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On inverse probability-weighted estimators in the presence of interference

Author

Listed:
  • L. Liu
  • M. G. Hudgens
  • S. Becker-Dreps

Abstract

We consider inference about the causal effect of a treatment or exposure in the presence of interference, i.e., when one individual’s treatment affects the outcome of another individual. In the observational setting where the treatment assignment mechanism is not known, inverse probability-weighted estimators have been proposed when individuals can be partitioned into groups such that there is no interference between individuals in different groups. Unfortunately this assumption, which is sometimes referred to as partial interference, may not hold, and moreover existing weighted estimators may have large variances. In this paper we consider weighted estimators that could be employed when interference is present. We first propose a generalized inverse probability-weighted estimator and two Hájek-type stabilized weighted estimators that allow any form of interference. We derive their asymptotic distributions and propose consistent variance estimators assuming partial interference. Empirical results show that one of the Hájek estimators can have substantially smaller finite-sample variance than the other estimators. The different estimators are illustrated using data on the effects of rotavirus vaccination in Nicaragua.

Suggested Citation

  • L. Liu & M. G. Hudgens & S. Becker-Dreps, 2016. "On inverse probability-weighted estimators in the presence of interference," Biometrika, Biometrika Trust, vol. 103(4), pages 829-842.
  • Handle: RePEc:oup:biomet:v:103:y:2016:i:4:p:829-842.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw047
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    References listed on IDEAS

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    1. Charles F. Manski, 2013. "Identification of treatment response with social interactions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-23, February.
    2. Halloran M. Elizabeth & Hudgens Michael G., 2012. "Causal Inference for Vaccine Effects on Infectiousness," The International Journal of Biostatistics, De Gruyter, vol. 8(2), pages 1-40, January.
    3. VanderWeele, Tyler J. & Tchetgen Tchetgen, Eric J., 2011. "Effect partitioning under interference in two-stage randomized vaccine trials," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 861-869, July.
    4. Xi Luo & Dylan S. Small & Chiang-Shan R. Li & Paul R. Rosenbaum, 2012. "Inference With Interference Between Units in an fMRI Experiment of Motor Inhibition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 530-541, June.
    5. Carolina Perez-Heydrich & Michael G. Hudgens & M. Elizabeth Halloran & John D. Clemens & Mohammad Ali & Michael E. Emch, 2014. "Assessing effects of cholera vaccination in the presence of interference," Biometrics, The International Biometric Society, vol. 70(3), pages 731-741, September.
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