Modelling competing risks data by a bivariate model with singularity originating from a shock model using the Lehmann family of distributions

In this article, a general family of bivariate distributions is used to model competing risks data with dependent causes. The general structure of competing risks data considered here includes ties. A comprehensive inferential framework for the proposed model for competing risks is presented, including maximum likelihood estimation and construction of confidence intervals. Model selection within the bivariate family of distributions for a given dependent competing risks data is discussed. A detailed Monte Carlo simulation study shows that the inferential methods provide quite reasonable results. Analysis of real data from the Diabetic Retinopathy Study is carried out as an illustrative example.