2023/09/13 by Jin‐Hong Du, Larry Wasserman, Du, Jin-Hong +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Biological sciences #FOS: Computer and information sciences #Gene expression and cancer classification #Genomics (q-bio.GN) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Single-cell and spatial transcriptomics #Statistical Methods and Inference
paper · doi:10.48550/arxiv.2309.07261
openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially biased. This paper investigates the large-scale hypothesis testing problem for multivariate generalized linear models in the presence of confounding effects. Under arbitrary confounding mechanisms, we propose a unified statistical estimation and inference framework that harnesses orthogonal structures and integrates linear projections into three key stages. It begins by disentangling marginal and uncorrelated confounding effects to recover the latent coefficients. Subsequently, latent factors and primary effects are jointly estimated through lasso-type optimization. Finally, we incorporate projected and weighted bias-correction steps for hypothesis testing. Theoretically, we establish the identification conditions of various effects and non-asymptotic error bounds. We show effective Type-I error control of asymptotic z-tests as sample and response sizes approach infinity. Numerical experiments demonstrate that the proposed method controls the false discovery rate by the Benjamini-Hochberg procedure and is more powerful than alternative methods. By comparing single-cell RNA-seq counts from two groups of samples, we demonstrate the suitability of adjusting confounding effects when significant covariates are absent from the model.