Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
Analysis of Population Pharmacokinetic Data01:12

Analysis of Population Pharmacokinetic Data

Analysis of population pharmacokinetic data involves studying the behavior of drugs within diverse populations to understand their pharmacokinetic parameters. Traditional pharmacokinetic methods typically involve collecting samples from a few individuals and estimating these parameters. While these methods are commonly used, they have limitations in capturing the variability in drug response among individuals or heterogeneous populations. Population pharmacokinetics is employed to address these...
Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same authorSame journal

Advancing quantitative clinical pharmacology competencies in Francophone Africa through an on-line learning framework.

Journal of pharmacokinetics and pharmacodynamics·2026
Same author

Impact of fludarabine exposure on CAR T-cell outcomes in patients with large B-cell lymphoma.

Blood advances·2026
Same author

A QSP Model of Valproic Acid Toxicity in Pediatric and Adult Populations: Implications for Formulation Selection and L-Carnitine Supplementation.

CPT: pharmacometrics & systems pharmacology·2026
Same author

Forecasting the Biological Effect of PEGylated-rHuEPO Candidates in Chronic Kidney Disease Patients using a Middle-out Translation Approach.

Pharmaceutical research·2026
Same author

Design Optimization for Developing Population Pharmacokinetic Models in Critically Ill Children: Application to Teicoplanin, Piperacillin and Meropenem.

Clinical pharmacokinetics·2025
Same author

Leveraging in vitro Tumor Cell Killing and Cytokine Release to Predict Cytokine Release Syndrome Associated with CD3 T-cell Bispecifics in Oncology: a Retrospective Analysis.

The AAPS journal·2025

Related Experiment Video

Updated: Jun 21, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

Performance in population models for count data, part I: maximum likelihood approximations.

Elodie L Plan1, Alan Maloney, Iñaki F Trocóniz

  • 1Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Uppsala, Sweden. Elodie.Plan@farmbio.uu.se

Journal of Pharmacokinetics and Pharmacodynamics
|August 5, 2009
PubMed
Summary
This summary is machine-generated.

Maximum likelihood approximation methods for non-linear mixed effects models of count data show useful estimation accuracy. Both Laplacian approximation and Gaussian Quadrature methods provide reliable population parameter estimates for various count models.

More Related Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Related Experiment Videos

Last Updated: Jun 21, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Area of Science:

  • Pharmacometrics
  • Statistical Modeling
  • Biostatistics

Background:

  • Non-linear mixed effects (NLME) models are crucial for analyzing complex biological data, especially count data.
  • Limited evaluation exists for maximum likelihood approximation methods in NLME for count data.

Purpose of the Study:

  • To assess the estimation accuracy of population parameters for six count data models using two approximation methods.
  • To compare the performance of Laplacian approximation (LAPLACE) and Gaussian Quadrature (GQ) methods in NONMEM and SAS.

Main Methods:

  • Simulated 100 datasets for Poisson, Poisson with Markov elements, Poisson mixture, Zero Inflated Poisson, Generalized Poisson, and Negative Binomial models.
  • Applied LAPLACE in NONMEM and LAPLACE/Gaussian Quadrature (GQ) in SAS for parameter estimation.
  • Used parameter values derived from a real case study of 551 epileptic patients.

Main Results:

  • LAPLACE showed low bias for fixed effects (1.02% AVB) and mean count random effects (0.32-8.24%).
  • Overdispersion parameters in ZIP, GP, and NB models were underestimated by LAPLACE (-15.73% to -25.87% bias).
  • GQ (9 points) improved bias for overdispersion parameters (3.80% AVB) but was slower and had fewer successful minimizations in SAS.

Conclusions:

  • Despite some bias, all investigated methods provide useful population parameter estimates for count data models.
  • Parameter estimates, even when biased, yield simulated data closely resembling data from the true model.
  • Gaussian Quadrature offers improved accuracy for overdispersion parameters but at a computational cost.