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Cited by 1,081Climate Change and Health ImpactsStatistical Methods in EpidemiologyAir Quality and Health Impacts

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Reducing and meta-analysing estimates from distributed lag non-linear models

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Gasparrini, Antonio, Armstrong, Ben·2013·BMC Medical Research Methodology
DOI 10.1186/1471-2288-13-1PMC PMC3599933
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Abstract

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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Figure 1 Temperature-mortality association in the North-East region of England, 1993–2006.Top-left: 3-D graph (with black reference line at 17°C). Top-right: predictor-specific summary at 22°C (red line parallel to the reference in the 3-D graph). Bottom-left: lag-specific summary at lag 4 (red line perpendicular to the reference in the 3-D graph). Bottom-right: overall cumulative summary. The 95%CI are reported as grey areas.
Figure 1 Temperature-mortality association in the North-East region of England, 1993–2006.Top-left: 3-D graph (with black reference line at 17°C). Top-right: predictor-specific summary at 22°C (red line parallel to the reference in the 3-D graph). Bottom-left: lag-specific summary at lag 4 (red line perpendicular to the reference in the 3-D graph). Bottom-right: overall cumulative summary. The 95%CI are reported as grey areas.CC BY · PubMed Central
Figure 2 Pooled overall cumulative temperature-mortality association in 10 regions of England and Wales, 1993–2006.Left panel: first-stage region-specific and pooled (95%CI as grey area) summaries from the main model. Right panel: comparison of alternative models.
Figure 2 Pooled overall cumulative temperature-mortality association in 10 regions of England and Wales, 1993–2006.Left panel: first-stage region-specific and pooled (95%CI as grey area) summaries from the main model. Right panel: comparison of alternative models.CC BY · PubMed Central
Figure 3 Pooled predictor-specific temperature-mortality association in 10 regions of England and Wales, 1993–2006. First-stage region-specific and pooled (95%CI as grey area) summaries at 22°C (left panel) and 0°C (right panel). Reference at 17°C.
Figure 3 Pooled predictor-specific temperature-mortality association in 10 regions of England and Wales, 1993–2006. First-stage region-specific and pooled (95%CI as grey area) summaries at 22°C (left panel) and 0°C (right panel). Reference at 17°C.CC BY · PubMed Central
Figure 4 Pooled temperature-mortality association by latitude in 10 regions of England and Wales, 1993–2006. Predictions for the 25th (dot-dashed line) and 75th (dashed line) percentiles of latitude from meta-regression for overall cumulative summary (top panel), and predictor-specific summaries at 22°C (bottom-left panel) and 0°C (bottom-right panel). Reference at 17°C. The 95%CI are reported as shaded areas.
Figure 4 Pooled temperature-mortality association by latitude in 10 regions of England and Wales, 1993–2006. Predictions for the 25th (dot-dashed line) and 75th (dashed line) percentiles of latitude from meta-regression for overall cumulative summary (top panel), and predictor-specific summaries at 22°C (bottom-left panel) and 0°C (bottom-right panel). Reference at 17°C. The 95%CI are reported as shaded areas.CC BY · PubMed Central

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Metadata

Authors
Gasparrini, A., & Armstrong, B.
Affiliations
London School of Hygiene & Tropical Medicine (GB)
Corresponding author
Gasparrini, Antonio
ORCID
Venue
BMC Medical Research Methodology
Publisher
Springer Science and Business Media LLC
Published
2013-01-09
Volume
13
Issue
1
Pages
1-1
ISSN
1471-2288 (ISSN-L)
DOI
10.1186/1471-2288-13-1
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
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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