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

Pharmaceutics ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 42
Author(s):  
Walter M. Yamada ◽  
Michael N. Neely ◽  
Jay Bartroff ◽  
David S. Bayard ◽  
James V. Burke ◽  
...  

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.

Author(s):  
Walter M. Yamada ◽  
Michael N. Neely ◽  
Jay Bartroff ◽  
David S. Bayard ◽  
James V. Burke ◽  
...  

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.


2021 ◽  
Vol 11 (10) ◽  
pp. 4429
Author(s):  
Ana Šarčević ◽  
Damir Pintar ◽  
Mihaela Vranić ◽  
Ante Gojsalić

The prediction of sport event results has always drawn attention from a vast variety of different groups of people, such as club managers, coaches, betting companies, and the general population. The specific nature of each sport has an important role in the adaption of various predictive techniques founded on different mathematical and statistical models. In this paper, a common approach of modeling sports with a strongly defined structure and a rigid scoring system that relies on an assumption of independent and identical point distributions is challenged. It is demonstrated that such models can be improved by introducing dynamics into the match models in the form of sport momentums. Formal mathematical models for implementing these momentums based on conditional probability and empirical Bayes estimation are proposed, which are ultimately combined through a unifying hybrid approach based on the Monte Carlo simulation. Finally, the method is applied to real-life volleyball data demonstrating noticeable improvements over the previous approaches when it comes to predicting match outcomes. The method can be implemented into an expert system to obtain insight into the performance of players at different stages of the match or to study field scenarios that may arise under different circumstances.


2015 ◽  
Vol 101 (1) ◽  
pp. e1.41-e1
Author(s):  
Wei Zhao ◽  
Daolun Zhang ◽  
Thomas Storme ◽  
André Baruchel ◽  
Xavier Declèves ◽  
...  

BackgroundChildren with haematological malignancy represent an identified subgroup of the paediatric population with specific pharmacokinetic parameters. In these patients, inadequate empirical antibacterial therapy may result in infection-related morbidity and increased mortality, making optimization of the dosing regimen essential. As paediatric data are limited, our aim was to evaluate the population pharmacokinetics of teicoplanin in order to define the appropriate dosing regimen in this high-risk population.MethodsThe current dose of teicoplanin was evaluated in children with haematological malignancy. Population pharmacokinetics of teicoplanin was analysed using NONMEM software. The dosing regimen was optimised based on the final model.ResultsEighty-five children (age range: 0.5 to 16.9 years) were included. Therapeutic drug monitoring and opportunistic samples (n=143) were available for analysis. With the current recommended dose of 10 mg/kg/day, 41 children (48%) had sub-therapeutic steady-state trough concentrations (Css,min<10 mg/liter). A two-compartment pharmacokinetic model with first-order elimination was developed. Systematic covariate analysis identified that bodyweight (size) and creatinine clearance significantly influenced teicoplanin clearance. The model was validated internally. Its predictive performance was further confirmed in an external validation. In order to reach the target AUC of 750 mg·h/L, 18 mg/kg was required for infants, 14 mg/kg for children and 12 mg/kg for adolescents. A patient-tailored dose regimen was further developed and reduced variability in AUC and Css,min values compared to the mg/kg-basis dose, making the modelling approach an important tool for dosing individualization.ConclusionsThis first population pharmacokinetic study of teicoplanin in children with haematological malignancy provided evidence-based support to individualize teicoplanin therapy in this vulnerable population.


2002 ◽  
Vol 14 (4) ◽  
pp. 435-448 ◽  
Author(s):  
R. J. Karunamuni ◽  
R. S. Singh ◽  
S. Zhang

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