A Model for Association in Bivariate Survival Data

Inference for the parameter 0 governing the association between S and T, given a sample of size n from their bivariate distribution is considered, and an alternative non-parametric estimator based on Kendall's coefficient of concordance is proposed and its asymptotic variance evaluated.

Abstract

Summary A reparameterization of a model introduced by D. G. Clayton for association in bivariate life-tables is discussed. Inference for the parameter governing the association is considered when the marginal distributions are specified up to Lehmann alternatives. The information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters. The likelihood proposed by Clayton for the case that the marginal distributions are completely unknown is criticized. An alternative nonparametric estimator based on Kendall's coefficient of concordance is proposed and its asymptotic variance evaluated.