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Abstract:
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Estimating causal effects from non-experimental data is very difficult, because unmeasured confounders can bias estimates of causal effects. Sensitivity analysis, which explores the range of causal effects that are consistent with the observed data, can help us understand the potential impacts of unmeasured confounding. In this work, we focus on causal inference with multiple concurrent treatments and/or outcomes, where the structure among these variables can provide some information about unobserved confounders. Our sensitivity analysis is based on a copula factorization of the complete data distribution, and can be applied to arbitrary observed data models. We propose a practical implementation of this approach making use of the Gaussian copula, and establish conditions under which causal effects can be bounded theoretically in multi-treatment settings and practically in multi-outcome settings. We also describe approaches for reasoning about effects, including calibrating sensitivity parameters, quantifying robustness of effect estimates, and selecting models which are most consistent with prior hypotheses.
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