---
title: "Two-way fixed effects models in air pollution epidemiology: framework and recommendations"
id: "pubmed-41885476"
canonical_url: "https://medichelpline.com/clinical-feed/pubmed-41885476"
content_type: "clinical_feed_article"
specialty: "Critical Care"
source_name: "PubMed / NCBI"
source_url: "https://pubmed.ncbi.nlm.nih.gov/41885476/"
doi: "10.1093/aje/kwag069"
published_at: "2026-08-05T00:00:00.000Z"
evidence_level: "Journal Article"
license: "CC-BY-NC-4.0 / Informational Use"
---
# Two-way fixed effects models in air pollution epidemiology: framework and recommendations
## Provenance & Clinical Metadata
- **Canonical URL:** https://medichelpline.com/clinical-feed/pubmed-41885476
- **Specialty:** [Critical Care](https://medichelpline.com/clinical-feed/critical-care.md)
- **Primary Source:** PubMed / NCBI
- **Source URL:** [Original Journal Publication](https://pubmed.ncbi.nlm.nih.gov/41885476/)
- **DOI:** [10.1093/aje/kwag069](https://doi.org/10.1093%2Faje%2Fkwag069)
- **Published At:** 2026-08-05T00:00:00.000Z
- **Evidence Rating:** Journal Article
## Executive GIST (TL;DR)
- Two-way fixed effects (TWFE) models are being used more frequently in air pollution epidemiology to estimate associations between pollutant exposures and health outcomes. - The sensitivity of TWFE estimates to different choices of **fixed effects** (FEs) and model specifications is unclear and may affect inference. - The authors used a case study linking weekly ZIP Code Tabulation Area (ZCTA)-level mean **PM2.5** concentrations to weekly **respiratory hospitalizations** in California from 2011–2019. - They constructed 52 TWFE models covering all plausible spatiotemporal FE combinations to assess sensitivity across specifications. - A three-stage decision-making framework was proposed for selecting a final model, based on **permutation tests**, **equivalence testing**, and considerations of model complexity. - Estimates varied substantially across models with different FE combinations and interactions, demonstrating meaningful influence of FE choice on effect estimates. - The chosen final model (per the proposed framework) estimated that a 1 μg/m3 increase in weekly mean **PM2.5** was associated with a 0.06% increase in weekly respiratory hospitalizations (95% CI, 0.03%–0.09%), with standard errors clustered by ZCTA. - The study provides a practical guide for transparent model specification and selection when using **two-way fixed effects** in air pollution epidemiology. - Keywords reported include: fine particulate matter; model specification; respiratory hospitalization; two-way fixed effects model.
## Clinical Analysis & Structured Key Points
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Affiliations Expand ### Affiliations * 1 Scripps Institution of Oceanography, University of California, San Diego , La Jolla, CA, United States. * 2 Johns Hopkins University School of Medicine, Baltimore, MD, United States. * 3 Department of Epidemiology and Population Health, Stanford University School of Medicine, Stanford, CA, United States. * 4 Department of Health Policy, Stanford University School of Medicine, Stanford, CA, United States. * 5 Department of Medicine (Primary Care and Population Health), Stanford University School of Medicine, Stanford, CA, United States. * 6 Department of Environmental Health and Engineering, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, United States. * 7 Irset Institut de Recherche en Santé, Environnement et Travail, UMR-S 1085, Inserm, University of Rennes, EHESP, Rennes, France. * PMID: **41885476** * DOI: [ 10.1093/aje/kwag069 ](https://doi.org/10.1093/aje/kwag069) Free article Item in Clipboard # Two-way fixed effects models in air pollution epidemiology: a proposed framework for model specifications and recommendations for future studies Yiqun Ma et al. Am J Epidemiol. 2026. Free article Show details Display options Display options Format Abstract PubMed PMID Am J Epidemiol Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Am+J+Epidemiol%22%5Bjour%5D&sort=date&sort_order=desc) * [ Search in NLM Catalog ](https://www.ncbi.nlm.nih.gov/nlmcatalog?term=%22Am+J+Epidemiol%22%5BTitle+Abbreviation%5D) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/41885476/) . 2026 Aug 5;195(8):2253-2262. doi: 10.1093/aje/kwag069. ### Authors [Yiqun Ma](https://pubmed.ncbi.nlm.nih.gov/?term=Ma+Y&cauthor_id=41885476)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-1 "Scripps Institution of Oceanography, University of California, San Diego , La Jolla, CA, United States."), [Jordan Kaplan](https://pubmed.ncbi.nlm.nih.gov/?term=Kaplan+J&cauthor_id=41885476)[ 2 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-2 "Johns Hopkins University School of Medicine, Baltimore, MD, United States.")[ 3 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-3 "Department of Epidemiology and Population Health, Stanford University School of Medicine, Stanford, CA, United States."), [David H Rehkopf](https://pubmed.ncbi.nlm.nih.gov/?term=Rehkopf+DH&cauthor_id=41885476)[ 3 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-3 "Department of Epidemiology and Population Health, Stanford University School of Medicine, Stanford, CA, United States.")[ 4 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-4 "Department of Health Policy, Stanford University School of Medicine, Stanford, CA, United States.")[ 5 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-5 "Department of Medicine \(Primary Care and Population Health\), Stanford University School of Medicine, Stanford, CA, United States."), [Benjamin Q Huynh](https://pubmed.ncbi.nlm.nih.gov/?term=Huynh+BQ&cauthor_id=41885476)[ 6 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-6 "Department of Environmental Health and Engineering, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, United States."), [Mathew V Kiang](https://pubmed.ncbi.nlm.nih.gov/?term=Kiang+MV&cauthor_id=41885476)[ 3 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-3 "Department of Epidemiology and Population Health, Stanford University School of Medicine, Stanford, CA, United States."), [Tarik Benmarhnia](https://pubmed.ncbi.nlm.nih.gov/?term=Benmarhnia+T&cauthor_id=41885476)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-1 "Scripps Institution of Oceanography, University of California, San Diego , La Jolla, CA, United States.")[ 7 ](https://pubmed.ncbi.nlm.nih.gov/41885476/#short-view-affiliation-7 "Irset Institut de Recherche en Santé, Environnement et Travail, UMR-S 1085, Inserm, University of Rennes, EHESP, Rennes, France.") ### Affiliations * 1 Scripps Institution of Oceanography, University of California, San Diego , La Jolla, CA, United States. * 2 Johns Hopkins University School of Medicine, Baltimore, MD, United States. * 3 Department of Epidemiology and Population Health, Stanford University School of Medicine, Stanford, CA, United States. * 4 Department of Health Policy, Stanford University School of Medicine, Stanford, CA, United States. * 5 Department of Medicine (Primary Care and Population Health), Stanford University School of Medicine, Stanford, CA, United States. * 6 Department of Environmental Health and Engineering, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, United States. * 7 Irset Institut de Recherche en Santé, Environnement et Travail, UMR-S 1085, Inserm, University of Rennes, EHESP, Rennes, France. * PMID: **41885476** * DOI: [ 10.1093/aje/kwag069 ](https://doi.org/10.1093/aje/kwag069) Item in Clipboard Full text links Cite Display options Display options Format Abstract PubMed PMID ## Abstract Two-way fixed effects (TWFE) models are increasingly applied in air pollution epidemiology. However, it remains unclear how sensitive TWFE models are to different modeling choices and how to transparently select a final model from a wide range of options. This study aims to systematically assess the sensitivity of TWFE models to different fixed effects (FEs) and propose a comprehensive decision-making framework. As an illustrative case study, we investigated associations between weekly ZIP Code Tabulation Area (ZCTA)-level mean particulate matter (PM2.5) concentrations and respiratory hospitalizations in CA, 2011-2019. We proposed 52 TWFE models with all plausible spatiotemporal FE combinations and demonstrated a three-stage decision-making framework for final model selection based on permutation tests, equivalence testing, and model complexity. Substantial variations in estimates were observed among models with different combinations of FEs and their interactions. The final model estimated that a 1 μg/m3 increase in weekly mean PM2.5 concentration was associated with a 0.06% increase in weekly respiratory hospitalizations (95% CI, 0.03%, 0.09%; clustered SE by ZCTA). This study highlighted that the choice of FEs in TWFE models can have meaningful influences in the inference of interest. Our proposed decision-making offers a practical guide for future air pollution epidemiological studies using TWFE models. **Keywords:** fine particulate matter; model specification; respiratory hospitalization; two-way fixed effects model. © The Author(s) 2026. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. [PubMed Disclaimer](https://pubmed.ncbi.nlm.nih.gov/disclaimer/) ## Similar articles * [ Mortality and Morbidity Effects of Long-Term Exposure to Low-Level PM2.5, BC, NO2, and O3: An Analysis of European Cohorts in the ELAPSE Project. ](https://pubmed.ncbi.nlm.nih.gov/36106702/) Brunekreef B, Strak M, Chen J, Andersen ZJ, Atkinson R, Bauwelinck M, Bellander T, Boutron MC, Brandt J, Carey I, Cesaroni G, Forastiere F, Fecht D, Gulliver J, Hertel O, Hoffmann B, de Hoogh K, Houthuijs D, Hvidtfeldt U, Janssen N, Jorgensen J, Katsouyanni K, Ketzel M, Klompmaker J, Hjertager Krog N, Liu S, Ljungman P, Mehta A, Nagel G, Oftedal B, Pershagen G, Peters A, Raaschou-Nielsen O, Renzi M, Rodopoulou S, Samoli E, Schwarze P, Sigsgaard T, Stafoggia M, Vienneau D, Weinmayr G, Wolf K, Hoek G.Brunekreef B, et al.Res Rep Health Eff Inst. 2021 Sep;2021(208):1-127.Res Rep Health Eff Inst. 2021.PMID: 36106702Free PMC article. * [ Personality Theories. ](https://pubmed.ncbi.nlm.nih.gov/42475469/) Gallios JM, Iyer V, Kaylor LE.Gallios JM, et al.2026 Jun 20. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2026 Jan–.2026 Jun 20. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2026 Jan–.PMID: 42475469Free Books & Documents. * [ Mortality-Air Pollution Associations in Low Exposure Environments (MAPLE): Phase 2. ](https://pubmed.ncbi.nlm.nih.gov/36224709/) Brauer M, Brook JR, Christidis T, Chu Y, Crouse DL, Erickson A, Hystad P, Li C, Martin RV, Meng J, Pappin AJ, Pinault LL, Tjepkema M, van Donkelaar A, Weagle C, Weichenthal S, Burnett RT.Brauer M, et al.Res Rep Health Eff Inst. 2022 Jul;2022(212):1-91.Res Rep Health Eff Inst. 2022.PMID: 36224709Free PMC article. * [ Comparison of Long-Term Air Pollution Exposure from Mobile and Routine Monitoring, Low-Cost Sensors, and Dispersion Models. ](https://pubmed.ncbi.nlm.nih.gov/40405483/) Hoek G, Bouma F, Janssen N, Wesseling J, van Ratingen S, Kerckhoffs J, Gehring U, Hendricx W, Vermeulen R, de Hoogh K.Hoek G, et al.Res Rep Health Eff Inst. 2025 Mar;2025(226):1-101.Res Rep Health Eff Inst. 2025.PMID: 40405483Free PMC article. * [ [Meta-analysis of the Italian studies on short-term effects of air pollution]. ](https://pubmed.ncbi.nlm.nih.gov/11515188/) Biggeri A, Bellini P, Terracini B; Italian MISA Group.Biggeri A, et al.Epidemiol Prev. 2001 Mar-Apr;25(2 Suppl):1-71.Epidemiol Prev. 2001.PMID: 11515188Italian. 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