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

BMC Med Res Methodol. 2013 Jan 9:13:1. doi: 10.1186/1471-2288-13-1.


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Air Pollutants
  • Air Pollution
  • Algorithms
  • Data Interpretation, Statistical
  • England
  • Environmental Exposure
  • Environmental Monitoring / methods*
  • Epidemiological Monitoring*
  • Humans
  • Meta-Analysis as Topic*
  • Models, Theoretical
  • Multivariate Analysis
  • Nonlinear Dynamics*
  • Temperature
  • Wales


  • Air Pollutants