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Related Concept Videos

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...
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)...
Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches01:14

Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches

Drug disposition in the body is a complex process and can be studied using two major approaches: the model and the model-independent approaches.
The model approach uses mathematical models to describe changes in drug concentration over time. Pharmacokinetic models help characterize drug behavior in patients, predict drug concentration in the body fluids, calculate optimum dosage regimens, and evaluate the risk of toxicity. However, ensuring that the model fits the experimental data accurately...
Clearance Models: Noncompartmental Models01:17

Clearance Models: Noncompartmental Models

Clearance is a pharmacokinetic parameter traditionally defined by compartment models, signifying the rate at which a drug is expelled from the body. However, a noncompartmental model offers an alternative method for assessing clearance, primarily employing empirical data obtained after administering a single drug dose.
The noncompartmental approach capitalizes on extensive sampling data, correlating the volume of distribution to systemic exposure and the administered dosage. This method enables...
Model-Independent Approaches for Pharmacokinetic Data: Noncompartmental Analysis00:59

Model-Independent Approaches for Pharmacokinetic Data: Noncompartmental Analysis

Noncompartmental analyses offer an alternative method for describing drug pharmacokinetics without relying on a specific compartmental model. In this approach, the drug's pharmacokinetics are assumed to be linear, with the terminal phase log-linear. This assumption allows for simplified analysis and interpretation of the drug's behavior in the body.
One important characteristic of noncompartmental analyses is that drug exposure increases proportionally with increasing doses. This relationship...
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...

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Updated: Jun 4, 2026

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

Flexible nonhomogeneous markov models for panel observed data.

Andrew C Titman1

  • 1Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK. a.titman@lancaster.ac.uk

Biometrics
|February 11, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for analyzing time-dependent changes in nonhomogeneous Markov models using B-splines. The approach enhances understanding of complex biological processes like cardiac allograft vasculopathy.

Related Experiment Videos

Last Updated: Jun 4, 2026

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:

  • Biostatistics
  • Mathematical Modeling
  • Medical Statistics

Background:

  • Nonhomogeneous Markov models are crucial for analyzing time-dependent processes in panel data.
  • Existing methods often use piecewise constant intensities, limiting smoothness and flexibility.
  • Time-dependent covariates, such as age or calendar time, influence transition intensities.

Purpose of the Study:

  • To develop and evaluate a novel method for fitting nonhomogeneous Markov models to panel-observed data.
  • To propose B-spline based transition intensities as a smooth and generalized alternative to existing approaches.
  • To facilitate maximum likelihood estimation using derivatives of the likelihood function.

Main Methods:

  • Direct numerical solution of the Kolmogorov Forward equations for model fitting.
  • Utilizing B-splines to model smooth, time-dependent transition intensities.
  • Employing an expansion of differential equations for likelihood derivative calculation and Fisher scoring algorithm.

Main Results:

  • The proposed method allows for flexible and smooth modeling of time-varying transition intensities.
  • The Fisher scoring algorithm provides an efficient approach for maximum likelihood estimation.
  • The method was successfully evaluated through a simulation study.

Conclusions:

  • The developed method offers a robust and flexible framework for analyzing nonhomogeneous Markov models with time-dependent covariates.
  • This approach enhances the analysis of dynamic biological processes, exemplified by cardiac allograft vasculopathy.
  • B-spline based intensities represent a significant advancement over piecewise constant models.