The additive-multiplicative hazard model specifies that the hazard function for the counting process associated with a multidimensional covariate process Z = (WT, XT)T takes the form of λ(t Z) = g\βT₀ W(t)\ + λ₀(t)h\γT₀X(t)\, where θ₀ = (βT₀, γT₀)T is a vector of unknown regression parameters, g and h are known link functions and λ₀ is an unspecified "baseline hazard function." In this paper, we develop a class of simple estimating functions for θ₀, 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 Λ₀(t) = ∫ᵗ₀λ₀(u) du is also established. Furthermore, we construct adaptive estimators for θ₀ and Λ₀ that achieve the (semiparametric) information bounds. Finally, a real example is provided along with some simulation results.
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Lin et al. (1995) studied this question.