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Related Concept Videos

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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What are Estimates?01:06

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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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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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.
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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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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Constrained Maximum Likelihood Estimation for Model Calibration Using Summary-level Information from External Big

Nilanjan Chatterjee1, Yi-Hau Chen2, Paige Maas1

  • 1National Cancer Institute, Rockville MD 20852, U.S.A.

Journal of the American Statistical Association
|August 30, 2016
PubMed
Summary
This summary is machine-generated.

New statistical methods enable combining detailed internal study data with external big data for robust regression modeling. This approach enhances analysis by leveraging diverse data sources for improved research insights.

Keywords:
Case-control studyEmpirical likelihoodGeneralized regression estimatorMisspecified modelProfile-likelihood

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Data Science

Background:

  • Increasing availability of large-scale public and private datasets ('big data') for research.
  • Need for statistical methods to integrate detailed individual-level data with summary-level big data.
  • Existing methods like generalized regression (GR) calibration may have limitations.

Purpose of the Study:

  • To develop a framework for building regression models using internal individual-level data and external big data summary information.
  • To identify general constraints linking internal and external data models.
  • To propose semiparametric maximum likelihood inference for covariate distribution estimation.

Main Methods:

  • Developed a semiparametric maximum likelihood inference framework.
  • Utilized general constraints linking internal and external models.
  • Extended methods for complex sampling designs (e.g., case-control) and developed asymptotic theory and variance estimators.

Main Results:

  • Proposed a novel framework for integrating internal and external data sources in regression modeling.
  • Demonstrated the utility of identified constraints for model building.
  • Performance assessed via simulation studies and a real-data application, showing potential advantages over GR calibration.

Conclusions:

  • The proposed semiparametric framework effectively combines individual and summary-level data for regression analysis.
  • The methods are robust and adaptable to complex sampling designs.
  • Offers a valuable alternative to existing methodologies for big data research.