Identifying causal effects with proxy variables of an unmeasured confounder

Wang, Miao; Geng, Zhi; Tchetgen, Eric J. Tchetgen

doi:10.1093/biomet/asy038

Cited by 163 publications

(238 citation statements)

References 25 publications

(44 reference statements)

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“…When | Z |=| W |=| U |, P ( W | Z , a , x ) is full rank and the linear system (1) has a unique solution

h false(a, x false) = E false[Y false| boldZ, a, x false] P {(W | Z, a, x)}^{- 1} .

Therefore, lemma 1 implies the identification result of Miao et al . () under the stronger assumption that | Z |=| W |=| U |, which is stated in the following corollary.…”

Section: Identification and Reparameterizationmentioning

confidence: 94%

“…In fact, by theorem 2 of James (), the complete set of solutions to equation is given by

h false(a, x false) = E false[Y false| boldZ, a, x false] P {(W | Z, a, x)}^{+} + τ {(a, x)}^{normalT} false{double-struckI - P (W | Z, a, x) P {false(boldW false| boldZ, a, x false)}^{+} false}

, as τ ( a , x ), a vector function, varies over all possible values in

{f : false(a, x false) \to R^{| W |}}

. The second is to coarsen levels in Z and W until the coarsened variables satisfy assumption 5 (Kuroki and Pearl, ; Miao et al ., ). Suppose that there are m possible sets of coarsened negative control variables; then an estimator can be obtained by the generalized method of moments, i.e.…”

Section: Identification and Reparameterizationmentioning

confidence: 97%

“…Recently Miao et al . () proposed non‐parametric identification of causal effects by using a pair of negative control exposure and outcome variables under certain completeness conditions. Their work focused primarily on providing sufficient identification conditions and less so on inference.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we first extend the identification result of Miao et al . () to allow for a weaker set of conditions, and we provide an alternative representation of the identifying functional for the ATE. The representation is a difference between the standard g ‐formula of Robins () that fails to account for unmeasured confounding and an explicit bias correction term that adjusts for unmeasured confounding bias leveraging a pair of negative controls.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2 we extend the non‐parametric identification results of Miao et al . () and provide an alternative representation of their identifying functional for the ATE, which opens up an opportunity for multiply robust estimation. For ease of exposition, we describe our results in the simple case of binary negative controls and unmeasured confounder in Section 3, where we propose a variety of semiparametric estimators including a multiply robust estimator.…”

Section: Introductionmentioning

confidence: 99%

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Multiply Robust Causal Inference with Double-Negative Control Adjustment for Categorical Unmeasured Confounding

Shi

Wang

Nelson

et al. 2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Unmeasured confounding is a threat to causal inference in observational studies. In recent years, the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a long‐standing tradition in laboratory sciences and epidemiology to rule out non‐causal explanations, although they have been used primarily for bias detection. Recently, Miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non‐parametrically the average treatment effect (ATE) from observational data subject to uncontrolled confounding. We establish non‐parametric identification of the ATE under weaker conditions in the case of categorical unmeasured confounding and negative control variables. We also provide a general semiparametric framework for obtaining inferences about the ATE while leveraging information about a possibly large number of measured covariates. In particular, we derive the semiparametric efficiency bound in the non‐parametric model, and we propose multiply robust and locally efficient estimators when non‐parametric estimation may not be feasible. We assess the finite sample performance of our methods in extensive simulation studies. Finally, we illustrate our methods with an application to the post‐licensure surveillance of vaccine safety among children.

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“…When | Z |=| W |=| U |, P ( W | Z , a , x ) is full rank and the linear system (1) has a unique solution

h false(a, x false) = E false[Y false| boldZ, a, x false] P {(W | Z, a, x)}^{- 1} .

Therefore, lemma 1 implies the identification result of Miao et al . () under the stronger assumption that | Z |=| W |=| U |, which is stated in the following corollary.…”

Section: Identification and Reparameterizationmentioning

confidence: 94%

“…In fact, by theorem 2 of James (), the complete set of solutions to equation is given by

h false(a, x false) = E false[Y false| boldZ, a, x false] P {(W | Z, a, x)}^{+} + τ {(a, x)}^{normalT} false{double-struckI - P (W | Z, a, x) P {false(boldW false| boldZ, a, x false)}^{+} false}

, as τ ( a , x ), a vector function, varies over all possible values in

{f : false(a, x false) \to R^{| W |}}

Section: Identification and Reparameterizationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiply Robust Causal Inference with Double-Negative Control Adjustment for Categorical Unmeasured Confounding

Shi

Wang

Nelson

et al. 2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Causal Inference About the Effects of Interventions From Observational Studies in Medical Journals

Dahabreh,

Bibbins-Domingo

2024

JAMA

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ImportanceMany medical journals, including JAMA, restrict the use of causal language to the reporting of randomized clinical trials. Although well-conducted randomized clinical trials remain the preferred approach for answering causal questions, methods for observational studies have advanced such that causal interpretations of the results of well-conducted observational studies may be possible when strong assumptions hold. Furthermore, observational studies may be the only practical source of information for answering some questions about the causal effects of medical or policy interventions, can support the study of interventions in populations and settings that reflect practice, and can help identify interventions for further experimental investigation. Identifying opportunities for the appropriate use of causal language when describing observational studies is important for communication in medical journals.ObservationsA structured approach to whether and how causal language may be used when describing observational studies would enhance the communication of research goals, support the assessment of assumptions and design and analytic choices, and allow for more clear and accurate interpretation of results. Building on the extensive literature on causal inference across diverse disciplines, we suggest a framework for observational studies that aim to provide evidence about the causal effects of interventions based on 6 core questions: what is the causal question; what quantity would, if known, answer the causal question; what is the study design; what causal assumptions are being made; how can the observed data be used to answer the causal question in principle and in practice; and is a causal interpretation of the analyses tenable?Conclusions and RelevanceAdoption of the proposed framework to identify when causal interpretation is appropriate in observational studies promises to facilitate better communication between authors, reviewers, editors, and readers. Practical implementation will require cooperation between editors, authors, and reviewers to operationalize the framework and evaluate its effect on the reporting of empirical research.

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Machine Learning and Causal Inference

Zivich

Breskin

Kennedy

2022

Wiley StatsRef: Statistics Reference Online

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In this article, we review the motivation behind the use of machine learning or data‐adaptive algorithms for the estimation of causal effects. To guide our discussion, we focus on the estimation of the causal mean as a didactic example. Estimation of the causal mean involves estimation of at least one nuisance model for which machine learning is considered. Two key challenges to reliable application of machine learning for causal inference are reviewed: slower than parametric convergence, and complexity of the nuisance model and its estimator. Current approaches to address each of these challenges are then reviewed. We then summarize the extensions to other estimands, identification strategies, and estimators. We conclude with practical advice for application.

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Identifying causal effects with proxy variables of an unmeasured confounder

Cited by 163 publications

References 25 publications

Multiply Robust Causal Inference with Double-Negative Control Adjustment for Categorical Unmeasured Confounding

Multiply Robust Causal Inference with Double-Negative Control Adjustment for Categorical Unmeasured Confounding

Causal Inference About the Effects of Interventions From Observational Studies in Medical Journals

Machine Learning and Causal Inference

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