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

Year: 2020
Type: article
Abstract: In this paper we describe a nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions. Given $N$ independent observations, convexity theory shows that the NPML estimator is discrete with at most $N$ support points. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. The probability of the support 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 non-trivial 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.
DOI: 10.3390/pharmaceutics13010042
Authors: Walter M. Yamada, Michael N. Neely, Jay Bartroff, David S. Bayard, James V. Burke, Mike van Guilder, Roger W. Jelliffe, Alona Kryshchenko, Robert Leary, Tatiana Tatarinova, Alan Schumitzky
Institutions: Children's Hospital Los Angeles, University of Southern California, California Institute of Technology, Jet Propulsion Laboratory, University of Washington, California State University, Channel Islands, University of La Verne
Language: English
Open Access status: gold
Estimated APC paid: $1,901
Funders: National Science Foundation, National Institutes of Health, National Institute of General Medical Sciences, National Institute of Biomedical Imaging and Bioengineering, National Center for Research Resources, Eunice Kennedy Shriver National Institute of Child Health and Human Development
Awards: Population Pharmacokinetic Modeling and Dual Optimal Control, Optimizing Coordinated Combination Drug Therapy, New Decision Supports and Databases for Drug Dosage, Biomedical Simulations Resource (BMSR), POPULATION PHARMACOKINETICS MODELING ON A SUPERCOMPUTER, Ontogeny of Voriconazole Pharmaockinetics and Metabolism, Variational Analysis, Optimization of Eigenvalues, and Robust Stability, G9000136049
OpenAlex ID: W2990821920
FWCI: 1.375
Cites: 45
Cited by: 24
Related to: 10