Jiang, Zhichao, Kosuke Imai, and Anup Malani. (2023). ``Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments.'' Biometrics, Vol. 79, No. 3 (September), pp. 2370-2381.
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. |
Malani, Anup, Cynthia Kinnan, Gabriella Conti, Kosuke Imai, Morgen Miller, Shailender Swaminathan, Alessandra Voena, and Bartosz Woda
``Evaluating and Pricing Health Insurance in Lower-Income Countries: A Field Experiment in India.''
American Economic Journal: Economic Policy, Forthcoming.
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Zhou, Lingxiao, Kosuke Imai, Jason Lyall, and Georgia Papadogeorgou
(2026).
``Dynamic Policy Evaluation and Learning with Spatio-temporal Data.''
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Lo, Adeline, Santiago Olivella, and Kosuke Imai
(2026).
``A Statistical Model of Bipartite Networks: Application to Cosponsorship in the United States Senate.''
Political Analysis, Vol. 34, No. 3 (July 2026), pp. 451-470.
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Sengupta, Souhardya, Kosuke Imai, and Georgia Papadogeorgou
(2025).
``Low-rank Covariate Balancing Estimators under Interference.''
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Chattopadhyay, Ambarish, Kosuke Imai, and Jose R. Zubizarreta
(2024).
``Design-based inference for generalized network experiments with stochastic interventions.''
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Bertsimas, Dimitris, Kosuke Imai, and Michael Lingzhi Li
(2023).
``Distributionally Robust Causal Inference with Observational Data.''
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Olivella, Santiago, Tyler Pratt, and Kosuke Imai
(2022).
``Dynamic Stochastic Blockmodel Regression for Network Data: Application to International Militarized Conflicts.''
Journal of the American Statistical Association, Vol. 117, No. 539, pp. 1068-1081.
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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.
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Imai, Kosuke, and Zhichao Jiang
(2020).
``Identification and Sensitivity Analysis of Contagion Effects in Randomized Placebo-Controlled Trials.''
Journal of the Royal Statistical Society, Series A (Statistics in Society), Vol. 183, No. 4 (October), pp. 1637-1657.
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Kim, In Song, Steven Liao, and Kosuke Imai
(2020).
``Measuring Trade Profile with Granular Product-level Trade Data.''
American Journal of Political Science, Vol. 64, No. 1 (January), pp. 102-117.
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