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Two-stage randomized experiments are
becoming an increasingly popular experimental design for causal
inference when the outcome of one unit may be affected by the
treatment assignments of other units in the same cluster. In this
paper, we provide a methodological framework for general tools of
statistical inference and power analysis for two-stage randomized
experiments. Under the randomization-based framework, we consider
the estimation of a new direct effect of interest as well as the
average direct and spillover effects studied in the literature. We
provide unbiased estimators of these causal quantities and their
conservative variance estimators in a general setting. Using these
results, we then develop hypothesis testing procedures and derive
sample size formulas. We theoretically compare the two-stage
randomized design with the completely randomized and cluster
randomized designs, which represent two limiting designs. Finally,
we conduct simulation studies to evaluate the empirical performance
of our sample size formulas. For empirical illustration, the
proposed methodology is applied to the randomized evaluation of the
Indian national health insurance program. An open-source software
package is available for implementing the proposed
methodology. |
Imai, Kosuke, Zhichao Jiang, and Anup
Malani. (2021). ``Causal
Inference with Interference and Noncompliance in Two-Stage
Randomized Experiments.'' Journal of the American
Statistical Association, Vol. 116, No. 534,
pp. 632-644. |
Malani, Anup, Phoebe Holtzman, Kosuke
Imai, Cynthia Kinnan, Morgen Miller, Shailender Swaminathan,
Alessandra Voena, Bartosz Woda, and Gabriella Conti. ``Effect of Health Insurance in India: A
Randomized Controlled Trial.'' |
Chattopadhyay, Ambarish, Kosuke Imai, and
Jose R. Zubizarreta. ``Design-based inference for generalized
network experiments with stochastic interventions.''
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Zhang, Yi and Kosuke Imai. ``Individualized Policy Evaluation and
Learning under Clustered Network Interference.''
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Huang, Karissa, Zhichao Jiang, and Kosuke
Imai. ``RCT2:
Designing and Analyzing Two-Stage Randomized
Experiments.'' available through The Comprehensive R
Archive Network and GitHub.
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