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Related Concept Videos

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Prediction Intervals

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
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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.
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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Likelihood interval for nonlinear regression.

Moon Hee Lee1, Kyun-Seop Bae1

  • 1Department of Clinical Pharmacology and Therapeutics, Asan Medical Center, University of Ulsan College of Medicine, Seoul 05505, Korea.

Translational and Clinical Pharmacology
|July 13, 2023
PubMed
Summary
This summary is machine-generated.

Wald confidence intervals are limited for nonlinear models. This study introduces likelihood intervals in R software, offering a more accurate estimation reflecting the likelihood profile

Keywords:
Likelihood FunctionsMaximum Likelihood Estimate

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Area of Science:

  • Pharmacometrics and statistical modeling.
  • Computational statistics and software development.

Background:

  • Wald confidence intervals are standard for nonlinear models but fail to capture likelihood profile asymmetry.
  • Existing statistical software lacked tools for likelihood-based interval estimation and profile visualization in nonlinear regression.

Purpose of the Study:

  • To implement likelihood interval estimation and likelihood profile plotting for nonlinear models in R.
  • To address the limitations of Wald intervals by providing accurate, profile-aware estimations.
  • To enhance the capabilities of the wnl R package for nonlinear modeling.

Main Methods:

  • Development and integration of functions for likelihood interval calculation within the wnl R package.
  • Implementation of likelihood profile plotting to visualize parameter uncertainty.
  • Demonstration using a pharmacokinetic model fitted to concentration-time data.

Main Results:

  • Successful implementation of likelihood interval estimation and profile plotting in the wnl R package.
  • The new functions provide a more accurate representation of parameter uncertainty compared to Wald intervals.
  • The pharmacokinetic model example illustrates the practical application and benefits of the implemented methods.

Conclusions:

  • The wnl R package now offers robust tools for likelihood-based inference in nonlinear models.
  • These implementations overcome previous software limitations, facilitating more reliable parameter estimation.
  • The study advances the application of likelihood profiles in nonlinear regression analysis and pharmacometrics.