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

Abstract

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.

Keywords

• Lehmann family
• dependent competing risks
• singular distribution
• maximum likelihood estimator
• confidence interval
• model selection