Reducing and meta-analysing estimates from distributed lag non-linear models
Open accessAbstract
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.
“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”
From Mixed-methods feasibility outcomes for a novel ACT-based video game ‘ACTing Minds’ to support mental health (2024) · cites this paper as [27]
The Methods and Results passages describe two-stage time-series analysis and meta-analysis across locations, not recruitment for feasibility studies. Searches for median participant numbers, sample-size justification, and studies combining quantitative and qualitative elements found no passage addressing the claim; no page numbers were available in our copy. (LLM, conf=0.75)
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- 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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