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An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume n...

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Autores principales: Yamada, Walter M., Neely, Michael N., Bartroff, Jay, Bayard, David S., Burke, James V., van Guilder, Mike, Jelliffe, Roger W., Kryshchenko, Alona, Leary, Robert, Tatarinova, Tatiana, Schumitzky, Alan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823953/
https://www.ncbi.nlm.nih.gov/pubmed/33396749
http://dx.doi.org/10.3390/pharmaceutics13010042
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author Yamada, Walter M.
Neely, Michael N.
Bartroff, Jay
Bayard, David S.
Burke, James V.
van Guilder, Mike
Jelliffe, Roger W.
Kryshchenko, Alona
Leary, Robert
Tatarinova, Tatiana
Schumitzky, Alan
author_facet Yamada, Walter M.
Neely, Michael N.
Bartroff, Jay
Bayard, David S.
Burke, James V.
van Guilder, Mike
Jelliffe, Roger W.
Kryshchenko, Alona
Leary, Robert
Tatarinova, Tatiana
Schumitzky, Alan
author_sort Yamada, Walter M.
collection PubMed
description Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.
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spelling pubmed-78239532021-01-24 An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics Yamada, Walter M. Neely, Michael N. Bartroff, Jay Bayard, David S. Burke, James V. van Guilder, Mike Jelliffe, Roger W. Kryshchenko, Alona Leary, Robert Tatarinova, Tatiana Schumitzky, Alan Pharmaceutics Article Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing. MDPI 2020-12-30 /pmc/articles/PMC7823953/ /pubmed/33396749 http://dx.doi.org/10.3390/pharmaceutics13010042 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Yamada, Walter M.
Neely, Michael N.
Bartroff, Jay
Bayard, David S.
Burke, James V.
van Guilder, Mike
Jelliffe, Roger W.
Kryshchenko, Alona
Leary, Robert
Tatarinova, Tatiana
Schumitzky, Alan
An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics
title An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics
title_full An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics
title_fullStr An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics
title_full_unstemmed An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics
title_short An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics
title_sort algorithm for nonparametric estimation of a multivariate mixing distribution with applications to population pharmacokinetics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823953/
https://www.ncbi.nlm.nih.gov/pubmed/33396749
http://dx.doi.org/10.3390/pharmaceutics13010042
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