Wang, Wei; Wang, Jane-Ling; Wang, Qihua Proportional hazards regression with unknown link function. (English) Zbl 1271.62090 Rojo, Javier (ed.), Optimality. The third Erich L. Lehmann symposium. Selected papers based on the presentations at the symposium, Rice University, Houston, TX, USA, May 16–19, 2007. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-77-5/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 57, 47-66 (2009). Summary: Proportional hazards regression model assumes that the covariates affect the hazard function through a link function and an index which is a linear function of the covariates. Traditional approaches, such as the Cox proportional hazards model, focus on estimating the unknown index by assuming a known link function between the log-hazard function and covariates. A linear link function is often employed for convenience without any validation. This paper provides an approach to estimate the link function, which can then be used to guide the choice of a proper parametric link function. This is accomplished through a two-step algorithm to estimate the link function and the effects of the covariates iteratively without involving the baseline hazard estimate. The link function is estimated by a smoothing method based on a local version of partial likelihood, and the index function is then estimated using a full version of partial likelihood. Asymptotic properties of the non-parametric link function estimate are derived, which facilitates model checking of the adequacy of the Cox proportional hazards model. The approach is illustrated through a survival data and simulations.For the entire collection see [Zbl 1203.62003]. Cited in 1 Document MSC: 62G08 Nonparametric regression and quantile regression 62N02 Estimation in survival analysis and censored data 62N05 Reliability and life testing Keywords:partial likelihood; local partial likelihood; nonparametric smoothing; dimension reduction PDFBibTeX XMLCite \textit{W. Wang} et al., IMS Lect. Notes, Monogr. Ser. 57, 47--66 (2009; Zbl 1271.62090)