Integrative analysis of multiple data sets has the potential of fully leveraging the vast amount of high throughput biological data being generated. In particular such analysis will be powerful in making inference from publicly available collections of genetic, transcriptomic and epigenetic data sets which are designed to study shared biological processes, but which vary in their target measurements, biological variation, unwanted noise, and batch variation. Thus, methods that enable the joint analysis of multiple data sets are needed to gain insights into shared biological processes that would otherwise be hidden by unwanted intra-data set variation. Here, we propose a method called two-stage linked component analysis (2s-LCA) to jointly decompose multiple biologically related experimental data sets with biological and technological relationships that can be structured into the decomposition. The consistency of the proposed method is established and its empirical performance is evaluated via simulation studies. We apply 2s-LCA to jointly analyze four data sets focused on human brain development and identify meaningful patterns of gene expression in human neurogenesis that have shared structure across these data sets.

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