Maximum Likelihood Estimation for Cox's Regression Model Under Case–Cohort Sampling

Abstract.  Case–cohort sampling aims at reducing the data sampling and costs of large cohort studies. It is therefore important to estimate the parameters of interest as efficiently as possible. We present a maximum likelihood estimator (MLE) for a case–cohort study based on the proportional hazards assumption. The estimator shows finite sample properties that improve on those by the Self & Prentice [Ann. Statist. 16 (1988)] estimator. The size of the gain by the MLE varies with the level of the disease incidence and the variability of the relative risk over the considered population. The gain tends to be small when the disease incidence is low. The MLE is found by a simple EM algorithm that is easy to implement. Standard errors are estimated by a profile likelihood approach based on EM-aided differentiation.