Score tests for independence in parametric competing risks models

摘要

A popular model for competing risks postulates the existence of a latent unobserved failure time for each risk. Assuming that these underlying failure times are independent is attractive since it allows standard statistical tools for right-censored lifetime data to be used in the analysis. This paper proposes simple independence score tests for the validity of this assumption when parametric regression models are used to model the individual risks. The score tests are derived for the alternatives that specify that copulas are responsible for a possible dependency between competing risks. The test statistics are functions of the Cox and Snell residuals. A variance estimator is derived by writing the score function and the Fisher information matrix for the marginal models as stochastic integrals. A simulation study and a numerical example illustrate the methodology proposed in this paper.