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Related Concept Videos

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.
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...
96
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

281
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
281
Model Approaches for Pharmacokinetic Data: Compartment Models01:14

Model Approaches for Pharmacokinetic Data: Compartment Models

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Compartmental analysis is a widely adopted approach to characterizing drug pharmacokinetics. It uses compartment models that conceptualize the body as a collection of reversibly communicating compartments, each representing a group of tissues exhibiting similar drug distribution characteristics. The movement rate of the drug between these compartments is typically described by first-order kinetics.
Two primary types of compartment models are recognized: mammillary and catenary. The more...
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Basic Continuous Time Signals01:22

Basic Continuous Time Signals

239
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
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Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches01:14

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

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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...
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Multicompartment Models: Overview01:14

Multicompartment Models: Overview

183
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.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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A scalable approach for continuous time Markov models with covariates.

Farhad Hatami1, Alex Ocampo2, Gordon Graham2

  • 1Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, Nuffield, Department of Medicine, University of Oxford and Department of Statistics, University of Oxford, Oxford, OX3 7LF, UK.

Biostatistics (Oxford, England)
|July 11, 2023
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Summary

We developed a faster method for continuous time Markov models (CTMM) using stochastic gradient descent and Padé approximation. This optimization makes fitting large datasets feasible and improves performance for complex analyses.

Keywords:
Continuous-time Markov modelMultiple sclerosisMultistate modelPadéScalable optimizationapproximation

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Area of Science:

  • Computational Statistics
  • Biostatistics
  • Mathematical Biology

Background:

  • Continuous time Markov models (CTMM) are essential for analyzing time-to-event data.
  • Existing CTMM fitting methods face scalability challenges with large datasets due to computational costs.
  • High computational cost arises from repeated matrix exponential calculations for each observation.

Purpose of the Study:

  • To propose an optimized technique for fitting CTMM with covariates.
  • To address the scalability issues of existing CTMM fitting methods.
  • To enable feasible fitting of large-scale biological and medical data.

Main Methods:

  • Utilized stochastic gradient descent (SGD) for optimization.
  • Implemented differentiation of the matrix exponential via Padé approximation.
  • Developed two novel methods for standard error computation using Padé and power series expansions.

Main Results:

  • The proposed optimization technique significantly improves the feasibility of fitting large-scale CTMM.
  • Demonstrated improved performance compared to existing CTMM fitting methods through simulations.
  • Successfully applied the method to the large-scale multiple sclerosis NO.MS dataset.

Conclusions:

  • The novel optimization technique enhances the scalability of CTMM fitting.
  • This approach facilitates the analysis of large, complex datasets in various scientific fields.
  • The method provides a robust framework for incorporating covariates in CTMM analyses.