Integrative High Dimensional Multiple Testing with Heterogeneity under Data Sharing Constraints

Identifying informative predictors in a high dimensional regression model is a critical step for association analysis and predictive modeling. Signal detection in the high dimensional setting often fails due to the limited sample size. One approach to improve power is through meta-analyzing multiple studies on the same scientific question. However, integrative analysis of high dimensional data from multiple studies is challenging in the presence of between study heterogeneity. The challenge is even more pronounced with additional data sharing constraints under which only summary data but not individual level data can be shared across different sites. In this paper, we propose a novel data shielding integrative large-scale testing (DSILT) approach to signal detection by allowing between study heterogeneity and not requiring sharing of individual level data. Assuming the underlying high dimensional regression models of the data differ across studies yet share similar support, the DSILT approach incorporates proper integrative estimation and debiasing procedures to construct test statistics for the overall effects of specific covariates. We also develop a multiple testing procedure to identify significant effects while controlling for false discovery rate (FDR) and false discovery proportion (FDP). Theoretical comparisons of the DSILT procedure with the ideal individual--level meta--analysis (ILMA) approach and other distributed inference methods are investigated. Simulation studies demonstrate that the DSILT procedure performs well in both false discovery control and attaining power. The proposed method is applied to a real example on detecting interaction effect of the genetic variants for statins and obesity on the risk for Type 2 Diabetes.