### 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 language | English (US) |
---|---|

Pages (from-to) | 65-72 |

Number of pages | 8 |

Journal | Biometrics |

Volume | 56 |

Issue number | 1 |

State | Published - Mar 2000 |

### Fingerprint

### 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

*Biometrics*,

*56*(1), 65-72.

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

Research output: Contribution to journal › Article

*Biometrics*, vol. 56, no. 1, pp. 65-72.

}

TY - JOUR

T1 - Estimating data transformations in nonlinear mixed effects models

AU - Oberg, Ann L

AU - Davidian, Marie

PY - 2000/3

Y1 - 2000/3

N2 - 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.

AB - 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.

KW - Laplace's approximation

KW - Nonlinear mixed effects model

KW - Random effects

KW - Repeated measurements

KW - Small sigma

KW - Transform both sides

UR - http://www.scopus.com/inward/record.url?scp=0034061974&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034061974&partnerID=8YFLogxK

M3 - Article

C2 - 10783778

AN - SCOPUS:0034061974

VL - 56

SP - 65

EP - 72

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -