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.
• Unmeasured confounding effects can introduce substantial bias into standard statistical approaches.
• Accurate statistical methods are crucial for reliable gene expression analysis.

Purpose of the Study:

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

Main Methods:

• A novel framework is proposed that disentangles marginal and uncorrelated confounding effects.
• Latent factors and primary effects are jointly estimated using lasso-type optimization.
• Projected and weighted bias-correction steps are incorporated for hypothesis testing.

Main Results:

• The framework establishes identification conditions for various effects and provides non-asymptotic error bounds.
• Effective Type-I error control is demonstrated for asymptotic z-tests.
• Numerical experiments show the method controls the false discovery rate and offers superior power compared to alternatives.

Conclusions:

• The proposed method effectively adjusts for confounding effects, even when significant covariates are not explicitly modeled.
• This approach enhances the reliability of identifying differentially expressed genes in genomic studies.
• The framework is suitable for analyzing complex biological data, such as single-cell RNA-seq counts.