Semiparametric inference for a two-stage outcome-dependent sampling design with interval-censored failure time data

We propose a two-stage outcome-dependent sampling design and inference procedure for studies that concern interval-censored failure time outcomes. This design enhances the study efficiency by allowing the selection probabilities of the second-stage sample, for which the expensive exposure variable is ascertained, to depend on the first-stage observed interval-censored failure time outcomes. In particular, the second-stage sample is enriched by selectively including subjects who are known or observed to experience the failure at an early or late time. We develop a sieve semiparametric maximum pseudo likelihood procedure that makes use of all available data from the proposed two-stage design. The resulting regression parameter estimator is shown to be consistent and asymptotically normal, and a consistent estimator for its asymptotic variance is derived. Simulation results demonstrate that the proposed design and inference procedure performs well in practical situations and is more efficient than the existing designs and methods. An application to a phase 3 HIV vaccine trial is provided.