Absolute risk from double nested case-control designs: cause-specific proportional hazards models with and without augmented estimating equations

We estimate relative hazards and absolute risks (or cumulative incidence or crude risk) under cause-specific proportional hazards models for competing risks from double nested case-control (DNCC) data. In the DNCC design, controls are time-matched not only to cases from the cause of primary interest, but also to cases from competing risks (the phase-two sample). Complete covariate data are available in the phase-two sample, but other cohort members only have information on survival outcomes and some covariates. Design-weighted estimators use inverse sampling probabilities computed from Samuelsen-type calculations for DNCC. To take advantage of additional information available on all cohort members, we augment the estimating equations with a term that is unbiased for zero but improves the efficiency of estimates from the cause-specific proportional hazards model. We establish the asymptotic properties of the proposed estimators, including the estimator of absolute risk, and derive consistent variance estimators. We show that augmented design-weighted estimators are more efficient than design-weighted estimators. Through simulations, we show that the proposed asymptotic methods yield nominal operating characteristics in practical sample sizes. We illustrate the methods using prostate cancer mortality data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study of the National Cancer Institute.