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Abstract:
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Randomized experiments have been the gold standard to estimate the average causal effect (ACE) of a treatment on a response. However, many randomized experiments assume that participants are willing to share their response to treatment. This assumption, while trivial at first, is becoming difficult to satisfy today where there are more regulations to protect users’ data. The paper presents a simple experimental design that is differentially private, one of the strongest notions of privacy, and proposes unbiased and asymptotically Normal estimators for the ACE; we also present a doubly robust estimator for the ACE. Also, based on ideas from noncompliance in educational testing, our proposed design is robust against “adversarial” participants who may distrust the investigator with their personal data and provide false information. Finally, our design allows individual-level experimental data to be shared for replication without compromising user privacy. We conclude with a simulation study and a differentially private re-analysis of a randomized experiment among patients suffering from post-traumatic stress disorder.
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