New weighting methods when cases are only a subset of events in a nested case-control study.

Nested case control (NCC) is a sampling method widely used for developing and evaluating risk models with expensive biomarkers on large prospective cohort studies. In a typical NCC design, biomarker values are obtained on a subcohort, where cases consist of all the events (subjects who experience the event during the follow-up). However, when the number of events is not small, due to the cost and limited availability of biospecimen, one may select only a subset of events as cases. We refer to such a variation as the untypical NCC. Unfortunately, existing inverse probability weighted (IPW) estimators for the untypical NCC are biased, and they only focus on relative risk parameters under the proportional hazards (PH) model. In this manuscript, we propose new weighting methods that produce consistent IPW estimators for not only relative risk parameters but also several metrics that evaluate a risk model's predictive performance. We also provide the inference procedure via perturbation resampling, which captures all the variance and between-subject covariance induced by the sampling processes for both case and control selections. In addition, our methods are not limited to the PH model, and they can be applied to the time-specific generalized linear model. Under the typical NCC design, our new weights are equivalent to the weight proposed by Samuelsen; under the untypical NCC, the IPW estimators using our weights have smaller bias and variance than the existing methods. We will demonstrate this improved performance via both analytical and numerical investigations.