  Nested case-control (NCC) is a sampling method widely used for developing and
evaluating risk models with expensive biomarkers on large prospective cohort
studies. The biomarker values are typically obtained on a sub-cohort,
consisting of all the events and a subset of non-events. However, when the
number of events is not small, it might not be affordable to measure the
biomarkers on all of them. Due to the costs and limited availability of
bio-specimens, only a subset of events is selected to the sub-cohort as cases.
For these "untypical" NCC studies, we propose a new weighting method for the
inverse probability weighted (IPW) estimation. We also design a perturbation
method to estimate the variance of the IPW estimator with our new weights. It
accounts for between-subject correlations induced by the sampling processes for
both cases and controls through perturbing their sampling indicator variables,
and thus, captures all the variations. Furthermore, we demonstrate,
analytically and numerically, that when cases consist of only a subset of
events, our new weight produces more efficient IPW estimators than the weight
proposed in Samuelsen (1997) for a standard NCC design. We illustrate the
estimating procedure with a study that aims to evaluate a biomarker-based risk
prediction model using the Framingham cohort study.
