A New Criterion for Confounder Selection

VanderWeele, Tyler J.; Shpitser, Ilya

doi:10.1111/j.1541-0420.2011.01619.x

Cited by 325 publications

(291 citation statements)

References 30 publications

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“…One study proposed that a relevant criterion for estimating causal effects is to adjust for all covariates known to cause exposure, disease, or both (145). This criterion can identify covariate subsets sufficient for confounding control, but it has some practical drawbacks.…”

Section: Why Not Adjust For Every Available Covariate?mentioning

confidence: 99%

Statistical Foundations for Model-Based Adjustments

Greenland

Pearce²

2015

Annu. Rev. Public Health

216

198

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Most epidemiology textbooks that discuss models are vague on details of model selection. This lack of detail may be understandable since selection should be strongly influenced by features of the particular study, including contextual (prior) information about covariates that may confound, modify, or mediate the effect under study. It is thus important that authors document their modeling goals and strategies and understand the contextual interpretation of model parameters and model selection criteria. To illustrate this point, we review several established strategies for selecting model covariates, describe their shortcomings, and point to refinements, assuming that the main goal is to derive the most accurate effect estimates obtainable from the data and available resources. This goal shifts the focus to prediction of exposure or potential outcomes (or both) to adjust for confounding; it thus differs from the goal of ordinary statistical modeling, which is to passively predict outcomes. Nonetheless, methods and software for passive prediction can be used for causal inference as well, provided that the target parameters are shifted appropriately.

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Section: Why Not Adjust For Every Available Covariate?mentioning

confidence: 99%

Statistical Foundations for Model-Based Adjustments

Greenland

Pearce²

2015

Annu. Rev. Public Health

216

198

View full text Add to dashboard Cite

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“…Corollary 2.1 starts with such a sufficient set Z and provides conditions under which a direct cause of X included in Z can be excluded so that the resulting set Z 0 is also sufficient. Remark that this corollary is akin to Proposition 1 from VanderWeele and Shpitser [10]. In the sequel, the concept of d-separation is used to entail notions of conditional independence between variables.…”

Section: A Motivation Based On Directed Acyclic Graphsmentioning

confidence: 78%

“…For a brief review of this framework, we refer the reader to the appendix of VanderWeele and Shpitser [10]. Proposition 2.1 presented below gives a sufficient condition to identify a set Z that yields an unbiased estimatorβ of the causal effect of X in eq.…”

Section: A Motivation Based On Directed Acyclic Graphsmentioning

confidence: 99%

The Bayesian Causal Effect Estimation Algorithm

Talbot¹,

Lefebvre

Atherton

2015

Journal of Causal Inference

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Estimating causal exposure effects in observational studies ideally requires the analyst to have a vast knowledge of the domain of application. Investigators often bypass difficulties related to the identification and selection of confounders through the use of fully adjusted outcome regression models. However, since such models likely contain more covariates than required, the variance of the regression coefficient for exposure may be unnecessarily large. Instead of using a fully adjusted model, model selection can be attempted. Most classical statistical model selection approaches, such as Bayesian model averaging, do not readily address causal effect estimation. We present a new model averaged approach to causal inference, Bayesian causal effect estimation (BCEE), which is motivated by the graphical framework for causal inference. BCEE aims to unbiasedly estimate the causal effect of a continuous exposure on a continuous outcome while being more efficient than a fully adjusted approach.

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“…First, it is important to remind ourselves that the models in DM and the extended versions presented here are still toy models that most likely will not be representative of real research situations. I argue that in applied research it is still preferable to rely on methods that are guaranteed to minimize bias (under assumptions expressed, e.g., in a DAG), such as the back-door criterion [4], the adjustment criterion [8], or the disjunctive cause criterion [9]. All of these criteria rely on making certain assumptions, and are thus not "model-free."…”

Section: Resultsmentioning

confidence: 99%

M-bias, Butterfly Bias, and Butterfly Bias with Correlated Causes – A Comment on Ding and Miratrix (2015)

Thoemmes

2015

Journal of Causal Inference

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Ding and Miratrix [1] recently concluded that adjustment on a pre-treatment covariate is almost always preferable to reduce bias. I extend the examined parameter space of the models considered by Ding and Miratrix, and consider slight extensions of their models as well. Similar to the conclusion by Pearl [7], I identify constellations in which bias due to adjustment, or failing to adjust is symmetrical, but also confirm some findings of Ding and Miratrix.Keywords: M-bias, causal inference, butterfly bias Ding and Miratrix [1], henceforth DM, recently examined bias in graphical causal models. Their main interest was to explore whether it is beneficial to adjust on a variable that may have both confounder properties (being a common cause of two variables), or collider properties (being a common effect of two variables). This is an important question, as e.g., evidenced by the debate of Rubin [2], and Pearl [3,4], and I applaud the authors to tackle it, especially using the methodology expressed in Pearl [5], and Chen and Pearl [6].The main conclusion of DM was that typically adjustment is preferable, even if a variable may have bias-inducing properties. The authors justified this conclusion based on the fact that in a majority of their conditions for which they derived asymptotic bias, adjustment yielded smaller biases. DM however did note that some of their analyses were incomplete, because certain path coefficients were always fixed to be of equal magnitude, and importantly of equal sign. They explicitly left exploration of a broader parameter space (including negative correlations) to future studies.In a comment, Pearl [7] rebutted the claim of the authors, and argued that in the case of the M-bias structure with correlated causes, bias due to adjustment should be comparable in size to bias due to failing to adjust for a confounder. In the case of so-called butterfly bias, in which both confounding and M-bias are present, Pearl [7] also conjectured that bias due to adjustment and lack of adjustment would be largely symmetrical, an argument based on the equal prevalence of positive and negative correlations of unobserved causes in the M-bias structure.This comment extends the work of DM, by examining the same models, or slight extensions thereof, but also varying involved path coefficients over a much larger, and arguably more complete, parameter space. Asymptotic biasesI used the same methodology as DM to derive the asymptotic bias in the model depicted in Figure 1.1 Note that all models of DM are included in this model as special cases. If path coefficients e and f are set to 0,

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A New Criterion for Confounder Selection

Cited by 325 publications

References 30 publications

Statistical Foundations for Model-Based Adjustments

Statistical Foundations for Model-Based Adjustments

The Bayesian Causal Effect Estimation Algorithm

M-bias, Butterfly Bias, and Butterfly Bias with Correlated Causes – A Comment on Ding and Miratrix (2015)

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