Abstract: Retrospective sampling designs, including case-cohort and case-control designs, are commonly used for failure time data in the presence of censoring. In this paper, we propose a new retrospective sampling design, called end-point sampling, which improves the efficiency of the case-cohort and case-control designs. The regression analysis is conducted using the Cox model. Under different assumptions, the maximum likelihood approach with computational aid from the EM algorithm, and the inverse probability weighting approach are developed respectively to estimate the regression parameters. The resulting estimators are shown to be consistent and asymptotically normal. Simulation and a real data study show favorable evidence for the proposed design in comparison with existing ones.

Key words and phrases: Case-control sampling, Cox model, EM algorithm, inverse probability weighting, maximum likelihood estimation, retrospective sampling.