Recovering Causal Effects from Selection Bias

By Elias Bareinboim, Jin Tian. 2015

78 citations recorded by the source corpus.

Controlling for selection and confounding biases are two of the most challenging problems that appear in data analysis in the empirical sciences as well as in artificial intelligence tasks. The combination of previously studied methods for each of these biases in isolation is not directly applicable to certain non-trivial cases in which selection and confounding biases are simultaneously present. In this paper, we tackle these instances non-parametrically and in full generality. We provide graphical and algorithmic conditions for recoverability of interventional distributions for when selection and confounding biases are both present. Our treatment completely characterizes the class of causal effects that are recoverable in Markovian models, and is suffi- cient for Semi-Markovian models.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Simpson's Paradox in COVID-19 Case Fatality Rates: A Mediation Analysis of Age-Related Causal Effects (2020, background): “Building on recent (causal) work on recoverability from selection bias may help address this aspect of the problem [29], [30].”
Counterfactual Normalization: Proactively Addressing Dataset Shift and Improving Reliability Using Causal Mechanisms (2018, methodology): “Others have studied methods and conditions for identiﬁcation of causal effects under simultaneous selection and confounding bias (e.g., Bareinboim and Pearl (2012); Bareinboim and Tian (2015); Correa et al. (2018)).”
A Survey of Learning Causality with Data (2018, background): “e of back-door path (e.g., the path D ←X →Y in Fig.3a)4. Its formal definition is as follows: 4Confounding bias can exist even when there is no back-door path. One example is a type of selection bias [17], when the causal graph is D →Z ←X →Y and the dataset is collected only for instances with Zu = ”
A Review of Generalizability and Transportability (2021, methodology): “A corresponding set of assumptions under the structural equation model (SEM) framework has also been derived (Pearl and Bareinboim, 2014; Pearl, 2015; Pearl and Bareinboim, 2011; Bareinboim and Pearl, 2014; Bareinboim and Tian, 2015; Bareinboim and Pearl, 2016; Correa, Tian and Bareinboim, 2018).”
Causal inference and the data-fusion problem (2016, background): “Nevertheless, a do-calculus derivation allows for the estimation of the experimental distribution even without an unbiased dataset (39), leading to the expression P w1 ðP ðx, y,w1,w2,w3jS= 1Þ=Pðw2jw1, S= 1ÞÞ= P y,w1 ðP ðvjS= 1Þ= Pðw2jw1, S= 1ÞÞ, for any level W2 =w2.”
A Survey of Learning Causality with Data: Problems and Methods (2018, background): “One example is a type of selection bias [17], when the causal graph is D → Z ← X → Y and the dataset is collected only for instances with Zu = 1, then within this dataset, the estimated statistical association P (Y |D) can be non-zero although we know that there is no causal effect D → Y .”
Causal Effect Identification by Adjustment under Confounding and Selection Biases (2017, background): “Deﬁnition 5 (Generalized Adjustment Criterion Type 2) .”