Simultaneous inference for generalized linear models with unmeasured confounders

2080 

Contributed Abstract 

Paper 

Jin-Hong Du (1), Larry Wasserman (2), Kathryn Roeder (2)

(1) Carnegie Mellon University, United States, (2) Carnegie Mellon University, N/A

Larry Wasserman  
Carnegie Mellon University

Kathryn Roeder  
Carnegie Mellon University

Jin-Hong Du  
Carnegie Mellon University

Jin-Hong Du  
Carnegie Mellon University

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 latent coefficients. Then, latent factors and primary effects are jointly estimated by lasso-type optimization. Finally, we incorporate bias-correction steps for hypothesis testing. Theoretically, we establish identification conditions, non-asymptotic error bounds and effective Type-I error control as sample and response sizes approach infinity. 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.

Hidden variables|Surrogate variables analysis|Multivariate response regression|Hypothesis testing| |

IMS

Statistical Methodology