Regression and Causality

Abstract: The causal effect of an intervention (treatment/exposure) on an outcome can be estimated by: i) specifying knowledge about the data-generating process; ii) assessing under what assumptions a target quantity, such as for example a causal odds ratio, can be identified given the specified knowledge (and given the measured data); and then, iii) using appropriate statistical estimation techniques to estimate the desired parameter of interest. As regression is the cornerstone of statistical analysis, it seems obvious to ask: is it appropriate to use estimated regression parameters for causal effect estimation? It turns out that using regression for effect estimation is possible, but typically requires more assumptions than competing methods. This manuscript provides a comprehensive summary of the assumptions needed to identify and estimate a causal parameter using regression and, equally important, discusses the resulting implications for statistical practice.