Resampling Procedures for Making Inference Under Nested Case–Control Studies

Abstract

The nested case–control (NCC) design has been widely adopted as a cost-effective solution in many large cohort studies for risk assessment with expensive markers, such as the emerging biologic and genetic markers. To analyze data from NCC studies, conditional logistic regression and maximum likelihood-based methods have been proposed. However, most of these methods either cannot be easily extended beyond the Cox model or require additional modeling assumptions. More generally applicable approaches based on inverse probability weighting (IPW) have been proposed as useful alternatives. However, due to the complex correlation structure induced by repeated finite risk set sampling, interval estimation for such IPW estimators remain challenging especially when the estimation involves nonsmooth objective functions or when making simultaneous inferences about functions. Standard resampling procedures such as the bootstrap cannot accommodate the correlation and thus are not directly applicable. In this article, we propose a resampling procedure that can provide valid estimates for the distribution of a broad class of IPW estimators. Simulation results suggest that the proposed procedures perform well in settings when analytical variance estimator is infeasible to derive or gives less optimal performance. The new procedures are illustrated with data from the Framingham Offspring Study to characterize individual level cardiovascular risks over time based on the Framingham risk score, C-reactive protein, and a genetic risk score. Supplementary materials for this article are available online.

KEY WORDS:

• Biomarker study
• Interval estimation
• Inverse probability weighting
• Resampling methods
• Risk prediction
• Simultaneous confidence band
• Survival model

Acknowledgments

The Framingham Heart Study and the Framingham SHARe project are conducted and supported by the National Heart, Lung, and Blood Institute (NHLBI) in collaboration with Boston University. The Framingham SHARe data used for the analyses described in this manuscript were obtained through dbGaP (access number: phs000007.v3.p2). This manuscript was not prepared in collaboration with investigators of the Framingham Heart Study and does not necessarily reflect the opinions or views of the Framingham Heart Study, Boston University, or the NHLBI. This research was in part supported by grants P01 CA053996, R01 GM085047, U01 CA086368, U54 LM008748, and R01 GM079330.