Promoting Similarity of Sparsity Structures in Integrative Analysis with Penalization

Abstract: For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of pooling information and outperforms single-dataset analysis and some alternative multi-datasets approaches including meta-analysis. Under certain scenarios, multiple datasets are expected to share common important covariates, that is, the multiple models have similarity in sparsity structures. However, the existing methods do not have a mechanism to {\it promote} the similarity of sparsity structures in integrative analysis. In this study, we consider penalized variable selection and estimation in integrative analysis. We develop an $L_0$-penalty based approach, which is the first to explicitly promote the similarity of sparsity structures. Computationally it is realized using a coordinate descent algorithm. Theoretically it has the much desired consistency properties. In simulation, it significantly outperforms the competing alternative when the models in multiple datasets share common important covariates. It has better or similar performance as the alternative when the sparsity structures share no similarity. Thus it provides a "safe" choice for data analysis. Applying the proposed method to three lung cancer datasets with gene expression measurements leads to models with significantly more similar sparsity structures and better prediction performance.