Laplace regression with clustered censored data

In survival analysis, data may be correlated or clustered, because of some features such as shared genes and environmental background. A common approach to accommodate clustered data is the Cox frailty model that has proportional hazard assumption and complexity of interpreting hazard ratio lead to the misinterpretation of a direct effect on the time of event. In this paper, we considered Laplace quantile regression model for clustered survival data that interpret the effect of covariates on the time to event. A Bayesian approach with Markov Chain Monte Carlo method was used to fit the model. The results from a simulation study to evaluate the performance of proposed model showed that the Laplace regression model with frailty term performed well for different scenarios and the coverage rates of the pointwise 95% CIs were close to the nominal level (0.95). An application to data from breast cancer was presented to illustrate the theory and method developed in this paper.