Survival analysis under the Cox proportional hazards model with pooled covariates

Privacy-preserving analysis of time-to-event data under nested case-control sampling

Analyses of distributed data networks of rare diseases are constrained by legitimate privacy and ethical concerns. Analytical centers (e.g. research institutions) are thus confronted with the challenging task of obtaining data from recruiting sites that are often unable or unwilling to share personal records of participants. For time-to-event data, recently popularized disclosure techniques with privacy guarantees (e.g., Differentially Private Generative Adversarial Networks) are generally computationally expensive or inaccessible to applied researchers. To perform the widely used Cox proportional hazards regression, we propose an easy-to-implement privacy-preserving data analysis technique by pooling (i.e. aggregating) individual records of covariates at recruiting sites under the nested case-control sampling framework before sharing the pooled nested case-control subcohort. We show that the pooled hazard ratio estimators, under the pooled nested case-control subsamples from the contributing sites, are maximum likelihood estimators and provide consistent estimates of the individual level full cohort HRs. Furthermore, a sampling technique for generating pseudo-event times for individual subjects that constitute the pooled nested case-control subsamples is proposed. Our method is demonstrated using extensive simulations and analysis of the National Lung Screening Trial data. The utility of our proposed approach is compared to the gold standard (full cohort) and synthetic data generated using classification and regression trees. The proposed pooling technique performs to near-optimal levels comparable to full cohort analysis or synthetic data; the efficiency improves in rare event settings when more controls are matched on during nested case-control subcohort sampling.