A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data

Sangbum Choi, Xuelin Huang

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We propose a semiparametrically efficient estimation of a broad class of transformation regression models for nonproportional hazards data. Classical transformation models are to be viewed from a frailty model paradigm, and the proposed method provides a unified approach that is valid for both continuous and discrete frailty models. The proposed models are shown to be flexible enough to model long-term follow-up survival data when the treatment effect diminishes over time, a case for which the PH or proportional odds assumption is violated, or a situation in which a substantial proportion of patients remains cured after treatment. Estimation of the link parameter in frailty distribution, considered to be unknown and possibly dependent on a time-independent covariates, is automatically included in the proposed methods. The observed information matrix is computed to evaluate the variances of all the parameter estimates. Our likelihood-based approach provides a natural way to construct simple statistics for testing the PH and proportional odds assumptions for usual survival data or testing the short- and long-term effects for survival data with a cure fraction. Simulation studies demonstrate that the proposed inference procedures perform well in realistic settings. Applications to two medical studies are provided.

Original languageEnglish
Pages (from-to)1126-1135
Number of pages10
Issue number4
Publication statusPublished - 2012 Dec
Externally publishedYes


  • Compound Poisson frailty
  • Counting process
  • Cure fraction
  • Discrete frailty
  • Nonparametric likelihood
  • Survival analysis
  • Transformation models

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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