Fitting semiparametric transformation regression models to data from a modified case-cohort design

We consider the problem of fitting semiparametric transformation regression models to data from a modified case-cohort study in which the censoring times of all the censored subjects in the cohort are observed. We propose to maximise a conditional profile likelihood to obtain the estimator of the regression parameter. Under the assumption that the censoring is independent of the covariates, the estimator is shown to be consistent and asymptotically normally distributed. Numerical studies suggest that the relative efficiency of the estimator is very high and that the estimator is often less biased than the estimator from the complete-case analysis and more accurate than the pseudolikelihood estimator.