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. 2024 Mar 27;80(2):ujae027.
doi: 10.1093/biomtc/ujae027.

Single proxy control

Chan Park  1 , David B Richardson  2 , Eric J Tchetgen Tchetgen  1
Affiliations

Single proxy control

Chan Park et al. Biometrics. .

Abstract

Negative control variables are sometimes used in nonexperimental studies to detect the presence of confounding by hidden factors. A negative control outcome (NCO) is an outcome that is influenced by unobserved confounders of the exposure effects on the outcome in view, but is not causally impacted by the exposure. Tchetgen Tchetgen (2013) introduced the Control Outcome Calibration Approach (COCA) as a formal NCO counterfactual method to detect and correct for residual confounding bias. For identification, COCA treats the NCO as an error-prone proxy of the treatment-free counterfactual outcome of interest, and involves regressing the NCO on the treatment-free counterfactual, together with a rank-preserving structural model, which assumes a constant individual-level causal effect. In this work, we establish nonparametric COCA identification for the average causal effect for the treated, without requiring rank-preservation, therefore accommodating unrestricted effect heterogeneity across units. This nonparametric identification result has important practical implications, as it provides single-proxy confounding control, in contrast to recently proposed proximal causal inference, which relies for identification on a pair of confounding proxies. For COCA estimation we propose 3 separate strategies: (i) an extended propensity score approach, (ii) an outcome bridge function approach, and (iii) a doubly-robust approach. Finally, we illustrate the proposed methods in an application evaluating the causal impact of a Zika virus outbreak on birth rate in Brazil.

Keywords: confounding proxy; doubly robust; extended propensity score; negative controls; unmeasured confounding.

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Conflict of interest statement

None declared.

Figures

FIGURE 1
FIGURE 1
A Graphical Illustration of a simple causal model.
FIGURE 2
FIGURE 2
A graphical illustration of the assumptions for COCA. Thick arrows depict the deterministic relationship between Y and formula image, as established by the consistency assumption (Assumption 1).
FIGURE 3
FIGURE 3
A graphical illustration of a structural model compatible with (1). Measured covariates X are suppressed for simplicity. The thick arrows depict the deterministic relationships Ya = 0 = hy(U0) and Y = YA.
See this image and copyright information in PMC

References

    1. Angrist J. D., Pischke J.-S. (2009). Mostly Harmless Econometrics: An Empiricist’s Companion, Princeton: Princeton University Press.
    1. Athey S., Imbens G. W. (2006). Identification and inference in nonlinear difference-in-differences models. Econometrica, 74, 431–497.
    1. Bang H., Robins J. M. (2005). Doubly robust estimation in missing data and causal inference models. Biometrics, 61, 962–973. - PubMed
    1. Caniglia E. C., Murray E. J. (2020). Difference-in-difference in the time of cholera: a gentle introduction for epidemiologists. Current Epidemiology Reports, 7, 203–211. - PMC - PubMed
    1. Card D., Krueger A. B. (1994). Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania. The American Economic Review, 84, 772–793.

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