Kenneth A Frank, Qinyun Lin, Spiro J Maroulis
Cornfield et al.'s contributions included documenting epidemiological and policy debates regarding the effects of smoking on lung cancer. It was in the context of those debates that Cornfield et al. expressed sensitivity of the estimated effect of smoking to the dual components of confounding-relationship of a potential confounder (e.g., genes) to smoking (the focal predictor) and to lung cancer (the outcome). Current advancements have used various graphical and tabular representations to similarly express sensitivity to the dual components of confounding. As a representative of these advancements, we present Frank's Impact Threshold for a Confounding (ITCV), which resolves the dual components of confounding into a single term based on the product of the confounder's correlations with the focal predictor and with the outcome. We calculate the ITCV for an inference of an effect of kindergarten retention on achievement and provide benchmarks based on observed covariates to interpret the ITCV. Ultimately, any sensitivity analysis should only be applied after one has estimated the best possible model. The value of the sensitivity analysis is then to inform policy-oriented discourse among as wide a range of stakeholders as possible.