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Selection Bias When Using Instrumental Variable Methods to Compare Two Treatments But More Than Two Treatments Are Available

Author

Listed:
  • Ertefaie Ashkan

    (Department of Statistics, Center for Pharmacoepidemiology Research and Training, University of Pennsylvania, Philadelphia, PA, USA)

  • Small Dylan

    (Department of Statistics, University of Pennsylvania, Philadelphia, PA, USA)

  • Flory James

    (Weill-Cornell School of Medicine, New York, USA)

  • Hennessy Sean

    (Center for Pharmacoepidemiology Research and Training, Center for Clinical Epidemiology and Biostatistics, Perelman School of Medicine, Philadelphia, University of Pennsylvania, PA, USA)

Abstract

Instrumental variable (IV) methods are widely used to adjust for the bias in estimating treatment effects caused by unmeasured confounders in observational studies. It is common that a comparison between two treatments is focused on and that only subjects receiving one of these two treatments are considered in the analysis even though more than two treatments are available. In this paper, we provide empirical and theoretical evidence that the IV methods may result in biased treatment effects if applied on a data set in which subjects are preselected based on their received treatments. We frame this as a selection bias problem and propose a procedure that identifies the treatment effect of interest as a function of a vector of sensitivity parameters. We also list assumptions under which analyzing the preselected data does not lead to a biased treatment effect estimate. The performance of the proposed method is examined using simulation studies. We applied our method on The Health Improvement Network (THIN) database to estimate the comparative effect of metformin and sulfonylureas on weight gain among diabetic patients.

Suggested Citation

  • Ertefaie Ashkan & Small Dylan & Flory James & Hennessy Sean, 2016. "Selection Bias When Using Instrumental Variable Methods to Compare Two Treatments But More Than Two Treatments Are Available," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 219-232, May.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:1:p:219-232:n:2
    DOI: 10.1515/ijb-2015-0006
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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. Jack Hadley & Daniel Polsky & Jeanne S. Mandelblatt & Jean M. Mitchell & Jane C. Weeks & Qin Wang & Yi‐Ting Hwang & OPTIONS Research Team, 2003. "An exploratory instrumental variable analysis of the outcomes of localized breast cancer treatments in a medicare population," Health Economics, John Wiley & Sons, Ltd., vol. 12(3), pages 171-186, March.
    3. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    4. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    5. Qi Long & Roderick J. A. Little & Xihong Lin, 2010. "Estimating causal effects in trials involving multitreatment arms subject to non‐compliance: a Bayesian framework," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 513-531, May.
    6. Jing Cheng & Dylan S. Small, 2006. "Bounds on causal effects in three‐arm trials with non‐compliance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 815-836, November.
    7. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    8. Peter B. Gilbert & Ronald J. Bosch & Michael G. Hudgens, 2003. "Sensitivity Analysis for the Assessment of Causal Vaccine Effects on Viral Load in HIV Vaccine Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 531-541, September.
    9. 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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