Modeling Causal Effects Using SAS/STAT®
Abstract
An outcome causally depends on a prior event if and only if the occurrence of the prior event implies that the outcome will occur, and the absence of the prior event implies that the outcome will not occur. The fundamental problem of causality is that, at an individual level, the prior event is either observed or not, and the alternative can only be imagined. Therefore, we restrict causal analyses to population level relationships. To establish a causal relationship, we must isolate the prior event and the outcome from other possible causal prior events. We do this by intervening in the world we are measuring, perhaps by designed experimentation. However, designed experiments are not practical or even possible in some situations and an alternative method to establish causal relationships is needed.
This paper introduces structural causal modeling, an anlytical method that supports causal inference. A structural causal model is a set of pre-specified relationships between variables, usually represented graphically, that satisfy a set of conditions allowing causal inference. This paper introduces 1) graphical models, specifically directed acyclic graphs (DAGs), 2) the concept of identifiability, which allows causal inference, and 3) parameter estimation for the identified model. We use the CAUSAL family of procedures in SAS/STAT: CAUSALGRAPH, CAUSALMED, and CAUSALTRT.
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CONCLUSION
This paper is a gentle introduction to causality and structural causal models. The first step in a causal analysis using structural causal models is to draw your system of variables in a directed acyclic graph. Then code your DAG in PROC CAUSALGRAPH to identify adjustment sets of confounders that you must control in your causal analysis. With an adjustment set identified, if you can satisfy the four assumptions and if you practice good modeling principles, then you can safely make causal inferences.
We introduced to modeling procedures, PROC CAUSALMED, for mediation analyses, and PROC CAUSALTRT, for estimates of average treatment effect. PROC CAUSALTRT provides two modeling approaches; modeling the treatment by fitting a propensity score model, and modeling the outcome by fitting a structural causal model.
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ACKNOWLEDGMENTS
The author sincerely thanks Clay THompson of SAS Institute Inc. for his suggestions to improve an earlier version of this paper.
RECOMMENDED READING
Pearl, J. and Mackenzie, D. (2018). The Book of Why: The New Science of Cause and Effect. Basic Books. New York, NY.
CONTACT INFORMATION
Your comment and questions are valued and encouraged. Contact the author at:
John Amrhein
Vice President, Managing Director
McDougall Scientific Ltd.
jamrhein@mcdougallscientific.com
www.mcdougallscientific.com
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