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Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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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.
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Hazard Rate01:11

Hazard Rate

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The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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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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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.
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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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Efficient Computation of High-Dimensional Penalized Piecewise Constant Hazard Random Effects Models.

Hillary M Heiling1, Naim U Rashid1,2, Quefeng Li1

  • 1Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.

Statistics in Medicine
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Summary

This study introduces a new survival model to simplify complex proportional hazards mixed effects models (PHMMs). The method enables simultaneous variable selection for fixed and random effects, improving analysis of high-dimensional biomedical data.

Keywords:
factor modelmixed effectspiecewise constant hazardsurvival analysisvariable selection

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Area of Science:

  • Biostatistics
  • Genomics
  • Survival Analysis

Background:

  • Proportional hazards mixed effects models (PHMMs) are crucial for analyzing time-to-event data with clustered correlations in biomedical research.
  • High-dimensional data presents challenges in specifying and computationally handling fixed and random effects in PHMMs.

Purpose of the Study:

  • To develop a computationally efficient method for variable selection in high-dimensional survival data.
  • To approximate PHMMs with a more tractable piecewise constant hazard mixed effects survival model.
  • To enable simultaneous selection of important fixed and random effects.

Main Methods:

  • Approximation of PHMMs using a piecewise constant hazard mixed effects survival model.
  • Parameter estimation via a modified Monte Carlo expectation conditional minimization (MCECM) algorithm.
  • Incorporation of a factor model decomposition for random effects to enhance scalability.

Main Results:

  • The proposed method effectively performs simultaneous variable selection on fixed and random effects.
  • The factor model decomposition aids in scaling the variable selection to higher dimensions.
  • Demonstrated utility through simulations and application to a pancreatic cancer gene expression dataset.

Conclusions:

  • The developed approach offers a scalable and effective solution for variable selection in high-dimensional survival analysis.
  • The method aids in identifying key features influencing survival outcomes, particularly in complex datasets like gene expression studies.