Transfer functions: learning about a lagged exposure-outcome association in time-series data

Many population exposures in time-series analysis, including food marketing, exhibit a time-lagged association with population health outcomes such as food purchasing. A common approach to measuring patterns of associations over different time lags relies on a finite-lag model, which requires correct specification of the maximum duration over which the lagged association extends. However, the maximum lag is frequently unknown due to the lack of substantive knowledge or the geographic variation of lag length. We describe a time-series analytical approach based on an infinite lag specification under a transfer function model that avoids the specification of an arbitrary maximum lag length. We demonstrate its application to estimate the lagged exposure-outcome association in food environmental research: display promotion of sugary beverages with lagged sales.