Partial marginal likelihood estimation for general transformation models

We consider a large class of transformation models introduced by Gu et al. (2005)  [14]. They proposed an estimation procedure for calculating the maximum partial marginal likelihood estimator (MPMLE) of regression parameters. A big advantage of MPMLE is that it avoids estimating two infinitely dimensional nuisance parameters: baseline and censoring survival functions. And they showed the validity of MPMLE through extensive simulations. In this paper, we establish the asymptotic properties of MPMLE in the general transformation models for either right or left censored data. The difficulty in establishing these asymptotic results comes from the fact that the score function derived from the partial marginal likelihood does not have ordinary independence or martingale structure. We develop a novel discretization method to resolve the difficulty. The estimation procedure is further examined using simulation studies and the analysis of the ACTG019 data.