On local polynomial modelling of the additive risk model

Wanrong Liu, Xuewen Lu, Yongcheng Qi

Research output: Contribution to journalArticle

Abstract

The additive risk model provides an alternative modelling technique for failure time data to the proportional hazards model. In this article, we consider the additive risk model with a nonparametric risk effect. We study estimation of the risk function and its derivatives with a parametric and an unspecified baseline hazard function respectively. The resulting estimators are the local likelihood and the local score estimators. We establish the asymptotic normality of the estimators and show that both methods have the same formula for asymptotic bias but different formula for variance. It is found that, in some special cases, the local score estimator is of the same efficiency as the local likelihood estimator though it does not use the information about the baseline hazard function. Another advantage of the local score estimator is that it has a closed form and is easy to implement. Some simulation studies are conducted to evaluate and compare the performance of the two estimators. A numerical example is used for illustration.

Original languageEnglish (US)
Pages (from-to)1958-1981
Number of pages24
JournalCommunications in Statistics - Theory and Methods
Volume42
Issue number11
DOIs
StatePublished - Jun 1 2013

Keywords

  • Additive risk model
  • Asymptotic normality
  • Censoring
  • Counting process
  • Local likelihood estimator
  • Local score estimator

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