Testing for independence in a competing risks model

This paper examines the performance of the conventional likelihood ratio test when testing for independence between failure times in a competing risks framework. The dependence between failure times arises by stochastically related unobserved components. The unobserved components are estimated non-parametrically. Although the non-parametric method is appealing in empirical work, large-sample properties of the estimators are hard to come by analytically. This paper considers large-sample as well as small-sample properties of the likelihood ratio statistic by means of Monte Carlo simulations. The model is a dependent competing risks model of the mixed proportional hazard type. The failure times are Weibull distributed and the unobserved heterogeneity is generated by a bivariate normal. Simulations suggest that the distribution of the statistic is close to the chi(2) distribution for large sample sizes while for smaller sample sizes, the empirical distribution is more heavy-tailed than the chi(2) distribution.