Attributable risk from distributed lag models

Measures of attributable risk are an integral part of epidemiological analyses, particularly when aimed at the planning and evaluation of public health interventions. However, the current definition of such measures does not consider any temporal relationships between exposure and risk. In this contribution, we propose extended definitions of attributable risk within the framework of distributed lag non-linear models, an approach recently proposed for modelling delayed associations in either linear or non-linear exposure-response associations.

We classify versions of attributable number and fraction expressed using either a forward or backward perspective. The former specifies the future burden due to a given exposure event, while the latter summarizes the current burden due to the set of exposure events experienced in the past. In addition, we illustrate how the components related to sub-ranges of the exposure can be separated.