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 Statistic al Association 84, 1065-1073) and Lee, Wei, and Amato (1992, in Surviv al Analysis: State of the Art) showed that, if the marginal distributi ons of the correlated sur?rival times follow a proportional hazards mo del, then the estimates from Cox's partial likelihood (Cox, D. R., 197 2, Journal of the Royal Statistical Society, Series B 24, 187-220), na ively treating the correlated survival times as independent, give cons istent 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. W ei et al. (1989) and Lee et al. (1992) proposed a robust variance esti mate that is consistent for the asymptotic variance. We show that a '' one-step'' jackknife estimator of variance is asymptotically equivalen t to their variance estimator. The jackknife variance estimator may be preferred because an investigator needs only to write a simple loop i n a computer package instead of a more involved program to compute Wei et al. (1989) and Lee et al.'s (1992) estimator.