# Two-stage Hypothesis Tests for Variable Interactions with FDR Control

arXiv: https://arxiv.org/abs/2209.00077 · HTML: https://mlsanity.com/paper/2209.00077/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 31 Aug 2022.

## Builds on (most cited first, 6 of 6)

- [Gaussian Graphical Model Estimation with False Discovery Rate Control](https://mlsanity.com/paper/1306.0976/) (2013)
- [Hierarchical Sparse Modeling: A Choice of Two Group Lasso Formulations](https://mlsanity.com/paper/1512.01631/) (2015)
- [Innovated interaction screening for high-dimensional nonlinear classification](https://mlsanity.com/paper/1501.01029/) (2015)
- [High-dimensional Interactions Detection with Sparse Principal Hessian Matrix](https://mlsanity.com/paper/1901.07970/) (2019)
- [RaSE: A Variable Screening Framework via Random Subspace Ensembles](https://mlsanity.com/paper/2102.03892/) (2021)
- [Paired Test of Matrix Graphs and Brain Connectivity Analysis](https://mlsanity.com/paper/1908.08095/) (2019)

## Abstract (arXiv)

In many scenarios such as genome-wide association studies where dependences between variables commonly exist, it is often of interest to infer the interaction effects in the model. However, testing pairwise interactions among millions of variables in complex and high-dimensional data suffers from low statistical power and huge computational cost. To address these challenges, we propose a two-stage testing procedure with false discovery rate (FDR) control, which is known as a less conservative multiple-testing correction. Theoretically, the difficulty in the FDR control dues to the data dependence among test statistics in two stages, and the fact that the number of hypothesis tests conducted in the second stage depends on the screening result in the first stage. By using the Cram'er type moderate deviation technique, we show that our procedure controls FDR at the desired level asymptotically in the generalized linear model (GLM), where the model is allowed to be misspecified. In addition, the asymptotic power of the FDR control procedure is rigorously established. We demonstrate via comprehensive simulation studies that our two-stage procedure is computationally more efficient than the classical BH procedure, with a comparable or improved statistical power. Finally, we apply the proposed method to a bladder cancer data from dbGaP where the scientific goal is to identify genetic susceptibility loci for bladder cancer.