Reflection on modern methods: visualizing the effects of collinearity in distributed lag models

Abstract

Collinearity can be a problem in regression models. When examining the effects of an exposure at different time points, constrained distributed lag models can alleviate some of the problems caused by collinearity. Still, some consequences of collinearity may remain and they are often unexplored. We aimed to illustrate the effects of collinearity in the context of distributed lag models, and to provide a tool to assess whether the results of a study could be influenced by collinearity. We used simulations under different scenarios of hypothesized effects of an exposure to visualize the resulting curves of lagged effects. We analysed three real datasets: a cohort study looking for windows of vulnerability to air pollution, a time series study examining the linear association of air pollution with hospital admissions, and a time series study examining the non-linear association between temperature and mortality. We showed that collinearity could be the explanation for some unexpected results, e.g. for statistically significant associations in the opposite direction from that expected, or for wrongly suggesting that some periods are more important than others. We implemented the collin R package to explore the potential consequences of collinearity in the context of distributed lag models. Our visual tool can be a useful way to assess if the results of an analysis may be influenced by collinearity.

Keywords: Collinearity; correlated data; distributed lag models; multicollinearity; protracted exposures; simulation; software; time series; windows of susceptibility.