De-biased Distribution Estimation for Locally Differential Private Survival Data

Sharing time-to-event data can leak sensitive information about individual participants in clinical studies. To protect the privacy of data, differential privacy (DP) framework offers rigorous protection for data sharing. The local variant of differential privacy is particularly appealing because each record is perturbed before it leaves the data owner or contributor. However, the injected perturbation distorts the true distribution of the source data, yielding low utility and invalid statistical inference with the released data. In this work, we propose a nonparametric estimator for the true survivor function via the deconvolution kernel function with locally differential private (LDP) right-censored survival data in which both the event times and the event indicators are privatized. Our estimator simultaneously de-biases the perturbation applied to the times and the errors induced by flipping the event indicators due to LDP. Theoretically, we establish the uniform consistency and point-wise asymptotic normality of the de-biased distribution estimator, and derive its uniform convergence rate together with the optimal bandwidth attaining that rate. Simulation studies and the analysis of a semi-synthetic dataset generated from the METABRIC breast cancer cohort demonstrate the performance of the proposed estimator across privacy budgets, censoring levels, and sample sizes. By the post-processing property of DP, the proposed de-biased estimator inherits the privacy guarantee while restoring valid inference on the survivor function.