Sieve maximum likelihood estimation for a general class of accelerated hazards models with bundled parameters

In semiparametric hazard regression, nonparametric components may involve unknown regression parameters. Such intertwining effects make model estimation and inference much more difficult than the case in which the parametric and nonparametric components can be separated out. We study the sieve maximum likelihood estimation for a general class of hazard regression models, which include the proportional hazards model, the accelerated failure time model, and the accelerated hazards model. Coupled with the cubic B-spline, we propose semiparametric efficient estimators for the parameters that are bundled inside the non parametric component. We overcome the challenges due to intertwining effects of the bundled parameters, and establish the consistency and asymptotic normality properties of the estimators. We carry out simulation studies to examine the finite-sample properties of the proposed method, and demonstrate its efficiency gain over the conventional estimating equation approach. For illustration, we apply our proposed method to a study of bone marrow transplantation for patients with acute leukemia.