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Related Concept Videos

Longitudinal Studies01:26

Longitudinal Studies

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Longitudinal studies are also widely used in other medical and social science fields. For instance, in cardiovascular research, they can monitor patients' health over decades to identify risk factors for heart disease, such as high cholesterol or smoking, and evaluate the long-term effectiveness of preventive measures. Similarly, in mental health studies, researchers might follow individuals from adolescence into adulthood to understand the development and progression of conditions like...
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Multicompartment Models: Overview01:14

Multicompartment Models: Overview

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Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
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Longitudinal Research02:20

Longitudinal Research

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Sometimes we want to see how people change over time, as in studies of human development and lifespan. When we test the same group of individuals repeatedly over an extended period of time, we are conducting longitudinal research. Longitudinal research is a research design in which data-gathering is administered repeatedly over an extended period of time. For example, we may survey a group of individuals about their dietary habits at age 20, retest them a decade later at age 30, and then again...
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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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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.
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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

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

Mechanistic Models: Compartment Models in Individual and Population Analysis

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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...
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Kimesurface Representation and Tensor Linear Modeling of Longitudinal Data.

Rongqian Zhang1,2, Yupeng Zhang3,2, Yuyao Liu1,2

  • 1Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA.

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This study introduces complex time (kime) to model longitudinal data as kimesurfaces. This novel approach enhances time-series analysis for prediction and classification using tensor regression.

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Area of Science:

  • Computational Statistics and Data Analysis
  • Mathematical Modeling of Biological Systems

Background:

  • Traditional analysis of time-varying longitudinal data often uses parametric models.
  • Existing methods aim to model trends, predict trajectories, and characterize relations.
  • Tensor-based linear modeling provides an algebraic approach to longitudinal data.

Purpose of the Study:

  • To introduce a novel method for representing, modeling, and analyzing longitudinal data.
  • To generalize event order from real numbers to the complex plane using complex time (kime).
  • To develop new inference, prediction, classification, and regression techniques based on kimesurfaces.

Main Methods:

  • Introduction of complex time (kime) to transform time-varying signals into 2D manifolds called kimesurfaces.
  • Utilizing the Laplace transform and its inverse for bijective mapping between time-series and kimesurfaces.
  • Development and validation of a general tensor regression-based linear model using functional Magnetic Resonance Imaging (fMRI) data.

Main Results:

  • Demonstrated the transformation of classical time-series data into kimesurface manifolds.
  • Validated the proposed tensor regression model using fMRI data, showcasing its applicability.
  • Established the potential of kimesurface representation for various machine learning and AI algorithms.

Conclusions:

  • Complex time (kime) and kimesurfaces offer a generalized framework for longitudinal data analysis.
  • This method extends classical time-series analysis, enabling novel analytical techniques.
  • The kimesurface representation is versatile and applicable to multivariate, complex-domain, and complex-range longitudinal processes.