Effects of unmeasured heterogeneity in the linear transformation model for censored data

Bin Zhang, Yi Li, Rebecca A. Betensky

Research output: Contribution to journalArticle

Abstract

We investigate the effect of unobserved heterogeneity in the context of the linear transformation model for censored survival data in the clinical trials setting. The unobserved heterogeneity is represented by a frailty term, with unknown distribution, in the linear transformation model. The bias of the estimate under the assumption of no unobserved heterogeneity when it truly is present is obtained. We also derive the asymptotic relative efficiency of the estimate of treatment effect under the incorrect assumption of no unobserved heterogeneity. Additionally we investigate the loss of power for clinical trials that are designed assuming the model without frailty when, in fact, the model with frailty is true. Numerical studies under a proportional odds model show that the loss of efficiency and the loss of power can be substantial when the heterogeneity, as embodied by a frailty, is ignored.

Original languageEnglish (US)
Pages (from-to)191-203
Number of pages13
JournalLifetime Data Analysis
Volume12
Issue number2
DOIs
StatePublished - Jun 2006

Keywords

  • Frailty
  • Omitted covariate

ASJC Scopus subject areas

  • Applied Mathematics

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