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Related Concept Videos

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Poisson Probability Distribution01:09

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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)...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...

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Related Experiment Video

Updated: Jul 10, 2026

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

Minimum Hellinger distance estimation for k-component poisson mixture with random effects.

Liming Xiang1, Kelvin K W Yau, Yer Van Hui

  • 1Department of Management Sciences, City University of Hong Kong, Hong Kong.

Biometrics
|November 1, 2007
PubMed
Summary

This study introduces a robust Minimum Hellinger Distance (MHD) estimation for Poisson mixture models with random effects, improving accuracy for clustered count data, especially with outliers. The new method outperforms traditional REML when data is contaminated.

Related Experiment Videos

Last Updated: Jul 10, 2026

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

Area of Science:

  • Statistical modeling
  • Robust statistics
  • Biostatistics

Background:

  • Clustered count data often exhibits heterogeneity due to latent subpopulations.
  • Traditional Residual Maximum Likelihood (REML) estimation in these models can be unstable with outliers.
  • Minimum Hellinger Distance (MHD) estimation offers a robust alternative for finite Poisson mixtures.

Purpose of the Study:

  • To develop a robust Minimum Hellinger Distance (MHD) estimation approach for k-component Poisson mixtures with normally distributed random effects.
  • To enhance the reliability of statistical inferences for clustered count data, particularly in the presence of contamination.

Main Methods:

  • Developed a robust MHD estimation for k-component Poisson mixtures incorporating random effects.
  • Utilized Gaussian quadrature to approximate integrals in the marginal distribution.
  • Approximated the marginal probability function using a summation of finite Poisson mixtures.

Main Results:

  • The MHD estimates demonstrated satisfactory performance for uncontaminated data.
  • MHD estimates outperformed REML estimates significantly when data contained outlying observations.
  • The method proved practical in analyzing recurrent urinary tract infections (UTI) data with random institution effects.

Conclusions:

  • The proposed robust MHD estimation method is effective for analyzing k-component Poisson mixtures with random effects.
  • This approach provides a reliable alternative to REML, especially for datasets prone to contamination.
  • The method has demonstrated practical utility in real-world epidemiological studies.