Definition and research guide
This page combines a MeSH definition, publication statistics and selected research abstracts. It is a starting point for reading the literature, not a medical textbook or a systematic evidence review.
Content available: 4 complete abstracts (734 words), 10 references. Full article text is not stored or reproduced here; follow the PMID, DOI or PMC links to read the original sources and their access terms.
Definition
Statistical models in which the value of a parameter for a given value of a factor is assumed to be equal to a + bx, where a and b are constants. The models predict a linear regression.
Definition: NLM Medical Subject Headings (MeSH) scope note (Public domain (U.S. National Library of Medicine); attribution requested). View the MeSH record.
Also known as: Models, Linear; Linear Model; Model, Linear; Linear Regression; Linear Regressions; Regression, Linear; Regressions, Linear; Log-Linear Models.
Where it fits in the MeSH classification
- Broader topics
- Models, Statistical; Regression Analysis
Research landscape
PubMed indexes 91,200 records tagged with the MeSH heading “Linear Models” (counts retrieved 2026-10-29). 10,135 of them (11.1%) were published from 2020 onward, and the busiest period so far is 2010-2019 with 47,941 records.
Reviews account for 1,437 records (1.6%) and meta-analyses for 525. Randomized controlled trials number 4,044 (4.4%) as a share of all records on the topic.
Show the data
| Period | Records |
|---|---|
| through 1999 | 8,930 |
| 2000-2009 | 24,194 |
| 2010-2019 | 47,941 |
| 2020 onward | 10,135 |
Publication-type chart data
| Type | Records | Share |
|---|---|---|
| Reviews | 1,437 | 1.6% |
| Meta-analyses | 525 | 0.6% |
| Randomized controlled trials | 4,044 | 4.4% |
Method: PubMed query "Linear Models"[MeSH Terms] with publication-type and date filters, retrieved 2026-10-29.
Reading the evidence in clinical research
Research methods determine how much a result can be trusted. Randomized trials guard against confounding, systematic reviews and meta-analyses combine many studies, and observational designs are valuable but can show only association. Reporting standards, trial registration and pre-specified outcomes reduce bias. When reading about a method, ask what problem it is designed to solve and which problems it does not solve.
Evidence from open-access studies
These open-access studies come from PubMed’s best-match results for this heading (papers whose main topic it is), ranked here by citation count, with one recent addition. Each abstract is reproduced in full under its recorded open licence so that you can read the authors’ own words. They illustrate the literature; they are not a systematic summary of it. Citation counts measure attention, not reliability or clinical benefit.
| Study / authors | Year | Source label / design | Europe PMC citations | Licence / source |
|---|---|---|---|---|
| voom: Precision weights unlock linear model analysis tools for RNA-seq read counts | 2014 | Research article Design not recorded in structured metadata | 5,434 | cc by PMID 24485249 · DOI · PMC4053721 |
| Permutation inference for the general linear model | 2014 | Research article Design not recorded in structured metadata | 3,184 | cc by PMID 24530839 · DOI · PMC4010955 |
| Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology | 2016 | Research article Design not recorded in structured metadata | 362 | cc by PMID 26787347 · DOI · PMC4726296 |
| Individualized Atrophy-Based Prediction of Dementia Progression in Familial Frontotemporal Lobar Degeneration With Bayesian Linear Mixed-Effects Modeling | 2026 | Research article Design not recorded in structured metadata | 1 | cc by PMID 41608854 · DOI · PMC12950279 |
voom: Precision weights unlock linear model analysis tools for RNA-seq read counts [1]
Abstract reading summary — source excerpts
- Opening excerpt
- New normal linear modeling strategies are presented for analyzing read counts from RNA-seq experiments.
- Closing excerpt
- Two case studies illustrate the use of linear modeling and gene set testing methods.
- Interpretation limits
- Verbatim excerpts from the authors’ abstract; the closing excerpt may describe a finding, limitation or recommendation. Design, population, effect size and uncertainty have not been independently extracted or appraised. Read the complete abstract and linked paper before interpreting the findings.
Read complete abstract (98 words)
New normal linear modeling strategies are presented for analyzing read counts from RNA-seq experiments. The voom method estimates the mean-variance relationship of the log-counts, generates a precision weight for each observation and enters these into the limma empirical Bayes analysis pipeline. This opens access for RNA-seq analysts to a large body of methodology developed for microarrays. Simulation studies show that voom performs as well or better than count-based RNA-seq methods even when the data are generated according to the assumptions of the earlier methods. Two case studies illustrate the use of linear modeling and gene set testing methods.
Abstract reproduced from the open-access article under the recorded cc by licence; © the authors. PMID 24485249 · DOI · PMC4053721
Permutation inference for the general linear model [2]
Abstract reading summary — source excerpts
- Opening excerpt
- Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data.
- Closing excerpt
- Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm - the "randomise" algorithm - for permutation inference with the GLM.
- Interpretation limits
- Verbatim excerpts from the authors’ abstract; the closing excerpt may describe a finding, limitation or recommendation. Design, population, effect size and uncertainty have not been independently extracted or appraised. Read the complete abstract and linked paper before interpreting the findings.
Read complete abstract (198 words)
Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (GLMS) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on GLM parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm - the "randomise" algorithm - for permutation inference with the GLM.
Abstract reproduced from the open-access article under the recorded cc by licence; © the authors. PMID 24530839 · DOI · PMC4010955
Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology [3]
Abstract reading summary — source excerpts
- Opening excerpt
- Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits.
- Closing excerpt
- Therefore, the MRMLM provides an alternative for multi-locus GWAS.
- Interpretation limits
- Verbatim excerpts from the authors’ abstract; the closing excerpt may describe a finding, limitation or recommendation. Design, population, effect size and uncertainty have not been independently extracted or appraised. Read the complete abstract and linked paper before interpreting the findings.
Read complete abstract (200 words)
Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.
Abstract reproduced from the open-access article under the recorded cc by licence; © the authors. PMID 26787347 · DOI · PMC4726296
Individualized Atrophy-Based Prediction of Dementia Progression in Familial Frontotemporal Lobar Degeneration With Bayesian Linear Mixed-Effects Modeling [4]
Abstract reading summary — source excerpts
- Opening excerpt
- ObjectiveAge of symptom onset is highly variable in familial frontotemporal lobar degeneration (f-FTLD).
- Closing excerpt
- ANN NEUROL 20269999:n/a-n/a.
- Interpretation limits
- Verbatim excerpts from the authors’ abstract; the closing excerpt may describe a finding, limitation or recommendation. Design, population, effect size and uncertainty have not been independently extracted or appraised. Read the complete abstract and linked paper before interpreting the findings.
Read complete abstract (238 words)
ObjectiveAge of symptom onset is highly variable in familial frontotemporal lobar degeneration (f-FTLD). Accurate prediction of onset would inform clinical management and trial enrollment. Prior studies indicate that individualized maps of brain atrophy can predict conversion to dementia in f-FTLD. We used a Bayesian linear mixed-effect (BLME) prediction method for identifying accelerated brain volume loss to predict conversion to dementia.MethodsParticipants included 234 asymptomatic or prodromal carriers of C9orf72, GRN, or MAPT mutations (including 21 dementia converters) with ≥3 longitudinal magnetic resonance imaging (MRI) T1-weighted scans. The BLME models established individual voxel-wise gray matter trajectories using the first 2 scans. Person-specific clusters of accelerated volume loss were estimated in subsequent scans and tested as predictors of dementia conversion compared with other approaches in time-varying Cox proportional hazard models covarying for age. Receiver-operating characteristic (ROC) curves estimated utility of cluster volume in discriminating which participants converted to dementia within 24 months.ResultsThe BLME cluster volume predicted conversion to dementia in f-FTLD mutation carriers overall and separately in C9orf72, GRN, and MAPT, with comparable hazard ratios observed for atrophy W-maps and regional volumes. Within a 24-month timeframe, BLME cluster volume discriminated dementia converters from non-converters with larger areas under the curve (AUCs) than other approaches.InterpretationBayesian-modeled individualized atrophy scores predict dementia progression among asymptomatic f-FTLD mutation carriers and may have increased utility compared with other structural imaging methods when studying individuals over shorter timeframes that align with clinical trial design. ANN NEUROL 20269999:n/a-n/a.
Abstract reproduced from the open-access article under the recorded cc by licence; © the authors. PMID 41608854 · DOI · PMC12950279
Key reviews and meta-analyses
The most cited review-type papers among PubMed’s best-match results for this heading, listed with bibliographic details only. Follow the links for the full text and access terms.
- Research article Generalized linear mixed models: a practical guide for ecology and evolution [5]
- Research article Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data [6]
- Research article Multilevel analysis in public health research [7]
- Research article Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines [8]
- Research article Correlation and simple linear regression [9]
- Research article The tumor radiobiology of SRS and SBRT: are more than the 5 Rs involved? [10]
References
- Law CW, Chen Y, Shi W, Smyth GK. voom: Precision weights unlock linear model analysis tools for RNA-seq read counts. . 2014. PMID 24485249 · DOI · PMC4053721
- Winkler AM, Ridgway GR, Webster MA, Smith SM, Nichols TE. Permutation inference for the general linear model. . 2014. PMID 24530839 · DOI · PMC4010955
- Wang SB, Feng JY, Ren WL, Huang B, Zhou L, Wen YJ, et al.. Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology. . 2016. PMID 26787347 · DOI · PMC4726296
- Dutt S, Leichter D, Cobigo Y, Wolf A, Kornak J, Clark A, et al.. Individualized Atrophy-Based Prediction of Dementia Progression in Familial Frontotemporal Lobar Degeneration With Bayesian Linear Mixed-Effects Modeling. . 2026. PMID 41608854 · DOI · PMC12950279
- Bolker BM, Brooks ME, Clark CJ, Geange SW, Poulsen JR, Stevens MH, et al.. Generalized linear mixed models: a practical guide for ecology and evolution. Trends Ecol Evol. 2009. PMID 19185386 · DOI
- Cnaan A, Laird NM, Slasor P. Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. Stat Med. 1997. PMID 9351170 · DOI
- Diez-Roux AV. Multilevel analysis in public health research. Annu Rev Public Health. 2000. PMID 10884951 · DOI
- Marshall A, Altman DG, Holder RL, Royston P. Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines. BMC Med Res Methodol. 2009. PMID 19638200 · DOI · PMC2727536
- Zou KH, Tuncali K, Silverman SG. Correlation and simple linear regression. Radiology. 2003. PMID 12773666 · DOI
- Brown JM, Carlson DJ, Brenner DJ. The tumor radiobiology of SRS and SBRT: are more than the 5 Rs involved?. Int J Radiat Oncol Biol Phys. 2014. PMID 24411596 · DOI · PMC3893711
About this article
- Sources
- NLM Medical Subject Headings (definition, synonyms); NCBI PubMed (counts, identifiers); Europe PMC (open-access abstracts and citation counts).
- Verification
- Every reference was resolved against PubMed on 2026-10-31; title, year and DOI matched.
- Review state
- automated source verified; no human expert review has been recorded yet.
- Version
- 1, last updated 2026-10-29.
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Evidence strength
EvidenceHelix's computed view of the study designs behind this topic: how common meta-analyses, randomized trials and reviews are, how recent the literature is, and a plain-language reading. It describes the design mix of the literature. It is not a quality appraisal of any study, and it is not medical advice.