Semiparametric inference in a model for association in bivanate survival data

Clayton's (1978) model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem, that is a problem where inference about a parameter is required in the presence of nuisance functions. We derive the asymptotic variance of Clayton's estimator, obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship. Some comparisons are made with results derived by Oakes (1982) for other estimators within this model. In the absence of censoring the exact null variance of the score statistic corresponding to Clayton's estimator is derived and compared with that of the locally most powerful rank test given by Cuzick (1982).