False Discovery Rate Control via Data Splitting

The systematic comparison between Gaussian mirror and Model-X knockoff models

While the high-dimensional biological data have provided unprecedented data resources for the identification of biomarkers, consensus is still lacking on how to best analyze them. The recently developed Gaussian mirror (GM) and Model-X (MX) knockoff-based methods have much related model assumptions, which makes them appealing for the detection of new biomarkers. However, there are no guidelines for their practical use. In this research, we systematically compared the performance of MX-based and GM methods, where the impacts of the distribution of explanatory variables, their relatedness and the signal-to-noise ratio were evaluated. MX with knockoff generated using the second-order approximates (MX-SO) has the best performance as compared to other MX-based methods. MX-SO and GM have similar levels of power and computational speed under most of the simulations, but GM is more robust in the control of false discovery rate (FDR). In particular, MX-SO can only control the FDR well when there are weak correlations among explanatory variables and the sample size is at least moderate. On the contrary, GM can have the desired FDR as long as explanatory variables are not highly correlated. We further used GM and MX-based methods to detect biomarkers that are associated with the Alzheimer's disease-related PET-imaging trait and the Parkinson's disease-related T-tau of cerebrospinal fluid. We found that MX-based and GM methods are both powerful for the analysis of big biological data. Although genes selected from MX-based methods are more similar as compared to those from the GM method, both MX-based and GM methods can identify the well-known disease-associated genes for each disease. While MX-based methods can have a slightly higher power than that of the GM method, it is less robust, especially for data with small sample sizes, unknown distributions, and high correlations.

Deep neural networks with controlled variable selection for the identification of putative causal genetic variants

Deep neural networks (DNNs) have been successfully utilized in many scientific problems for their high prediction accuracy, but their application to genetic studies remains challenging due to their poor interpretability. Here we consider the problem of scalable, robust variable selection in DNNs for the identification of putative causal genetic variants in genome sequencing studies. We identified a pronounced randomness in feature selection in DNNs due to its stochastic nature, which may hinder interpretability and give rise to misleading results. We propose an interpretable neural network model, stabilized using ensembling, with controlled variable selection for genetic studies. The merit of the proposed method includes: flexible modelling of the nonlinear effect of genetic variants to improve statistical power; multiple knockoffs in the input layer to rigorously control the false discovery rate; hierarchical layers to substantially reduce the number of weight parameters and activations, and improve computational efficiency; and stabilized feature selection to reduce the randomness in identified signals. We evaluate the proposed method in extensive simulation studies and apply it to the analysis of Alzheimer's disease genetics. We show that the proposed method, when compared with conventional linear and nonlinear methods, can lead to substantially more discoveries.