Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 19 September 2019 / Approved: 20 September 2019 / Online: 20 September 2019 (05:17:17 CEST)

How to cite: Yamada, W.M.; Neely, M.N.; Bartroff, J.; Bayard, D.S.; Burke, J.V.; van Guilder, M.; Jelliffe, R.W.; Kryshchenko, A.; Leary, R.; Tatarinova, T.; Schumitzky, A. An Algorithm for Nonparametric Estimation of A Multivariate Mixing Distribution with Applications to Population Pharmacokinetics. Preprints 2019, 2019090231 (doi: 10.20944/preprints201909.0231.v1). Yamada, W.M.; Neely, M.N.; Bartroff, J.; Bayard, D.S.; Burke, J.V.; van Guilder, M.; Jelliffe, R.W.; Kryshchenko, A.; Leary, R.; Tatarinova, T.; Schumitzky, A. An Algorithm for Nonparametric Estimation of A Multivariate Mixing Distribution with Applications to Population Pharmacokinetics. Preprints 2019, 2019090231 (doi: 10.20944/preprints201909.0231.v1).

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.

Subject Areas

mixture distribution; mixture model; high dimensional statistics; nonparametric maximum likelihood; primal-dual interior-point method; adaptive grid