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 (868 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
Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see linear models) the relationship is constrained to be a straight line and least-squares analysis is used to determine the best fit. In logistic regression (see logistic models) the dependent variable is qualitative rather than continuously variable and likelihood functions are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.
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: Regression Diagnostics; Diagnostics, Regression; Statistical Regression; Regressions, Statistical; Regression, Statistical; Statistical Regressions; Analysis, Regression; Analyses, Regression.
Where it fits in the MeSH classification
- Broader topics
- Statistics as Topic
- Narrower topics
- Least-Squares Analysis; Linear Models; Logistic Models; Proportional Hazards Models; Spatial Regression
Related concepts
- Linear Models
- Least-Squares Analysis
- Logistic Models
- Likelihood Functions
Research landscape
PubMed indexes 491,698 records tagged with the MeSH heading “Regression Analysis” (counts retrieved 2026-10-29). 65,926 of them (13.4%) were published from 2020 onward, and the busiest period so far is 2010-2019 with 230,530 records.
Reviews account for 8,960 records (1.8%) and meta-analyses for 4,814. Randomized controlled trials number 18,952 (3.9%) as a share of all records on the topic.
Show the data
| Period | Records |
|---|---|
| through 1999 | 67,752 |
| 2000-2009 | 127,490 |
| 2010-2019 | 230,530 |
| 2020 onward | 65,926 |
Publication-type chart data
| Type | Records | Share |
|---|---|---|
| Reviews | 8,960 | 1.8% |
| Meta-analyses | 4,814 | 1.0% |
| Randomized controlled trials | 18,952 | 3.9% |
Method: PubMed query "Regression Analysis"[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 |
|---|---|---|---|---|
| So you think you can PLS-DA? | 2020 | Research article Design not recorded in structured metadata | 257 | cc by PMID 33297937 · DOI · PMC7724830 |
| Minimum sample size for developing a multivariable prediction model using multinomial logistic regression | 2023 | Research article Design not recorded in structured metadata | 111 | cc by PMID 36660777 · DOI · PMC10012398 |
| Feature-space selection with banded ridge regression | 2022 | Research article Design not recorded in structured metadata | 86 | cc by PMID 36334814 · DOI · PMC9807218 |
| 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 |
So you think you can PLS-DA? [1]
Abstract reading summary — source excerpts
- Opening excerpt
- BackgroundPartial Least-Squares Discriminant Analysis (PLS-DA) is a popular machine learning tool that is gaining increasing attention as a useful feature selector and classifier.
- Closing excerpt
- edu/plsda CONCLUSIONS: Our results highlighted the strengths and weaknesses of PLS-DA in comparison with PCA for different underlying data models.
- 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 (197 words)
BackgroundPartial Least-Squares Discriminant Analysis (PLS-DA) is a popular machine learning tool that is gaining increasing attention as a useful feature selector and classifier. In an effort to understand its strengths and weaknesses, we performed a series of experiments with synthetic data and compared its performance to its close relative from which it was initially invented, namely Principal Component Analysis (PCA).ResultsWe demonstrate that even though PCA ignores the information regarding the class labels of the samples, this unsupervised tool can be remarkably effective as a feature selector. In some cases, it outperforms PLS-DA, which is made aware of the class labels in its input. Our experiments range from looking at the signal-to-noise ratio in the feature selection task, to considering many practical distributions and models encountered when analyzing bioinformatics and clinical data. Other methods were also evaluated. Finally, we analyzed an interesting data set from 396 vaginal microbiome samples where the ground truth for the feature selection was available. All the 3D figures shown in this paper as well as the supplementary ones can be viewed interactively at http://biorg.cs.fiu.edu/plsda CONCLUSIONS: Our results highlighted the strengths and weaknesses of PLS-DA in comparison with PCA for different underlying data models.
Abstract reproduced from the open-access article under the recorded cc by licence; © the authors. PMID 33297937 · DOI · PMC7724830
Minimum sample size for developing a multivariable prediction model using multinomial logistic regression [2]
Abstract reading summary — source excerpts
- Opening excerpt
- AimsMultinomial logistic regression models allow one to predict the risk of a categorical outcome with > 2 categories.
- Closing excerpt
- We will embed our proposed criteria within the pmsampsize R library and Stata modules.
- 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 (247 words)
AimsMultinomial logistic regression models allow one to predict the risk of a categorical outcome with > 2 categories. When developing such a model, researchers should ensure the number of participants (n) is appropriate relative to the number of events (Ek) and the number of predictor parameters (pk) for each category k. We propose three criteria to determine the minimum n required in light of existing criteria developed for binary outcomes.Proposed criteriaThe first criterion aims to minimise the model overfitting. The second aims to minimise the difference between the observed and adjusted R2 Nagelkerke. The third criterion aims to ensure the overall risk is estimated precisely. For criterion (i), we show the sample size must be based on the anticipated Cox-snell R2 of distinct 'one-to-one' logistic regression models corresponding to the sub-models of the multinomial logistic regression, rather than on the overall Cox-snell R2 of the multinomial logistic regression.Evaluation of criteriaWe tested the performance of the proposed criteria (i) through a simulation study and found that it resulted in the desired level of overfitting. Criterion (ii) and (iii) were natural extensions from previously proposed criteria for binary outcomes and did not require evaluation through simulation.SummaryWe illustrated how to implement the sample size criteria through a worked example considering the development of a multinomial risk prediction model for tumour type when presented with an ovarian mass. Code is provided for the simulation and worked example. We will embed our proposed criteria within the pmsampsize R library and Stata modules.
Abstract reproduced from the open-access article under the recorded cc by licence; © the authors. PMID 36660777 · DOI · PMC10012398
Feature-space selection with banded ridge regression [3]
Abstract reading summary — source excerpts
- Opening excerpt
- Encoding models provide a powerful framework to identify the information represented in brain recordings.
- Closing excerpt
- All implementations are released in an open-source Python package called Himalaya.
- 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 (186 words)
Encoding models provide a powerful framework to identify the information represented in brain recordings. In this framework, a stimulus representation is expressed within a feature space and is used in a regularized linear regression to predict brain activity. To account for a potential complementarity of different feature spaces, a joint model is fit on multiple feature spaces simultaneously. To adapt regularization strength to each feature space, ridge regression is extended to banded ridge regression, which optimizes a different regularization hyperparameter per feature space. The present paper proposes a method to decompose over feature spaces the variance explained by a banded ridge regression model. It also describes how banded ridge regression performs a feature-space selection, effectively ignoring non-predictive and redundant feature spaces. This feature-space selection leads to better prediction accuracy and to better interpretability. Banded ridge regression is then mathematically linked to a number of other regression methods with similar feature-space selection mechanisms. Finally, several methods are proposed to address the computational challenge of fitting banded ridge regressions on large numbers of voxels and feature spaces. All implementations are released in an open-source Python package called Himalaya.
Abstract reproduced from the open-access article under the recorded cc by licence; © the authors. PMID 36334814 · DOI · PMC9807218
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 Projected number of people with Parkinson disease in the most populous nations, 2005 through 2030 [6]
- Research article Regression to the mean: what it is and how to deal with it [7]
- Research article A systematic review shows no performance benefit of machine learning over logistic regression for clinical prediction models [8]
- Research article A comparison of goodness-of-fit tests for the logistic regression model [9]
- Research article How common are the "common" neurologic disorders? [10]
References
- Ruiz-Perez D, Guan H, Madhivanan P, Mathee K, Narasimhan G. So you think you can PLS-DA?. . 2020. PMID 33297937 · DOI · PMC7724830
- Pate A, Riley RD, Collins GS, van Smeden M, Van Calster B, Ensor J, et al.. Minimum sample size for developing a multivariable prediction model using multinomial logistic regression. . 2023. PMID 36660777 · DOI · PMC10012398
- Dupré la Tour T, Eickenberg M, Nunez-Elizalde AO, Gallant JL. Feature-space selection with banded ridge regression. . 2022. PMID 36334814 · DOI · PMC9807218
- 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
- Dorsey ER, Constantinescu R, Thompson JP, Biglan KM, Holloway RG, Kieburtz K, et al.. Projected number of people with Parkinson disease in the most populous nations, 2005 through 2030. Neurology. 2007. PMID 17082464 · DOI
- Barnett AG, van der Pols JC, Dobson AJ. Regression to the mean: what it is and how to deal with it. Int J Epidemiol. 2005. PMID 15333621 · DOI
- Christodoulou E, Ma J, Collins GS, Steyerberg EW, Verbakel JY, Van Calster B. A systematic review shows no performance benefit of machine learning over logistic regression for clinical prediction models. J Clin Epidemiol. 2019. PMID 30763612 · DOI
- Hosmer DW, Hosmer T, Le Cessie S, Lemeshow S. A comparison of goodness-of-fit tests for the logistic regression model. Stat Med. 1997. PMID 9160492 · DOI
- Hirtz D, Thurman DJ, Gwinn-Hardy K, Mohamed M, Chaudhuri AR, Zalutsky R. How common are the "common" neurologic disorders?. Neurology. 2007. PMID 17261678 · DOI
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.