Resampling Procedures for Making Inference under Nested Case-control Studies.

The nested case-control (NCC) design have 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 (Goldstein and Langholz, 1992; Borgan et al., 1995) and maximum likelihood (Scheike and Juul, 2004; Zeng et al., 2006) based methods have been proposed. However, most of these methods either cannot be easily extended beyond the Cox model (Cox, 1972) or require additional modeling assumptions. More generally applicable approaches based on inverse probability weighting (IPW) have been proposed as useful alternatives (Samuelsen, 1997; Chen, 2001; Samuelsen et al., 2007). 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 non-smooth 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 paper, 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 (CRP) and a genetic risk score.