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Reducing and meta-analysing estimates from distributed lag non-linear models
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BACKGROUND: The two-stage time series design represents a powerful analytical tool in environmental epidemiology. Recently, models for both stages have been extended with the development of distributed lag non-linear models (DLNMs), a methodology for investigating simultaneously non-linear and lagged relationships, and multivariate meta-analysis, a methodology to pool estimates of multi-parameter associations. However, the application of both methods in two-stage analyses is prevented by the high-dimensional definition of DLNMs. METHODS: In this contribution we propose a method to synthesize DLNMs to simpler summaries, expressed by a reduced set of parameters of one-dimensional functions, which are compatible with current multivariate meta-analytical techniques. The methodology and modelling framework are implemented in R through the packages dlnm and mvmeta. RESULTS: As an illustrative application, the method is adopted for the two-stage time series analysis of temperature-mortality associations using data from 10 regions in England and Wales. R code and data are available as supplementary online material. DISCUSSION AND CONCLUSIONS: The methodology proposed here extends the use of DLNMs in two-stage analyses, obtaining meta-analytical estimates of easily interpretable summaries from complex non-linear and delayed associations. The approach relaxes the assumptions and avoids simplifications required by simpler modelling approaches.
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“The sample size was justified on the basis of past research reporting the median numbers of participants recruited for similar feasibility studies incorporating both quantitative and qualitative elements.27”
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Self-citation
Metadata
- Authors
- Gasparrini, A., & Armstrong, B.
- Affiliations
- London School of Hygiene & Tropical Medicine (GB)
- Corresponding author
- Gasparrini, Antonio
- Venue
- BMC Medical Research Methodology
- Published
- 2013-01-09
- Volume
- 13
- Issue
- 1
- Pages
- 1-1
- ISSN
- 1471-2288 (ISSN-L)
- PMC
- PMC3599933
- OpenAlex
- W2074344667
- Cited by
- 1,081
- References
- 27
- Citations by year
- 2026: 54 · 2025: 115 · 2024: 120 · 2023: 66 · 2022: 83 · 2021: 189 · 2020: 88 · 2019: 63 · 2018: 84 · 2017: 104 · 2016: 68 · 2015: 29 · 2014: 17 · 2013: 1
- FWCI
- 28.13
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- BMC Medical Research Methodology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- LSHTM Research Online (London School of Hygiene and Tropical Medicine) (acceptedVersion)
- Funders
- Medical Research Council (G1002296)
- Topics
- Physical Sciences › Environmental Science › Health, Toxicology and Mutagenesis › Climate Change and Health Impacts
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Environmental Science › Health, Toxicology and Mutagenesis › Air Quality and Health Impacts
- Keywords
- distributed lag non-linear model, multivariate meta-analysis, parameter reduction, temperature-mortality relationship, heat-related mortality, environmental epidemiology
- MeSH terms
- Air Pollutants, Air Pollution, Algorithms, Data Interpretation, Statistical, England, Environmental Exposure, Environmental Monitoring, Humans, Models, Theoretical, Temperature, Wales, Meta-Analysis as Topic, Multivariate Analysis, Nonlinear Dynamics, Epidemiological Monitoring
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