Statistical Science

On Negative Outcome Control of Unobserved Confounding as a Generalization of Difference-in-Differences

Tamar Sofer, David B. Richardson, Elena Colicino, Joel Schwartz, and Eric J. Tchetgen Tchetgen

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Abstract

The difference-in-differences (DID) approach is a well-known strategy for estimating the effect of an exposure in the presence of unobserved confounding. The approach is most commonly used when pre- and post-exposure outcome measurements are available, and one can assume that the association of the unobserved confounder with the outcome is equal in the two exposure groups, and constant over time. Then one recovers the treatment effect by regressing the change in outcome over time on the exposure. In this paper, we interpret the difference-in-differences as a negative outcome control (NOC) approach. We show that the pre-exposure outcome is a negative control outcome, as it cannot be influenced by the subsequent exposure, and it is affected by both observed and unobserved confounders of the exposure-outcome association of interest. The relation between DID and NOC provides simple conditions under which negative control outcomes can be used to detect and correct for confounding bias. However, for general negative control outcomes, the DID-like assumption may be overly restrictive and rarely credible, because it requires that both the outcome of interest and the control outcome are measured on the same scale. Thus, we present a scale-invariant generalization of the DID that may be used in broader NOC contexts. The proposed approach is demonstrated in simulations and on a Normative Aging Study data set, in which Body Mass Index is used for NOC of the relationship between air pollution and inflammatory outcomes.

Article information

Source
Statist. Sci., Volume 31, Number 3 (2016), 348-361.

Dates
First available in Project Euclid: 27 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.ss/1475001233

Digital Object Identifier
doi:10.1214/16-STS558

Mathematical Reviews number (MathSciNet)
MR3552739

Zentralblatt MATH identifier
06946230

Keywords
Location-scale models quantile–quantile transformation air pollution inflammation

Citation

Sofer, Tamar; Richardson, David B.; Colicino, Elena; Schwartz, Joel; Tchetgen Tchetgen, Eric J. On Negative Outcome Control of Unobserved Confounding as a Generalization of Difference-in-Differences. Statist. Sci. 31 (2016), no. 3, 348--361. doi:10.1214/16-STS558. https://projecteuclid.org/euclid.ss/1475001233


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References

  • Abadie, A. (2005). Semiparametric difference-in-differences estimators. Rev. Econ. Stud. 72 1–19.
  • Angrist, J. D. and Krueger, A. B. (1999). Empirical strategies in labor economics. In Handbook of Labor Economics 3A (O. Ashenfelter and D. Card, eds.) 1277–1366. Elsevier, Amsterdam.
  • Angrist, J. D. and Pischke, J.-S. (2008). Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton Univ. Press, Princeton, NJ.
  • Athey, S. and Imbens, G. W. (2006). Identification and inference in nonlinear difference-in-differences models. Econometrica 74 431–497.
  • Bickel, P. J., Klaassen, C. A., Bickel, P. J., Ritov, Y., Klaassen, J., Wellner, J. A. and Ritov, Y. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins Univ. Press, Baltimore, MD.
  • Blundell, R. and MaCurdy, T. (2000). Labor supply. In Handbook of Labor Economics 3A (O. Ashenfelter and D. Card, eds.) 1559–1695. Elsevier, Amsterdam.
  • Card, D. (1990). The impact of the Mariel boatlift on the Miami labor market. Industrial & Labor Relations Review 43 245–257.
  • Cox, D. R. and Oakes, D. (1984). Analysis of Survival Data 21. CRC Press, Boca Raton. FL.
  • Flanders, W. D., Klein, M., Darrow, L. A., Strickland, M. J., Sarnat, S. E., Sarnat, J. A., Waller, L. A., Winquist, A. and Tolbert, P. E. (2011). A method for detection of residual confounding in time-series and other observational studies. Epidemiology 22 59.
  • Gryparis, A., Coull, B. A., Schwartz, J. and Suh, H. H. (2007). Semiparametric latent variable regression models for spatiotemporal modelling of mobile source particles in the greater Boston area. J. Roy. Statist. Soc. Ser. C 56 183–209.
  • Hernán, M. A., Hernández-Díaz, S. and Robins, J. M. (2004). A structural approach to selection bias. Epidemiology 15 615–625.
  • Lipsitch, M., Tchetgen Tchetgen, E. and Cohen, T. (2010). Negative controls: A tool for detecting confounding and bias in observational studies. Epidemiology 21 383–388.
  • Meyer, B. D. (1995). Natural and quasi-experiments in economics. J. Bus. Econom. Statist. 13 151–161.
  • Meyer, B. D., Kip Viscusi, W. and Durbin, D. L. (1995). Workers’ compensation and injury duration: Evidence from a natural experiment. The American Economic Review 85 322–340.
  • Pearl, J. (2009). Causality: Models, Reasoning, and Inference, 2nd ed. Cambridge Univ. Press, Cambridge.
  • Richardson, D. B., Laurier, D., Schubauer-Berigan, M. K., Tchetgen, E. T. and Cole, S. R. (2014). Assessment and indirect adjustment for confounding by smoking in cohort studies using relative hazards models. Am. J. Epidemiol. 180 933–940.
  • Robins, J. and Tsiatis, A. A. (1992). Semiparametric estimation of an accelerated failure time model with time-dependent covariates. Biometrika 79 311–319.
  • Tchetgen Tchetgen, E. J. (2014). The control outcome calibration approach for causal inference with unobserved confounding. Am. J. Epidemiol. 179 633–640.
  • Tchetgen Tchetgen, E. J. and Vansteelandt, S. (2013). Alternative identification and inference for the effect of treatment on the treated with an instrumental variable. Technical report, Harvard Univ. Biostatistics Working Paper Series.
  • Zeger, S. L., Thomas, D., Dominici, F., Samet, J. M., Schwartz, J., Dockery, D. and Cohen, A. (2000). Exposure measurement error in time-series studies of air pollution: Concepts and consequences Environ. Health Perspect. 108 419.
  • Zeka, A., Sullivan, J. R., Vokonas, P. S., Sparrow, D. and Schwartz, J. (2006). Inflammatory markers and particulate air pollution: Characterizing the pathway to disease. Int. J. Epidemiol. 35 1347–1354.