Invited commentary: How big is that interaction (in my community)--and in which direction?

In an accompanying article, Turner et al. (Am J Epidemiol. 2014;180(12):1145-1149) compare the joint effects of smoking and air pollution to make inferences about the reduction in lung cancer mortality achieved when reducing each exposure separately and when reducing both together. In this commentary, we use first principles to quantify the difference between the risk or mortality reduction obtained from reducing each of 2 exposures together and the sum of the risk differences obtained from reducing the 2 exposures separately. Metrics of the impact of joint effects or comparisons of joint effects presented in units of absolute risk, such as Rothman's I, can provide more meaningful quantitative measures of public health impact than unitless metrics (e.g., ratios) and standardized metrics (e.g., the population attributable fraction) of potential interventions for reducing smoking and air pollution exposure. In particular, the venerable attributable community risk metric can provide an estimate of the community impact of such interventions in units of absolute risk. A spreadsheet we provide demonstrates the calculation of the various metrics for hypothetical data similar to those reported by Turner et al. Using algebra, graphics, and examples, we show that positive interaction, or synergy, on the additive scale implies that the impact on risk reduction from a program that applies both interventions will be lesser than the sum of the impacts of the separate interventions.