Abstract
In this commentary, we describe several extensions to the interesting and important negative control exposure approach for partial confounding adjustment in time-series analysis proposed by Flanders et al. (Am J Epidemiol. 2017;185(10):941-949). Specifically, by leveraging the availability of exposure time series, we show that under certain additional fairly reasonable assumptions, one can incorporate both past and future exposures as multiple negative control exposures to further attenuate confounding bias. We further describe 2 specific settings in which multiple controls can be used to fully account for confounding bias; the first assumes a forward-in-time version of the familiar autoregressive model for the exposure time series, while the second combines a negative control exposure with a negative control outcome for joint indirect adjustment of confounding. We briefly illustrate how one might apply our proposed framework in time-series studies. Both the original method of Flanders et al. and our proposed extensions are particularly well-suited for time-series data such as the air pollution study considered in their paper, and as such should be considered in routine environmental health studies.