Locally Private Causal Inference

Local differential privacy (LDP) is a differential privacy (DP) paradigm in which individuals first apply a DP mechanism to their data (often by adding noise) before transmiting the result to a curator. LDP ensures strong user privacy protection because the curator does not have access to any of the user's original information. On the curator's side, however, the noise for privacy results in additional bias and variance in their analyses; thus it is of great importance for analysts to incorporate the privacy noise into valid statistical inference. In this article, we develop methodologies to infer causal effects from privatized data under the Rubin Causal Model framework. First, we present asymptotically unbiased and consistent estimators with their variance estimators and plug-in confidence intervals. Second, we develop a Bayesian nonparametric methodology along with a blocked Gibbs sampling algorithm, which performs well in terms of MSE for tight privacy budgets. Finally, we present simulation studies to evaluate the performance of our proposed frequentist and Bayesian methodologies for various privacy budgets, resulting in useful suggestions for performing causal inference for privatized data.