Abstract: Three widely used sampling designs—the nested case-control, case-cohort, and classical case-control designs—can be categorized as generalized case-cohort designs. Maximum likelihood methods are used to perform regression analysis of linear transformation models with these sampling designs, and the resulting estimator is proved to be consistent, asymptotically normal and semiparametrically efficient. Simulation studies and an application to the Stanford heart transplant data are presented.

Key words and phrases: Linear transformation models, maximum likelihood estimation, missing at random, nested case-control sampling.