Recent advances in next-generation sequencing technology have yielded huge amounts of transcriptomic data. The discreteness and the high dimensions of RNA-seq data have posed great challenges in biological network analysis. Although estimation theories for high-dimensional modified Poisson-type graphical models have been proposed for the network analysis of count-valued data, the statistical inference of these models is still largely unknown. We herein propose a two-step procedure in both edgewise and global statistical inference of these modified Poisson-type graphical models using a cutting-edge generalized low-dimensional projection approach for bias correction. Extensive simulations and a real example with ground truth illustrate asymptotic normality of edgewise inference and more accurate inferential results in multiple testing compared to the sole estimation and the inferential method under normal assumption. Furthermore, the application of our method to novel RNA-seq data of childhood atopic asthma in Puerto Ricans demonstrates more biologically meaningful results compared to the sole estimation and the inferential methods based on Gaussian and nonparanormal graphical models.
The first and second authors were supported in part by NSF Grant DMS-1812030.
The third and fourth authors were supported by NIH Grants HL079966, HL117191, and MD011764.
The authors are grateful to the four anonymous referees, an Associate Editor and the Editor for their highly valuable comments that improved the quality of this paper.
"Inference of large modified Poisson-type graphical models: Application to RNA-seq data in childhood atopic asthma studies." Ann. Appl. Stat. 15 (2) 831 - 855, June 2021. https://doi.org/10.1214/20-AOAS1413