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Dissonant Conclusions When Testing the Validity of an Instrumental Variable

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  • Fan Yang
  • José R. Zubizarreta
  • Dylan S. Small
  • Scott Lorch
  • Paul R. Rosenbaum

Abstract

An instrument or instrumental variable is often used in an effort to avoid selection bias in inference about the effects of treatments when treatment choice is based on thoughtful deliberation. Instruments are increasingly used in health outcomes research. An instrument is a haphazard push to accept one treatment or another, where the push can affect outcomes only to the extent that it alters the treatment received. There are two key assumptions here: (R) the push is haphazard or essentially random once adjustments have been made for observed covariates, (E) the push affects outcomes only by altering the treatment, the so-called "exclusion restriction." These assumptions are often said to be untestable; however, that is untrue if testable means checking the compatibility of assumptions with other things we think we know. A test of this sort may result in a collection of claims that are individually plausible but mutually inconsistent, without clear indication as to which claim is culpable for the inconsistency. We discuss this subject in the context of our on-going study of the effects of delivery by cesarean section on the survival of extremely premature infants of 23-24 weeks gestational age. Supplementary materials for this article are available online.

Suggested Citation

  • Fan Yang & José R. Zubizarreta & Dylan S. Small & Scott Lorch & Paul R. Rosenbaum, 2014. "Dissonant Conclusions When Testing the Validity of an Instrumental Variable," The American Statistician, Taylor & Francis Journals, vol. 68(4), pages 253-263, November.
    • Handle: RePEc:taf:amstat:v:68:y:2014:i:4:p:253-263
    DOI: 10.1080/00031305.2014.962764
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    References listed on IDEAS

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    1. Brookhart M. Alan & Schneeweiss Sebastian, 2007. "Preference-Based Instrumental Variable Methods for the Estimation of Treatment Effects: Assessing Validity and Interpreting Results," The International Journal of Biostatistics, De Gruyter, vol. 3(1), pages 1-25, December.
    2. Tan, Zhiqiang, 2006. "Regression and Weighting Methods for Causal Inference Using Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1607-1618, December.
    3. Guido W. Imbens & Paul R. Rosenbaum, 2005. "Robust, accurate confidence intervals with a weak instrument: quarter of birth and education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 109-126, January.
    4. Dubay, Lisa & Kaestner, Robert & Waidmann, Timothy, 1999. "The impact of malpractice fears on cesarean section rates," Journal of Health Economics, Elsevier, vol. 18(4), pages 491-522, August.
    5. Rosenbaum, Paul R. & Silber, Jeffrey H., 2009. "Amplification of Sensitivity Analysis in Matched Observational Studies," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1398-1405.
    6. Jing Cheng & Jing Qin & Biao Zhang, 2009. "Semiparametric estimation and inference for distributional and general treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 881-904, September.
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