Efficient and model-agnostic parameter estimation under privacy-preserving post-randomization data

Balancing data privacy with public access is critical for sensitive datasets. However, even after de-identification, the data are still vulnerable to, for example, inference attacks (by matching some keywords with external datasets). Statistical disclosure control (SDC) methods offer additional protection, and the post-randomization method (PRAM) adds noise to data to achieve this goal. However, PRAM-perturbed data pose challenges for analysis, as directly using the perturbed data leads to biased parameter estimates. This article addresses parameter estimation when data are perturbed using PRAM for privacy. While existing methods suffer from limitations like being parameter-specific, model-dependent and lacking optimality guarantees, our proposed method overcomes these limitations. Our approach applies to general parameters defined through estimating equations and makes no assumptions about the underlying data model. Furthermore, we prove that the proposed estimator achieves the semiparametric efficiency bound, making it asymptotically optimal in terms of estimation efficiency.