Approximating counterfactual bounds while fusing observational, biased and randomised data sources

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset affected by a selection bias. We show that the likelihood of the available data has no local maxima. This enables us to use the causal expectation-maximisation scheme to approximate the bounds for partially identifiable counterfactual queries, which are the focus of this paper. We then show how the same approach can address the general case of multiple datasets, no matter whether interventional or observational, biased or unbiased, by remapping it into the former one via graphical transformations. Systematic numerical experiments and a case study on palliative care show the effectiveness of our approach, while hinting at the benefits of fusing heterogeneous data sources to get informative outcomes in case of partial identifiability.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

This paper addresses the integration of data from multiple observational and interventional studies, which may be biased, in order to compute counterfactuals in structural causal models. The paper proposes a causal expectation-maximization scheme to approximate the bounds for partially identifiable counterfactual queries. Additionally, the paper demonstrates how this approach can be extended to handle multiple datasets, regardless of their type or bias, by using graphical transformations. The effectiveness of the proposed approach is validated through numerical experiments and a case study on palliative care, indicating the benefits of fusing heterogeneous data sources in the presence of partial identifiability.