Testing for independence in a competing risks model

Abstract

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 χ 2 distribution for large sample sizes while for smaller sample sizes, the empirical distribution is more heavy-tailed than the χ 2 distribution.