Lin, D. Y.; Ying, Zhiliang Semiparametric analysis of general additive-multiplicative hazard models for counting processes. (English) Zbl 0844.62082 Ann. Stat. 23, No. 5, 1712-1734 (1995). 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. Cited in 2 ReviewsCited in 55 Documents MSC: 62M99 Inference from stochastic processes 62P10 Applications of statistics to biology and medical sciences; meta analysis 62G05 Nonparametric estimation Keywords:asymptotic efficiency; censoring; Cox regression; failure time; information bound; martingale; partial likelihood; survival data; time-dependent covariate; consistency; asymptotic normality; lung cancer data; weak convergence; additive-multiplicative hazard model; counting process; multidimensional covariate process; estimating functions; partial likelihood score function; proportional hazards models; Aalen-Breslow type estimators; baseline hazard function; adaptive estimators; simulation results × Cite Format Result Cite Review PDF Full Text: DOI