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Many students of statistics and econometrics express frustration with the way a problem known as “bad control” is treated in the traditional literature. The issue arises when the addition of a variable to a regression equation produces an unintended discrepancy between the regression coefficient and the effect that the coefficient is intended to represent. Avoiding such discrepancies presents a challenge to all analysts in the data intensive sciences. This note describes graphical tools for understanding, visualizing, and resolving the problem through a series of illustrative examples. By making this “crash course” accessible to instructors and practitioners, we hope to avail these tools to a broader community of scientists concerned with the causal interpretation of regression models. 

Randomized clinical trials (RCTs) like those conducted by the FDA provide medical practitioners with average effects of treatments, and are generally more desirable than observational studies due to their control of unobserved confounders (UCs), viz., latent factors that influence both treatment and recovery. However, recent results from causal inference have shown that randomization results in a subsequent loss of information about the UCs, which may impede treatment efficacy if left uncontrolled in practice (Bareinboim, Forney, and Pearl 2015). Our paper presents a novel experimental design that can be noninvasively layered atop past and future RCTs to not only expose the presence of UCs in a system, but also reveal patient- and practitioner-specific treatment effects in order to improve decision-making. Applications are given to personalized medicine, second opinions in diagnosis, and employing offline results in online recommender systems.