Modelling multivariate failure time associations in the presence of a competing risk

There has been much research on analysing multivariate failure times, but little that has accommodated failures that arise in the presence of a competing failure process.This paper studies the problem of describing associations among times to such failures. It proposes a modified conditional hazard ratio measure of association that is tailored to competing risks data, develops frailty models and a nonparametric method for describing the proposed measure, and contrasts estimation by proposed methods with the ‘standard’ of treating competing risks as independently censoring failure times due to targeted causes. The methods are investigated on simulated and real data.