Evidence
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Card 1 · Graphical Criteria for Efficient Total Effect Estimation Via Adjustment in Causal Linear Models
Abstract Covariate adjustment is a commonly used method for total causal effect estimation. In recent years, graphical criteria have been developed to identify all valid adjustment sets, that is, all covariate sets that can be used for this purpose. Different valid adjustment sets typically provide…
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Abstract Covariate adjustment is a commonly used method for total causal effect estimation. In recent years, graphical criteria have been developed to identify all valid adjustment sets, that is, all covariate sets that can be used for this purpose. Different valid adjustment sets typically provide total causal effect estimates of varying accuracies. Restricting ourselves to causal linear models, we introduce a graphical criterion to compare the asymptotic variances provided by certain valid adjustment sets. We employ this result to develop two further graphical tools. First, we introduce a simple variance decreasing pruning procedure for any given valid adjustment set. Second, we give a graphical characterization of a valid adjustment set that provides the optimal asymptotic variance among all valid adjustment sets. Our results depend only on the graphical structure and not on the specific error variances or edge coefficients of the underlying causal linear model. They can be applied …
Card 2 · Efficient adjustment sets for population average treatment effect estimation in non-parametric causal graphical models
The method of covariate adjustment is often used for estimation of population average causal treatment effects in observational studies. Graphical rules for determining all valid covariate adjustment sets from an assumed causal graphical model are well known. Restricting attention to causal linear m…
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The method of covariate adjustment is often used for estimation of population average causal treatment effects in observational studies. Graphical rules for determining all valid covariate adjustment sets from an assumed causal graphical model are well known. Restricting attention to causal linear models, a recent article ( Henckel et al.,, 2019 ) derived two novel graphical criteria: one to compare the asymptotic variance of linear regression treatment effect estimators that control for certain distinct adjustment sets and another to identify the optimal adjustment set that yields the adjusted least squares treatment effect estimator with the smallest asymptotic variance among consistent adjusted least squares estimators.
Card 3 · Efficient adjustment sets in causal graphical models with hidden variables
Summary We study the selection of adjustment sets for estimating the interventional mean under a point exposure dynamic treatment regime, that is, a treatment rule that depends on the subject’s covariates. We assume a nonparametric causal graphical model with, possibly, hidden variables and at least…
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Summary We study the selection of adjustment sets for estimating the interventional mean under a point exposure dynamic treatment regime, that is, a treatment rule that depends on the subject’s covariates. We assume a nonparametric causal graphical model with, possibly, hidden variables and at least one adjustment set comprised of observable variables. We provide the definition of a valid adjustment set for a point exposure dynamic treatment regime, which generalizes the existing definition for a static intervention. We show that there exists an adjustment set, referred to as optimal minimal, that yields the nonparametric estimator of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal adjustment sets. An observable minimal adjustment set is a valid adjustment set such that all its variables are observable and the removal of any of its variables destroys its validity. We provide similar optimality results for the class of obser …
Card 4 · Towards unique and unbiased causal effect estimation from data with hidden variables
Causal effect estimation from observational data is a crucial but challenging task. Currently, only a limited number of data-driven causal effect estimation methods are available. These methods either provide only a bound estimation of the causal effect of a treatment on the outcome, or generate a u…
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Causal effect estimation from observational data is a crucial but challenging task. Currently, only a limited number of data-driven causal effect estimation methods are available. These methods either provide only a bound estimation of the causal effect of a treatment on the outcome, or generate a unique estimation of the causal effect, but making strong assumptions on data and having low efficiency. In this paper, we identify a practical problem setting and propose an approach to achieving unique and unbiased estimation of causal effects from data with hidden variables. For the approach, we have developed the theorems to support the discovery of the proper covariate sets for confounding adjustment (adjustment sets). Based on the theorems, two algorithms are proposed for finding the proper adjustment sets from data with hidden variables to obtain unbiased and unique causal effect estimation. Experiments with synthetic datasets generated using five benchmark Bayesian networks and four r …
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Card 2 · fact
Affected output: graphical criteria for comparing the asymptotic variance of estimators based on distinct valid adjustment sets and for identifying the adjustment set that yields the smallest asymptotic variance among consistent estimators
Model explanation: This row supplied the specific two-part content of the graphical criteria (variance comparison and optimal set identification) that the generated sentence reports as prior work.
Card 3 · fact
Affected output: an optimal minimal adjustment set that minimizes the asymptotic variance among estimators based on observable minimal adjustment sets
Model explanation: This row supplied the concrete optimality result for the hidden-variable setting, including the term 'optimal minimal adjustment set' and the scope 'among observable minimal adjustment sets', which the generated sentence attributes to Rotnitzky and Smucler (2019).
Card 1 · terminology
Affected output: comparing the asymptotic variance of estimators based on distinct valid adjustment sets
Model explanation: This row provided the field-native phrasing 'compare the asymptotic variances provided by valid adjustment sets', which shaped the terminology of the first clause.