Distributed lag non‐linear models

TLDR

Environmental stressors often have delayed effects, necessitating flexible statistical models that capture the time dimension of exposure‑response relationships. The authors develop distributed lag non‑linear models (DLNM) to simultaneously capture non‑linear exposure‑response relationships and delayed effects. DLNM uses a cross‑basis bi‑dimensional function to model predictor and lag effects, is implemented in the R package dlnm, and is illustrated with temperature‑mortality data from NMMAPS (NY, 1987‑2000). DLNM unifies previously used models and introduces more flexible variants for delayed exposure‑response analysis.

Abstract

Environmental stressors often show effects that are delayed in time, requiring the use of statistical models that are flexible enough to describe the additional time dimension of the exposure-response relationship. Here we develop the family of distributed lag non-linear models (DLNM), a modelling framework that can simultaneously represent non-linear exposure-response dependencies and delayed effects. This methodology is based on the definition of a 'cross-basis', a bi-dimensional space of functions that describes simultaneously the shape of the relationship along both the space of the predictor and the lag dimension of its occurrence. In this way the approach provides a unified framework for a range of models that have previously been used in this setting, and new more flexible variants. This family of models is implemented in the package dlnm within the statistical environment R. To illustrate the methodology we use examples of DLNMs to represent the relationship between temperature and mortality, using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) for New York during the period 1987-2000.