## Semiparametric analysis of general additive-multiplicative hazard models for counting processes.(English)Zbl 0844.62082

Summary: 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 $$\lambda(t \mid Z) = g\{\beta^T_0 W(t)\} + \lambda_0(t) h\{\gamma_0^T X(t)\}$$, where $$\theta_0 = (\beta^T_0, \gamma^T_0)^T$$ is a vector of unknown regression parameters, $$g$$ and $$h$$ are known link functions and $$\lambda_0$$ is an unspecified “baseline hazard function”.
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 $$\Lambda_0(t) = \int^t_0 \lambda_0 (u) du$$ 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.

### MSC:

 62M99 Inference from stochastic processes 62P10 Applications of statistics to biology and medical sciences; meta analysis 62G05 Nonparametric estimation
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