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.

Reader reaction to "Outcome-adaptive lasso: Variable selection for causal inference" by Shortreed and Ertefaie (2017).

Shortreed and Ertefaie introduced a clever propensity score variable selection approach for estimating average causal effects, namely, the outcome adaptive lasso (OAL). OAL aims to select desirable covariates, confounders, and predictors of outcome, to build an unbiased and statistically efficient propensity score estimator. Due to its design, a potential limitation of OAL is how it handles the collinearity problem, which is often encountered in high-dimensional data. As seen in Shortreed and Ertefaie, OAL's performance degraded with increased correlation between covariates. In this note, we propose the generalized OAL (GOAL) that combines the strengths of the adaptively weighted L1 penalty and the elastic net to better handle the selection of correlated covariates. Two different versions of GOAL, which differ in their procedure (algorithm), are proposed. We compared OAL and GOAL in simulation scenarios that mimic those examined by Shortreed and Ertefaie. Although all approaches performed equivalently with independent covariates, we found that both GOAL versions were more performant than OAL in low and high dimensions with correlated covariates.