Meta-analyzing multiple omics data with robust variable selection

High-throughput omics data are becoming more and more popular in various areas of science. Given that many publicly available datasets address the same questions, researchers have applied meta-analysis to synthesize multiple datasets to achieve more reliable results for model estimation and prediction. Due to the high dimensionality of omics data, it is also desirable to incorporate variable selection into meta-analysis. Existing meta-analyzing variable selection methods are often sensitive to the presence of outliers, and may lead to missed detections of relevant covariates, especially for lasso-type penalties. In this paper, we develop a robust variable selection algorithm for meta-analyzing high-dimensional datasets based on logistic regression. We first search an outlier-free subset from each dataset by borrowing information across the datasets with repeatedly use of the least trimmed squared estimates for the logistic model and together with a hierarchical bi-level variable selection technique. We then refine a reweighting step to further improve the efficiency after obtaining a reliable non-outlier subset. Simulation studies and real data analysis show that our new method can provide more reliable results than the existing meta-analysis methods in the presence of outliers.