider a shared frailty semi-competing model with measurement errors in covariates for cluster data to study the correlation between competing events and the effects of covariates. Firstly, model parameter estimators are derived by integrating the corrected maximum likelihood method, Bayesian method, and expectation-maximization algorithm. Secondly, simulation studies show that the proposed estimator has a smaller bias and mean squared error when compared with the estimation method by Lee et al. (2016). Lastly, the empirical analysis of monoclonal gammopathy of undetermined significance data reveals that age is significant for all baseline hazards, while the size of the monoclonal protein spike only affects the baseline hazard of plasma cell malignancy significantly.