External comparisons from nested case-control designs.

The nested case-control design, used to sample within cohorts, is usually employed for internal comparisons. We propose to use this design for external comparisons. We present two probability-weighted estimators of the expected number of cases under a given exposure, based on external rates, for two versions of the nested case-control design. These estimators are used, along with their variance estimators, to form confidence intervals for standardized mortality ratios. The estimators are practically unbiased, whereas the naive estimator that treats the nested case-control sample as a random sample of the cohort is clearly biased. An estimator from the alternative Cox model-based approach is found to be substantially biased when applied in this context. Comparing the proposed estimators for nested case-control designs to a corresponding estimator for the case-cohort design, we found that the correlation between follow-up time and exposure time (that is, the amount of time under the exposure effect) has an impact on which type of design is more efficient for external comparisons. A small correlation favors the case-cohort design and a large correlation the nested case-control design. We examine empirical properties of these estimators through computer simulations, using a cohort study of the incidence of second cancer in 2,189 patients with Hodgkin's disease.