Simultaneous inference for generalized linear models with unmeasured confounders.

Area of Science:

• Genomics
• Statistical Genetics
• Bioinformatics

Background:

• Genomic studies often involve tens of thousands of simultaneous hypothesis tests to identify differentially expressed genes.
• Standard statistical approaches can be substantially biased due to unmeasured confounding effects.
• Accurate statistical inference is crucial for reliable identification of gene expression differences.

Purpose of the Study:

• To develop a unified statistical framework for large-scale hypothesis testing in multivariate generalized linear models with confounding effects.
• To address the challenge of unmeasured confounders in genomic data analysis.
• To improve the accuracy and power of identifying differentially expressed genes.

Main Methods:

• A novel framework using orthogonal structures and linear projections is proposed.
• The method disentangles confounding effects, jointly estimates latent factors and primary effects via lasso-type optimization.
• Bias-correction steps are incorporated for hypothesis testing, with theoretical guarantees on identification and error bounds.

Main Results:

• The proposed method demonstrates effective Type-I error control for asymptotic z-tests.
• Numerical experiments show the method controls the false discovery rate and offers increased power compared to alternatives.
• Application to single-cell RNA-seq data validates its suitability for adjusting confounding effects, even without explicit covariates.

Conclusions:

• The developed statistical framework provides a robust solution for hypothesis testing in the presence of arbitrary confounding mechanisms.
• The method enhances the reliability of findings in large-scale genomic studies.
• It offers a practical approach for adjusting confounding effects in complex biological data.