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Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses

Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses
Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses
Many applications in biostatistics rely on nonlinear regression models, such as, for example, population pharmacokinetic and pharmacodynamic modeling, or modeling approaches for dose-response characterization and dose selection. Such models are often expressed as nonlinear mixed-effects models, which are implemented in all major statistical software packages. Inference on the model curve can be based on the estimated parameters, from which pointwise confidence intervals for the mean profile at any single point in the covariate region (time, dose, etc.) can be derived. These pointwise confidence intervals, however, should not be used for simultaneous inferences beyond that single covariate value. If assessment over the entire covariate region is required, the joint coverage probability by using the combined pointwise confidence intervals is likely to be less than the nominal coverage probability. In this paper we consider simultaneous confidence bands for the mean profile over the covariate region of interest and propose two large-sample methods for their construction. The first method is based on the Schwarz inequality and an asymptotic ? 2 distribution. The second method relies on simulating from a multivariate normal distribution. We illustrate the methods with the pharmacokinetics of theophylline. In addition, we report the results of an extensive simulation study to investigate the operating characteristics of the two construction methods. Finally, we present extensions to construct simultaneous confidence bands for the difference of two models and to assess equivalence between two models in biosimilarity applications
1054-3406
708-725
Gsteiger, S.
4698e09d-d925-48d5-8a1c-9622aeff07df
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Gsteiger, S.
4698e09d-d925-48d5-8a1c-9622aeff07df
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a

Gsteiger, S., Bretz, F. and Liu, W. (2011) Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses Journal of Biopharmaceutical Statistics, 21, (4), pp. 708-725. (doi:10.1080/10543406.2011.551332).

Record type: Article

Abstract

Many applications in biostatistics rely on nonlinear regression models, such as, for example, population pharmacokinetic and pharmacodynamic modeling, or modeling approaches for dose-response characterization and dose selection. Such models are often expressed as nonlinear mixed-effects models, which are implemented in all major statistical software packages. Inference on the model curve can be based on the estimated parameters, from which pointwise confidence intervals for the mean profile at any single point in the covariate region (time, dose, etc.) can be derived. These pointwise confidence intervals, however, should not be used for simultaneous inferences beyond that single covariate value. If assessment over the entire covariate region is required, the joint coverage probability by using the combined pointwise confidence intervals is likely to be less than the nominal coverage probability. In this paper we consider simultaneous confidence bands for the mean profile over the covariate region of interest and propose two large-sample methods for their construction. The first method is based on the Schwarz inequality and an asymptotic ? 2 distribution. The second method relies on simulating from a multivariate normal distribution. We illustrate the methods with the pharmacokinetics of theophylline. In addition, we report the results of an extensive simulation study to investigate the operating characteristics of the two construction methods. Finally, we present extensions to construct simultaneous confidence bands for the difference of two models and to assess equivalence between two models in biosimilarity applications

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More information

e-pub ahead of print date: 22 April 2011
Published date: 2011
Organisations: Statistics, Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 337147
URI: http://eprints.soton.ac.uk/id/eprint/337147
ISSN: 1054-3406
PURE UUID: 7d6a0961-9f26-4ce6-ac27-dca1adb2539b
ORCID for W. Liu: ORCID iD orcid.org/0000-0002-4719-0345

Catalogue record

Date deposited: 19 Apr 2012 13:54
Last modified: 18 Jul 2017 06:04

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Contributors

Author: S. Gsteiger
Author: F. Bretz
Author: W. Liu ORCID iD

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