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Related Concept Videos

Randomized Experiments01:13

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
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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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Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
Random and Systematic Errors01:20

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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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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 squares (OLS)...

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Testing Random Effects in Nonlinear Mixed-Effects Models.

Germaine Uwimpuhwe1, Reza Drikvandi1, Shelley A Blozis2

  • 1Department of Mathematical Sciences, Durham University, Durham, UK.

Statistics in Medicine
|May 20, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new nonparametric method for testing random effects in nonlinear mixed-effects models, crucial for analyzing complex medical data. The flexible framework and permutation test offer a robust solution for identifying necessary random effects without distributional assumptions.

Keywords:
method of momentsnonlinear mixed‐effects modelspermutation testrandom effectsvariance least squares method

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Longitudinal Data Analysis

Background:

  • Nonlinear mixed-effects models are vital for analyzing longitudinal and clustered medical data with subject-specific variability.
  • Identifying necessary random effects (variance components) is critical but challenging in these models.
  • Existing methods for testing random effects in nonlinear models are limited due to complexity and incorrect asymptotic distributions.

Purpose of the Study:

  • To develop a flexible nonparametric framework for testing random effects in nonlinear mixed-effects models.
  • To address the understudied problem of random effects testing in nonlinear models.
  • To provide a method that does not assume normality or specific distributions for random effects and errors.

Main Methods:

  • Proposed a flexible nonparametric framework for testing random effects.
  • Introduced a permutation procedure to approximate the finite-sample distribution of the test statistic.
  • Developed distribution-free estimates for variance components.
  • The framework supports testing all or subsets of random effects.

Main Results:

  • The nonparametric method demonstrated robust performance in extensive simulations.
  • The approach was validated through two motivating case studies.
  • An R package (TestREnlme) is available for implementing the proposed tests.

Conclusions:

  • The proposed nonparametric framework offers a flexible and robust solution for testing random effects in nonlinear mixed-effects models.
  • The permutation-based test provides accurate approximations for finite-sample distributions.
  • This work facilitates better model selection and analysis of complex medical study data.