On a specification test for competing risk models

We investigate the finite sample performance of a Lagrange Multiplier specification test for competing-risks duration models developed by Pudney and Thomas (1995). In their empirical work they employ a simple form of the test based on the Outer Product of the Gradient approximation (OPG) to the Hessian which although convenient may be severely oversized in finite samples. in this paper we compare the small sample performance of the OPG and Hessian forms of the test under the null and various alternatives. Our results suggest that provided the degrees of freedom are minimised the OPG variant is reliable for use in applied work.