The Nonparametric Adaptive Grid Algorithm for Population Pharmacokinetic Modeling

The nonparametric adaptive grid (NPAG) algorithm is described. NPAG is a primal dual interior point method for determining the nonparametric maximum likelihood distribution of random parameters for a nonlinear regression model. In pharmacokinetic (PK) population modeling, NPAG is useful for the case where a series of measurements are made on diverse individuals, distinguished by diverse measurement conditions. This paper includes sufficient mat hematical background and program detail to allow computational scientists to translate NPAG from PK

[1]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[2]  C. Carathéodory Über den variabilitätsbereich der fourier’schen konstanten von positiven harmonischen funktionen , 1911 .

[3]  J. Kiefer,et al.  CONSISTENCY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE PRESENCE OF INFINITELY MANY INCIDENTAL PARAMETERS , 1956 .

[4]  L. Baum,et al.  A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains , 1970 .

[5]  H. Faure Discrépance de suites associées à un système de numération (en dimension s) , 1982 .

[6]  B. Lindsay The Geometry of Mixture Likelihoods: A General Theory , 1983 .

[7]  A. Mallet A maximum likelihood estimation method for random coefficient regression models , 1986 .

[8]  Bennett L. Fox,et al.  Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators , 1986, TOMS.

[9]  Paul Bratley,et al.  Algorithm 659: Implementing Sobol's quasirandom sequence generator , 1988, TOMS.

[10]  A. Schumitzky Nonparametric EM Algorithms for estimating prior distributions , 1991 .

[11]  F Mentré,et al.  Handling covariates in population pharmacokinetics. , 1994, International journal of bio-medical computing.

[12]  Marie Davidian,et al.  Nonlinear Models for Repeated Measurement Data , 1995 .

[13]  L. Skovgaard NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[14]  J. Wakefield The Bayesian Analysis of Population Pharmacokinetic Models , 1996 .

[15]  Jack Dongarra,et al.  LAPACK Users' guide (third ed.) , 1999 .

[16]  R. Jelliffe Goal-oriented, model-based drug regimens: setting individualized goals for each patient. , 2000, Therapeutic drug monitoring.

[17]  D Bayard,et al.  Achieving target goals most precisely using nonparametric compartmental models and "multiple model" design of dosage regimens. , 2000, Therapeutic drug monitoring.

[18]  Roger W. Jelliffe,et al.  An adaptive grid non-parametric approach to pharmacokinetic and dynamic (PK/PD) population models , 2001, Proceedings 14th IEEE Symposium on Computer-Based Medical Systems. CBMS 2001.

[19]  Marie Davidian,et al.  Nonlinear models for repeated measurement data: An overview and update , 2003 .

[20]  Roger W. Jelliffe,et al.  A Bayesian Approach to Tracking Patients Having Changing Pharmacokinetic Parameters , 2004, Journal of Pharmacokinetics and Pharmacodynamics.

[21]  R. Savic,et al.  Importance of Shrinkage in Empirical Bayes Estimates for Diagnostics: Problems and Solutions , 2009, The AAPS Journal.

[22]  Djalil Chafaï,et al.  Comparison of nonparametric methods in nonlinear mixed effects models , 2009, Comput. Stat. Data Anal..

[23]  M. Karlsson,et al.  A Population Pharmacokinetic Model of Gabapentin Developed in Nonparametric Adaptive Grid and Nonlinear Mixed Effects Modeling , 2009, Therapeutic drug monitoring.

[24]  U. Holzgrabe,et al.  New Semiphysiological Absorption Model To Assess the Pharmacodynamic Profile of Cefuroxime Axetil Using Nonparametric and Parametric Population Pharmacokinetics , 2009, Antimicrobial Agents and Chemotherapy.

[25]  U. Holzgrabe,et al.  Population Pharmacokinetic Comparison and Pharmacodynamic Breakpoints of Ceftazidime in Cystic Fibrosis Patients and Healthy Volunteers , 2010, Antimicrobial Agents and Chemotherapy.

[26]  A. Prémaud,et al.  Population pharmacokinetics of mycophenolic acid in pediatric renal transplant patients using parametric and nonparametric approaches. , 2011, Pharmacological research.

[27]  Alan Schumitzky,et al.  Accurate Detection of Outliers and Subpopulations With Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation Package for R , 2012, Therapeutic drug monitoring.

[28]  R. Koenker,et al.  Convex Optimization in R , 2014 .

[29]  R. Koenker,et al.  Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules , 2014 .