Nested case–control sampling without replacement

Nested case-control design (NCC) is a cost-effective outcome-dependent design in epidemiology that collects all cases and a fixed number of controls at the time of case diagnosis from a large cohort. Due to inefficiency relative to full cohort studies, previous research developed various estimation methodologies but changing designs in the formulation of risk sets was considered only in view of potential bias in the partial likelihood estimation. In this paper, we study a modified design that excludes previously selected controls from risk sets in view of efficiency improvement as well as bias. To this end, we extend the inverse probability weighting method of Samuelsen which was shown to outperform the partial likelihood estimator in the standard setting. We develop its asymptotic theory and a variance estimation of both regression coefficients and the cumulative baseline hazard function that takes account of the complex feature of the modified sampling design. In addition to good finite sample performance of variance estimation, simulation studies show that the modified design with the proposed estimator is more efficient than the standard design. Examples are provided using data from NIH-AARP Diet and Health Cohort Study.