Semiparametric analysis of general additive-multiplicative hazard models for counting processes

The additive-multiplicative hazard model specifies that the hazard function for the counting process associated with a multidimensional covariate process Z = (W-T, X(T))(T) takes the form of lambda(t/Z) = g{beta(0)(T)W(t)} + lambda(0)(t)h{gamma(0)(T)X(t)}, where theta(0) = (beta(0)(T), <gamma(0)(T))(T) is a vector of unknown regression parameters, g and h are known link functions and lambda(0) is an unspecified ''baseline hazard function.'' In this paper, we develop a class of simple estimating functions for theta(0), which contains the partial likelihood score function in the special case of proportional hazards models. The resulting estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Weak convergence of the Aalen-Breslow type estimators for the cumulative baseline hazard function Lambda(0)(t) = integral(0)(t) lambda(0)(u) du is also established. Furthermore, we construct adaptive estimators for theta(0) and Lambda(0) that achieve the (semiparametric) information bounds. Finally, a real example is provided along with some simulation results.