Essential concepts of causal inference: a remarkable history and an intriguing future

ABSTRACT

Causal inference refers to the process of inferring what would happen in the future if we change what we are doing, or inferring what would have happened in the past, if we had done something different in the distant past. Humans adjust our behaviors by anticipating what will happen if we act in different ways, using past experiences to inform these choices. ‘Essential’ here means in the mathematical sense of excluding the unnecessary and including only the necessary, e.g. stating that the Pythagorean theorem works for an isosceles right triangle is bad mathematics because it includes the unnecessary adjective isosceles; of course this is not as bad as omitting the adjective ‘right.’ I find much of what is written about causal inference to be mathematically inapposite in one of these senses because the descriptions either include irrelevant clutter or omit conditions required for the correctness of the assertions. The history of formal causal inference is remarkable because its correct formulation is so recent, a twentieth century phenomenon, and its future is intriguing because it is currently undeveloped when applied to investigate interventions applied to conscious humans, and moreover will utilize tools impossible without modern computing.

KEYWORDS:

• Experiments
• observational studies
• randomization
• RCM (Rubin causal model)
• RCT (Randomized controlled trial)

Acknowledgments

The author thanks the editorial board and reviewers for careful and helpful comments on an earlier version of this article.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Donald B. Rubin

Dr Donald B. Rubin was Full Professor at Harvard University for over thirty years, and Chairman of the Department of Statistics for many of those years. He recently retired from Harvard to take a position as Professor at the Yau Mathematical Sciences Center, Tsinghua University and Murray Shusterman Senior Research Fellow, Department of Statistical Science, Fox School of Business, Temple University. He has accumulated many scholarly honors, such as honorary degrees from the US, EU, and Asia; memberships in scholarly organizations such as the US National Academy of Sciences, the American Academy of Art and Sciences, the British Academy; and elected fellowships in many associations, such as the American Statistical Association, the Institute of Mathematical Statistics, and the International Statistics Institute. He is also one the most highly cited scientific authors in the world, with well over 250,000 citations according to google scholar. Also, as of the end of 2019, he has ten singly authored publications, each with over a thousand citations.