A jackknife estimator of variance for Cox regression for correlated survival data

Studies in the health sciences often give rise to correlated survival data. Wei, Lin, and Weissfeld (1989, Journal of the American Statistical Association 84, 1065-1073) and Lee, Wei, and Amato (1992, in Survival Analysis: State of the Art) showed that, if the marginal distributions of the correlated survival times follow a proportional hazards model, then the estimates from Cox's partial likelihood (Cox, D.R., 1972, Journal of the Royal Statistical Society, Series B 24, 187-220), naively treating the correlated survival times as independent, give consistent estimates of the relative risk parameters. However, because of the correlation between survival times, the inverse of the information matrix may not be a consistent estimate of the asymptotic variance. Wei et al. (1989) and Lee et al. (1992) proposed a robust variance estimate that is consistent for the asymptotic variance. We show that a "one-step" jackknife estimator of variance is asymptotically equivalent to their variance estimator. The jackknife variance estimator may be preferred because an investigator needs only to write a simple loop in a computer package instead of a more involved program to compute Wei et al. (1989) and Lee et al.'s (1992) estimator.