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

Bin Zhang, Yi Li, Rebecca 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 1 2006

Fingerprint

Linear Transformation Model
Unobserved Heterogeneity
Frailty
Linear transformations
Censored Data
Clinical Trials
Proportional Odds Model
Censored Survival Data
Asymptotic Relative Efficiency
Treatment Effects
Estimate
Numerical Study
Unknown
Term
Model

Keywords

  • Frailty
  • Omitted covariate

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Effects of unmeasured heterogeneity in the linear transformation model for censored data. / Zhang, Bin; Li, Yi; Betensky, Rebecca.

In: Lifetime Data Analysis, Vol. 12, No. 2, 01.06.2006, p. 191-203.

Research output: Contribution to journalArticle

@article{813e32f2c66645d6a0f5669b3e5e0728,
title = "Effects of unmeasured heterogeneity in the linear transformation model for censored data",
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.",
keywords = "Frailty, Omitted covariate",
author = "Bin Zhang and Yi Li and Rebecca Betensky",
year = "2006",
month = "6",
day = "1",
doi = "10.1007/s10985-006-9008-y",
language = "English (US)",
volume = "12",
pages = "191--203",
journal = "Lifetime Data Analysis",
issn = "1380-7870",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Effects of unmeasured heterogeneity in the linear transformation model for censored data

AU - Zhang, Bin

AU - Li, Yi

AU - Betensky, Rebecca

PY - 2006/6/1

Y1 - 2006/6/1

N2 - 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.

AB - 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.

KW - Frailty

KW - Omitted covariate

UR - http://www.scopus.com/inward/record.url?scp=33747142448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747142448&partnerID=8YFLogxK

U2 - 10.1007/s10985-006-9008-y

DO - 10.1007/s10985-006-9008-y

M3 - Article

C2 - 16817004

AN - SCOPUS:33747142448

VL - 12

SP - 191

EP - 203

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

SN - 1380-7870

IS - 2

ER -