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Bounds on Treatment Effects from Studies with Imperfect Compliance
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1997
"... This paper establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect. The bounds provided are the tightest possible, given the distribution of assignments, treatment ..."
Abstract

Cited by 56 (13 self)
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This paper establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect. The bounds provided are the tightest possible, given the distribution of assignments, treatments, and responses. The formulas show that even with high rates of noncompliance, experimental data can yield useful and sometimes accurate information on the average e#ect of a treatment on the population.
Probabilities of Causation: Bounds and Identification
 Annals of Mathematics and Artificial Intelligence
, 2000
"... This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structuralsemantical definitions of the probabilities of necessary or sufficient causation (or both), we show h ..."
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Cited by 16 (10 self)
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This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structuralsemantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the datagenerating process. In particular, we strengthen the results of Pearl (1999) by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excessriskratio could be used for assessing attributional quantities such as the probability of causation. 1
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.
Probabilities of causation: Bounds and identi cation
 In Proceedings of the Sixteenth Conference on Uncertainty in Arti cial Intelligence
, 2000
"... This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structuralsemantical de nitions of the probabilities of necessary or su cient causation (or both), we show howto optimally bound these quantities from data obtained in ex ..."
Abstract

Cited by 6 (5 self)
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This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structuralsemantical de nitions of the probabilities of necessary or su cient causation (or both), we show howto optimally bound these quantities from data obtained in experimental and observational studies, making minimal assumptions concerning the datagenerating process. In particular, we strengthen the results of Pearl (1999) by weakening the datageneration assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely how empirical data can be used both in settling questions of attribution and in solving attributionrelated problems of decision making. 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.
Probabilities of Causation: Bounds and
, 2000
"... This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structuralsemantical de nitions of the probabilities of necessary or su cient causation (or both), we show how to b ..."
Abstract
 Add to MetaCart
This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structuralsemantical de nitions of the probabilities of necessary or su cient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the datagenerating process. In particular, we strengthen the results of Pearl (1999) by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excessriskratio could be used for assessing attributional quantities such as the probability of causation. 1
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.