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Bounds on Direct Effects in the Presence of Confounded Intermediate Variables
, 2007
"... Summary. This paper considers the problem of estimating the average controlled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where ..."
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Cited by 6 (0 self)
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Summary. This paper considers the problem of estimating the average controlled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded (hence identifiable). Kaufman et al. (2005) applied a linear programming software to find the minimum and maximum possible values of the ACDE for specific numerical data. In this paper, we apply the symbolic BalkePearl (1997) linear programming method to derive closedform formulas for the upper and lower bounds on the ACDE under various assumptions of monotonicity. These universal bounds enable clinical experimenters to assess the direct effect of treatment from observed data with minimum computational effort, and they further shed light on the sign of the direct effect and the accuracy of the assessments.
Polynomial constraints in causal Bayesian networks
 In Proceedings of the Seventeenth Annual Conference on Uncertainty in Artificial Intelligence (UAI07
"... We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce the complexity of the implicitization problem and make the p ..."
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Cited by 2 (1 self)
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We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce the complexity of the implicitization problem and make the problem tractable in certain causal Bayesian networks. We also show some preliminary results on the algebraic structure of polynomial constraints. The results have applications in distinguishing between causal models and in testing causal models with combined observational and experimental data. 1
DOI: 10.1111/j.15410420.2007.00949.x Bounds on Direct Effects in the Presence of Confounded Intermediate Variables
, 2008
"... Summary. This article considers the problem of estimating the average controlled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where ..."
Abstract
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Summary. This article considers the problem of estimating the average controlled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded (hence identifiable). Kaufman et al. (2005, Statistics in Medicine 24, 1683–1702) applied a linear programming software to find the minimum and maximum possible values of the ACDE for specific numerical data. In this article, we apply the symbolic Balke–Pearl (1997, Journal of the American Statistical Association 92, 1171–1176) linear programming method to derive closedform formulas for the upper and lower bounds on the ACDE under various assumptions of monotonicity. These universal bounds enable clinical experimenters to assess the direct effect of treatment from observed data with minimum computationaleffort, and they further shed light on the sign of the direct effect and the accuracy of the assessments.
Causal Bounds and Observable Constraints for Nondeterministic Models
"... Conditional independence relations involving latent variables do not necessarily imply observable independences. They may imply inequality constraints on observable parameters and causal bounds, which can be used for falsification and identification. The literature on computing such constraints ofte ..."
Abstract
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Conditional independence relations involving latent variables do not necessarily imply observable independences. They may imply inequality constraints on observable parameters and causal bounds, which can be used for falsification and identification. The literature on computing such constraints often involve a deterministic underlying data generating process in a counterfactual framework. If an analyst is ignorant of the nature of the underlying mechanisms then they may wish to use a model which allows the underlying mechanisms to be probabilistic. A method of computation for a weaker model without any determinism is given here and demonstrated for the instrumental variable model, though applicable to other models. The approach is based on the analysis of mappings with convex polytopes in a decision theoretic framework and can be implemented in readily available polyhedral computation software. Well known constraints and bounds are replicated in a probabilistic model and novel ones are computed for instrumental variable models without nondeterministic versions of the randomization, exclusion restriction and monotonicity assumptions respectively.