Parametric estimation of association in bivariate failure-time data subject to competing risks: sensitivity to underlying assumptions

There has arisen a considerable body of research addressing the estimation of association between paired failure times in the presence of competing risks. In a 2002 paper, Bandeen-Roche and Liang proposed the conditional cause-specific hazard ratio (CCSHR) as a measure of this association and a parametric method by which to estimate it. The method features an interpretable decomposition of the CCSHR into factors describing the association between a pair’s times to first failure among multiple failure causes and the association in pair members’ propensities to fail due to a common cause. There were indications of sensitivity to model assumptions, however, in the 2002 work. Here we report a detailed study of the method’s sensitivity to its parametric assumptions. We conclude that the method’s performance is most sensitive to mis-specification of temporality in the association between pair members’ first-failure times and of correlation between propensity to fail early or late and the propensity to fail of a specific cause. Implications for methods development are highlighted.