Generalizing experimental results by leveraging knowledge of mechanisms
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Generalizing experimental results by leveraging knowledge of mechanisms Carlos Cinelli1 · Judea Pearl1 Received: 30 December 2019 / Accepted: 22 September 2020 © Springer Nature B.V. 2020
Abstract We show how experimental results can be generalized across diverse populations by leveraging knowledge of local mechanisms that produce the outcome of interest, only some of which may differ in the target domain. We use structural causal models and a refined version of selection diagrams to represent such knowledge, and to decide whether it entails the invariance of probabilities of causation across populations, which then enables generalization. We further provide: (i) bounds for the target effect when some of these conditions are violated; (ii) new identification results for probabilities of causation and the transported causal effect when trials from multiple source domains are available; as well as (iii) a Bayesian approach for estimating the transported causal effect from finite samples. We illustrate these methods both with simulated data and with a real example that transports the effects of Vitamin A supplementation on childhood mortality across different regions. Keywords Generalizability · Probability of causation · Transportability · Causal inference · Mechanisms
Introduction Generalizing results of randomized control trials (RCT) is critical in many empirical sciences and demands an understanding of the conditions under which such generalizations are feasible. When the mechanisms that determine the outcome differ between the study population and the target population, generalization requires measuring the variables responsible for such differences or, if this is not possible, isolating them away by measuring other variables [20]. Recent We thank Anders Huitfeldt, Ricardo Silva, and anonymous reviewers for valuable comments and feedback. This research was supported in parts by grants from Defense Advanced Research Projects Agency [#W911NF-16-057], National Science Foundation [#IIS-1302448, #IIS-1527490, and #IIS-1704932], and Office of Naval Research [#N00014-17-S-B001]. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10654-020-00687-4) contains supplementary material, which is available to authorized users. * Carlos Cinelli [email protected] Judea Pearl [email protected] 1
Departments of Statistics and Computer Science, University of California, Los Angeles, Los Angeles, USA
work [9–11] describes an interesting situation under which transportability across populations is feasible without such measurements. This feasibility, however, is not immediately inferable using a standard (non-parametric) selection diagram [1, 20], because it relies on the invariance of only some components of the outcome mechanism, but not all. In this paper, we use the theory of Structural Causal Models (SCM) [17] to show how generalization in these settings can be modeled using ordinary structural equations, counterfactual logic and selection diagrams. We demonst
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