Privacy-preserving and homogeneity-pursuit integrative analysis for high-dimensional censored data

In the analysis of data with a censored survival outcome and high-dimensional covariates, when a single data source has a limited sample size/power, integrative analysis of data from multiple sources can effectively increase sample size and improve estimation and variable selection performance. Under certain circumstances, for example when it is desirable to preserve data privacy, only summary statistics, as opposed to raw data, can be pooled for integrative analysis. In this study, we consider summary statistics-based integrative analysis of multi-source data with a censored survival outcome and high-dimensional covariates under the Cox model. This data setting can be more challenging than many in the literature. We further consider the scenario where some (but not all) covariates have homogeneous effects, and note that properly identifying such homogeneity can lead to more efficient estimation and a deeper understanding of the underlying data generation mechanisms. To this end, we propose a privacy-preserving penalized integrative analysis method, which can simultaneously achieve regularized estimation, variable selection, and homogeneity pursuit. An effective computational algorithm is developed, and asymptotic consistency and distributional properties are rigorously established. Numerical studies, including simulation and the analysis of a bladder cancer data set, convincingly demonstrate the practical effectiveness of the proposed method.