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

Antonio Gasparrini, Ben Armstrong
2013 BMC Medical Research Methodology  
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
more » ... l 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. Background Research on the health effects of environmental stressors, such as air pollution and temperature, often relies on time series analysis using data from multiple locations, usually cities [1, 2] . The analytical design adopted in this setting is commonly based on two-stage procedures, where location-specific exposure-response relationships are estimated through a regression model in the first stage, and these estimates are then combined through meta-analysis in the second stage [3] . Recently, the first-stage modelling approaches have been extended with the introduction of distributed lag nonlinear models (DLNMs) [4, 5] , a methodology to describe simultaneously non-linear and delayed dependencies.
doi:10.1186/1471-2288-13-1 pmid:23297754 pmcid:PMC3599933 fatcat:fg4w53qiknc53agek3rzx5zjx4