The use of Gaussian quadrature for estimation in frailty proportional hazards models

Lei Liu*, Xuelin Huang

*Corresponding author for this work

Research output: Contribution to journalArticle

75 Scopus citations

Abstract

In paper, we propose a novel Gaussian quadrature estimation method in various frailty proportional hazards models. We approximate the unspecified baseline hazard by a piecewise constant one, resulting in a parametric model that can be fitted conveniently by Gaussian quadrature tools in standard software such as SAS Proc NLMIXED. We first apply our method to simple frailty models for correlated survival data (e.g. recurrent or clustered failure times), then to joint frailty models for correlated failure times with informative dropout or a dependent terminal event such as death. Simulation studies show that our method compares favorably with the well-received penalized partial likelihood method and the Monte Carlo EM (MCEM) method, for both normal and Gamma frailty models. We apply our method to three real data examples: (1) the time to blindness of both eyes in a diabetic retinopathy study, (2) the joint analysis of recurrent opportunistic diseases in the presence of death for HIV-infected patients, and (3) the joint modeling of local, distant tumor recurrences and patients survival in a soft tissue sarcoma study. The proposed method greatly simplifies the implementation of the (joint) frailty models and makes them much more accessible to general statistical practitioners.

Original languageEnglish (US)
Pages (from-to)2665-2683
Number of pages19
JournalStatistics in Medicine
Volume27
Issue number14
DOIs
StatePublished - Jun 30 2008

Keywords

  • Dependent censoring
  • Frailty models
  • Shared random effects model
  • Survival analysis

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

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