Causal inference at the population level

Azam Yazdani, Eric Boerwinkle


Three elements are needed to formalize a causal quantity at the population level: response, treatment, and the causal element, which are introduced here by notation. Inclusion of two essential causal assumptions, the monitoring and illumination assumptions, in a function distinguishes causal from association analyses. The discussion provides insight into causal inference.


Assignment mechanism, Causal inference, Observational study

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Rubin DB. Teaching statistical inference for causal effects in experiments and observational studies. J Educ Behav Stat Fall. 2004;29(3):343-67.

Rubin DB. Causal inference using potential outcomes: design, modeling, decisions. J Am Stat Assoc. 2005;100:322-31.

Rubin DB. Reflections stimulated by the comments of Shadish (2010) and West and Thoemmes (2010). Psychol Methods. 2010;15(1):38-46.

Imbens, GW. Nonparametric estimation of average treatment effects under exogeneity: a review. Rev Econom Stat. 2004;86(1):4-29.

Pearl J. Introduction to probabilities, graphs, and causal models. Pearl J, eds. In: Causality: Models, Reasoning and Inference. 2nd ed. New York: Cambridge University Press; 2009: 1-64.

Pearl J. An introduction to causal inference. Int J Biostat. 2010 Feb 26;6(2):Article 7.

Hoyle RH. The causal foundations of structural equation modeling. In: Pearl J, eds. Handbook of Structural Equation Modeling. 3rd ed. New York: Guilford Press; 2011: Chapter 5.

Dawid AP. Fundamentals of statistical causality. In: Dawid AP, eds. Research Report 279. London: Department of Statistical Science, University College London; 2007: 94.

Rubin DB. Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol. 1974;66:688-701.

Rubin DB. Discussion of “Randomization Analysis of experimental data in the fisher randomization test” by D. Basu. J Am Stat Assoc. 1980;75:591-3.

Rosenbaum PR. Causal inference in randomized experiments. In: Rosenbaum PR, eds. Design of Observational Studies. 2009th ed. New York: Springer; 2009: 21-64.