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Cited by 31Statistical Methods and Bayesian InferenceAgriculture, Soil, Plant ScienceReliability and Agreement in Measurement

Analysis of hierarchical biomechanical data structures using mixed-effects models

Open access
Tirrell, Timothy F., Rademaker, Alfred W., Lieber, Richard L.·2018·Journal of Biomechanics
DOI 10.1016/j.jbiomech.2018.01.013PMC PMC5913736
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Abstract

Rigorous statistical analysis of biomechanical data is required to understand tissue properties. In biomechanics, samples are often obtained from multiple biopsies in the same individual, multiple samples tested per biopsy, and multiple tests performed per sample. The easiest way to analyze this hierarchical design is to simply calculate the grand mean of all samples tested. However, this may lead to incorrect inferences. In this report, three different analytical approaches are described with respect to the analysis of hierarchical data obtained from muscle biopsies. Each method was used to analyze an actual experimental data set obtained from muscle biopsies of three different muscles in the human forearm. The results illustrate the conditions under which mixed-models or simple models are acceptable for analysis of these types of data.

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Crossref · 10.1016/j.jbiomech.2018.01.013

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  • Intra-individual variance is larger than inter-individual variance appears typical with scRNA-seq data.

    “This is due to an overestimation of the mean-square error relative to mixed-effects models, particularly when imbalance exists and the intra-individual variance is larger than the inter-individual variance, as appears to be typical with scRNA-seq data25,26.”

    From A practical solution to pseudoreplication bias in single-cell studies (2021) · cites this paper as [26]

    The Discussion reports that within-subject variance exceeded between-subject variance in the paper’s biomechanical fiber and bundle data (page not provided). It does not establish that this pattern is typical of scRNA-seq data. Its Results discuss overestimation of the standard error under unequal subject sample sizes, not overestimation of mean-square error. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • Aggregation overestimates the mean-square error relative to mixed-effects models, particularly when imbalance exists and the intra-individual variance is larger than the inter-individual variance.

    “This is due to an overestimation of the mean-square error relative to mixed-effects models, particularly when imbalance exists and the intra-individual variance is larger than the inter-individual variance, as appears to be typical with scRNA-seq data25,26.”

    From A practical solution to pseudoreplication bias in single-cell studies (2021) · cites this paper as [26]

    The Results and Discussion report that averaging subject-level means overestimates the standard error of the mean relative to a random-effects model when observations per subject are imbalanced; the paper’s data also have greater within-subject than between-subject variance. It does not establish overestimation of mean-square error, and its other aggregation method—the grand mean—underestimates the standard error. No page numbers are available in our copy. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • When within-subject variability is large with respect to between-subject variability, averaging within-subject measurements fails to estimate the true data variability.

    “Furthermore, when within-subject variability is large with respect to between-subject variability, averaging within-subject measurements fails to estimate the true data variability26.”

    From A practical solution to pseudoreplication bias in single-cell studies (2021) · cites this paper as [26]

  • Applying statistical inference to replicates that are not statistically independent without properly accounting for their correlation structure will inflate type 1 error rates and lead to spurious results.

    “Here we hope to address pseudoreplication in single-cell analyses by demonstrating what a large and long-standing body of statistical literature already confirms: applying statistical inference to replicates that are not statistically independent without properly accounting for their correlation structure will inflate type 1 error rates and lead to spurious results4–6,9,25–28.”

    From A practical solution to pseudoreplication bias in single-cell studies (2021) · cites this paper as [26]

  • Mixed-effects models lead to the most accurate results when analyzing data with a hierarchical structure.

    “Overall, mixed-effects models lead to the most accurate results when analyzing data with a hierarchical structure6,25,26.”

    From A practical solution to pseudoreplication bias in single-cell studies (2021) · cites this paper as [26]

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Authors
Tirrell, T. F., Rademaker, A. W., & Lieber, R. L.
Affiliations
  • Edward Hines, Jr. VA Hospital (US)
  • Northwestern University (US)
Corresponding author
Lieber, Richard L.
ORCID
Venue
Journal of Biomechanics
Publisher
Elsevier BV
Published
2018-03
Volume
69
Pages
34-39
ISSN
0021-9290 (ISSN-L)
DOI
10.1016/j.jbiomech.2018.01.013
PMC
PMC5913736
OpenAlex
W2782955687
Cited by
30
References
9
Citations by year
2026: 6 · 2025: 3 · 2024: 3 · 2022: 2 · 2021: 9 · 2020: 4 · 2019: 2 · 2018: 1
FWCI
3.32
Type
journal article
Language
en
Open access
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • Journal of Biomechanics (publishedVersion)
  • PubMed (publishedVersion)
  • Europe PMC (PubMed Central) (acceptedVersion)
  • PubMed Central (acceptedVersion)
Funders
  • Department of Veterans Affairs (R24 HD050837, R01 AR057393)
  • National Institutes of Health
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Agriculture, Soil, Plant Science
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Reliability and Agreement in Measurement
Keywords
hierarchical data, mixed models, muscle biopsy, tissue properties, repeated measures
MeSH terms
Biomechanical Phenomena, Biopsy, Forearm, Humans, Models, Biological, Muscles, Weight-Bearing, Mechanical Phenomena

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