Case-cohort and case-control analysis with Cox's model

Prentice (1986) proposed the case-cohort design and studied a pseudolikelihood estimator of regression parameters in Cox's model. We derive a class of estimating equations for case-cohort sampling, each depending on a different estimator of the population distribution, which lead naturally to simple estimators that improve on Prentice's pseudolikelihood estimator. We also discuss an equivalence between case-control and case-cohort sampling in terms of the estimation of regression parameters in Cox's model.