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Prediction of Shrinkage of Individual Parameters Using the Bayesian Information Matrix in Non-Linear Mixed Effect Models with Evaluation in Pharmacokinetics

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ABSTRACT

Purpose

When information is sparse, individual parameters derived from a non-linear mixed effects model analysis can shrink to the mean. The objective of this work was to predict individual parameter shrinkage from the Bayesian information matrix (M BF ). We 1) Propose and evaluate an approximation of M BF by First-Order linearization (FO), 2) Explore by simulations the relationship between shrinkage and precision of estimates and 3) Evaluate prediction of shrinkage and individual parameter precision.

Methods

We approximated M BF using FO. From the shrinkage formula in linear mixed effects models, we derived the predicted shrinkage from M BF . Shrinkage values were generated for parameters of two pharmacokinetic models by varying the structure and the magnitude of the random effect and residual error models as well as the design. We then evaluated the approximation of M BF FO and compared it to Monte-Carlo (MC) simulations. We finally compared expected and observed shrinkage as well as the predicted and estimated Standard Errors (SE) of individual parameters.

Results

M BF FO was similar to M BF MC. Predicted and observed shrinkages were close . Predicted and estimated SE were similar.

Conclusions

M BF FO enables prediction of shrinkage and SE of individual parameters. It can be used for design optimization.

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Abbreviations

CL:

Clearance

CV:

Coefficient of Variation

FO:

First-Order linearization

IU:

International Units

Km :

Michaelis-Menten constant

MAP:

Maximum A Posteriori

M BF :

Bayesian Fisher Information Matrix

MC:

Monte-Carlo

M F :

Fisher Information Matrix

M IBF :

Individual Bayesian Fisher Information Matrix

M IF :

Individual Fisher Information Matrix

ML:

Maximum Likelihood

MONOLIX:

MOdèles NOn LInéaires à effets miXtes

NLMEM:

Non-Linear Mixed Effects Models

PK:

Pharmacokinetics

Q:

Intercompartmental clearance

RSE:

Relative Standard Errors

SE:

Standard Errors

Sh:

Shrinkage

V:

Volume of distribution

V1-V2 :

Volume of distribution of the central and peripheral compartment

Vm :

Maximum elimination rate

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ACKNOWLEDGMENTS AND DISCLOSURES

During this work, the PhD of F. Combes was sponsored by a Convention Industrielle de Formation par la Recherche (CIFRE) from the French government and the Institut Roche de Recherche et Médecine Translationnelle. The authors thank IFR02 and Dr. Hervé Le Nagard for the use of the Centre de Biomodélisation.

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Authors and Affiliations

  1. University Paris Diderot, Sorbonne Paris Cité INSERM, UMR 738, 16, rue Henri Huchard, F-75018, Paris, France

    François Pierre Combes & France Mentré

  2. Institut Roche de Recherche et Médecine Translationnelle, Boulogne-Billancourt, France

    François Pierre Combes & Sylvie Retout

  3. Pharma Research and Early Development, Clinical Pharmacology F. Hoffmann-La Roche ltd, Basel, Switzerland

    François Pierre Combes, Sylvie Retout & Nicolas Frey

Authors
  1. François Pierre Combes
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  2. Sylvie Retout
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  3. Nicolas Frey
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  4. France Mentré
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Correspondence to François Pierre Combes.

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Combes, F.P., Retout, S., Frey, N. et al. Prediction of Shrinkage of Individual Parameters Using the Bayesian Information Matrix in Non-Linear Mixed Effect Models with Evaluation in Pharmacokinetics. Pharm Res 30, 2355–2367 (2013). https://doi.org/10.1007/s11095-013-1079-3

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  • DOI: https://doi.org/10.1007/s11095-013-1079-3

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