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A key
methodological challenge in observational studies with interference
between units is twofold: (1) each unit's outcome may depend on many
others' treatments, and (2) treatment assignments may exhibit
complex dependencies across units. We develop a general statistical
framework for constructing robust causal effect estimators to
address these challenges. We first show that, without restricting
the patterns of interference, the standard inverse probability
weighting (IPW) estimator is the only uniformly unbiased estimator
when the propensity score is known. In contrast, no estimator has
such a property if the propensity score is unknown. We then
introduce a low-rank structure of potential outcomes as a
broad class of structural assumptions about interference. This
framework encompasses common assumptions such as anonymous,
nearest-neighbor, and additive interference, while flexibly allowing
for more complex study-specific interference assumptions. Under this
low-rank assumption, we show how to construct an unbiased weighting
estimator for a large class of causal estimands. The proposed
weighting estimator does not require knowledge of true propensity
scores and is therefore robust to unknown treatment assignment
dependencies that often exist in observational studies. If the true
propensity score is known, we can obtain an unbiased estimator that
is more efficient than the IPW estimator by leveraging a low-rank
structure. We establish the finite sample and asymptotic properties
of the proposed weighting estimator, develop a data-driven procedure
to select among candidate low-rank structures, and validate our
approach through simulation and empirical studies. |
Imai, Kosuke and Marc
Ratkovic. (2014). ``Covariate
Balancing Propensity Score.'' Journal of the Royal
Statistical Society, Series B (Statistical Methodology),
Vol. 76, No. 1 (January), pp. 243-263.
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Imai, Kosuke and Marc
Ratkovic. (2015). ``Robust Estimation
of Inverse Probability Weights for Marginal Structural
Models.'' Journal of the American Statistical
Association, Vol. 110, No. 511 (September), pp. 1013-1023.
(lead article)
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Fong, Christian, Chad Hazlett, and Kosuke
Imai. (2018). ``Covariate Balancing
Propensity Score for a Continuous Treatment: Application to the
Efficacy of Political Advertisements.'' Annals of
Applied Statistics, Vol. 12, No. 1,
pp. 156-177.
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Ning, Yang, Sida Peng, and Kosuke
Imai. (2020). ``Robust Estimation
of Causal Effects via High-Dimensional Covariate Balancing
Propensity Score..'' Biometrika, Vol. 107,
No. 3 (September), pp. 533-554. |
Fan, Jianqing, Kosuke Imai, Inbeom Lee, Han
Liu, Yang Ning, and Xiaolin Yang. (2023). ``Optimal Covariate Balancing Conditions
in Propensity Score Estimation.'' Journal of
Business & Economic Statistics, Vol. 41, No. 1,
pp. 97-110. |