Robust Variance Estimation for the Case-Cohort Design

Large cohort studies of rare outcomes require extensive data collection, often for many relatively uninformative subjects. Sampling schemes have been proposed that oversample certain groups. For example, the case-cohort design of Prentice (1986, Biometrika 73, 1-11) provides an efficient method of analysis of failure time data. However, the variance estimate must explicitly correct for correlated score contributions. A simple robust variance estimator is proposed that allows for more complicated sampling mechanisms. The variance estimate uses a jackknife estimate of the variance of the individual influence function and is shown to be equivalent to a robust variance estimator proposed by Lin and Wei (1989, Journal of the American Statistical Association 84, 1074-1078) for the standard Cox model. Simulation results indicate excellent agreement with corrected asymptotic estimates and appropriate test size. The technique is illustrated with data evaluating the efficacy of mammography screening in reducing breast cancer mortality.