An empirical assessment of differential privacy in real-world observational data: a case-control study of asthma exacerbation in UK Biobank linked with electronic health records

Abstract

Objectives: Electronic health records (EHRs) provide substantial resources for observational studies, yet present significant challenges in safeguarding patient privacy while maintaining research quality. Differential privacy (DP) offers a quantifiable privacy guarantee; however, its impact on observational studies remains underexplored. We empirically evaluated the effects of DP across varying values of its privacy parameter, epsilon, on case-control analysis outcomes using EHR data. This study aims to inform DP parameter selection and examines the influence of study characteristics on differentially private observational studies.

Materials and methods: We assessed the effects of DP on a case-control study of 1-year asthma exacerbations, including 22 165 participants with a history of asthma from UK Biobank linked to EHR data. Odds ratios (ORs) for sociodemographic factors and comorbidities were analyzed using adjusted and propensity score-matched models across epsilon values.

Results: DP influenced the magnitude, direction, and statistical significance of ORs, occasionally resembling patterns of misclassification, residual confounding, and false-positive bias. Rare and imbalanced covariates showed greater OR variability, especially in matched studies. Epsilons smaller than ln(2) led to noticeable OR fluctuations.

Discussion: The impact of DP on ORs and selection of an optimal epsilon depends on sample size, covariate prevalence, confounders, case-to-control ratios in propensity score matching, mitigation of random seed p-hacking, and trust models.

Conclusion: The effects of DP on ORs are highly context-dependent. In this study, epsilon values below ln(2) led to unstable ORs across random seeds. Averaging results or using predetermined seeds may help reduce variability and mitigate p-hacking.

Keywords: case-control studies; differential privacy; matched case-control studies; observational studies; patient data privacy.