Estimating data transformations in nonlinear mixed effects models

Ann L Oberg, Marie Davidian

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

A routine practice in the analysis of repeated measurement data is to represent individual responses by a mixed effects model on some transformed scale. For example, for pharmacokinetic, growth, and other data, both the response and the regression model are typically transformed to achieve approximate within-individual normality and constant variance on the new scale; however, the choice of transformation is often made subjectively or by default, with adoption of a standard choice such as the log. We propose a mixed effects framework based on the transform-both-sides model, where the transformation is represented by a monotone parametric function and is estimated from the data. For this model, we describe a practical fitting strategy based on approximation of the marginal likelihood. Inference is complicated by the fact that estimation of the transformation requires modification of the usual standard errors for estimators of fixed effects; however, we show that, under conditions relevant to common applications, this complication is asymptotically negligible, allowing straightforward implementation via standard software.

Original languageEnglish (US)
Pages (from-to)65-72
Number of pages8
JournalBiometrics
Volume56
Issue number1
StatePublished - Mar 2000

Fingerprint

Nonlinear Mixed Effects Model
Data Transformation
Mixed Effects
Mixed Effects Model
Marginal Likelihood
Repeated Measurements
Software
Pharmacokinetics
Fixed Effects
Standard error
Complications
Normality
Regression Model
Monotone
Growth
Transform
pharmacokinetics
Estimator
Mathematical transformations
Approximation

Keywords

  • Laplace's approximation
  • Nonlinear mixed effects model
  • Random effects
  • Repeated measurements
  • Small sigma
  • Transform both sides

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability

Cite this

Estimating data transformations in nonlinear mixed effects models. / Oberg, Ann L; Davidian, Marie.

In: Biometrics, Vol. 56, No. 1, 03.2000, p. 65-72.

Research output: Contribution to journalArticle

Oberg, Ann L ; Davidian, Marie. / Estimating data transformations in nonlinear mixed effects models. In: Biometrics. 2000 ; Vol. 56, No. 1. pp. 65-72.
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