DeepNull: an open-source method to improve the discovery power of genetic association studies

Friday, January 14, 2022

In our paper “DeepNull models non-linear covariate effects to improve phenotypic prediction and association power,” we proposed a new method, DeepNull, to model the complex relationship between covariate effects on phenotypes to improve Genome-wide association studies (GWAS) results. We have released DeepNull as open source software, with a Colab notebook tutorial for its use.

Human Genetics 101

Each individual’s genetic data carries health information such as why certain individuals have a lower risk of developing skin cancer compared to others or why certain drugs differ in effectiveness between individuals. Genetic data is encoded in the human genome—a DNA sequence—composed of a 3 billion long chain built from four possible nucleotides (A, C, G, and T). Only a small subset of the genome (~4-5 million positions) varies between two individuals. One of the goals of genetic studies is to detect variants that are associated with different phenotypes (e.g., risk of diseases such as Glaucoma or observed phenotypic values such as high-density lipoprotein (HDL), low-density lipoproteins (LDL), height, etc).

Genome-wide association studies

GWAS are used to associate genetic variants with complex traits and diseases. To more accurately determine an association strength between genotype and phenotype, the interactions between phenotypes (such as age and sex) and principal components (PCs) of genotypes, must be adjusted for as covariates. Covariate adjustment in GWAS can increase precision and correct for confounding. In the linear model setting, adjustment for a covariate will improve precision (i.e., statistical power) if the distribution of the phenotype differs across levels of the covariate. For example, when performing GWAS on height, males and females have different means. All state of the art methods (e.g., BOLT-LMM, regenie) perform GWAS assuming that the effect of genotypes and covariates to phenotype is linear and additive. However, we know that the assumption of linear and additive contributions of covariates often does not reflect underlying biology, so we sought a method to more comprehensively model and adjust for the interactions between phenotypes for GWAS.

DeepNull method overview

We proposed a new method, DeepNull, to relax the linear assumption of covariate effects on phenotypes. DeepNull trains a deep neural network (DNN) to predict phenotype using all covariates in a 5-fold cross-validation. After training the DeepNull model, we make phenotype predictions for all individuals and add this prediction as one additional covariate in the association test. Major advantages of DeepNull are its simplicity to use and that it requires only a minimal change to existing GWAS pipeline implementations. In other words, to use DeepNull, we just need to add one additional covariate, which is computed by DeepNull, to the existing pipeline to perform GWAS.

DeepNull improves statistical power

We simulated data under different genetic architectures (genetic conditions) to first check that DeepNull controls type I error and then compare DeepNull statistical power with current state of the art methods (hereafter referred to as “Baseline”). First, we simulated data under genetic architectures where covariates have a linear effect on phenotype and observed that both Baseline and DeepNull have tight control of type I error. It is interesting that DeepNull power does not decrease compared to Baseline under a setting in which covariates have only a linear effect on phenotype. Next, we simulated data under genetic architectures where covariates have non-linear effects on phenotype. Both Baseline and DeepNull have tight control of type I error while DeepNull increases the statistical power depending on the genetic architecture. We observed that for certain genetic architectures, DeepNull increases the statistical power up to 20%. Below, we compare the -log p-value of test statistics computed from DeepNull versus Baseline for Apolipoprotein B (ApoB) levels obtained from UK Biobank:
Figure 1. Significance level comparison of DeepNull vs Baseline. X-axis is the -log p-value of Baseline and Y-axis is the -log p-value of DeepNull. The orange dots indicate variants that are significant for Baseline but not significant for DeepNull and green dots indicate variants that are significant for DeepNull but not significant for Baseline.

DeepNull improves phenotype prediction

We applied DeepNull to predict phenotypes by utilizing polygenic risk score (PRS) and existing covariates such as age and sex. We considered 10 phenotypes obtained from UK Biobank. We observed that DeepNull on average increased the phenotype prediction (R2 where R is Pearson correlation) by 23%. More strikingly, in the case of Glaucoma, referral probability that is computed from the fundus images (Phene et al. Ophthalmology 2019, Alipanahi et al AJHG 2021), DeepNull improves the phenotype prediction by 83.4% and in the case of LDL, DeepNull improves the phenotype prediction by 40.3%. The summary of DeepNull results versus Baseline are shown in figure 2 below:


Figure 2. DeepNull improves phenotype prediction compared to Baseline. The Y-axis is the R2 where R is the Pearson’s correlation between true and predicted value of phenotypes. Phenotypic abbreviations: alkaline phosphatase (ALP), alanine aminotransferase (ALT), aspartate aminotransferase (AST), apolipoprotein B (ApoB), glaucoma referral probability (GRP), LDLcholesterol (LDL), sex hormone-binding globulin (SHBG), and triglycerides (TG).


We proposed a new framework, DeepNull, that can model the nonlinear effect of covariates on phenotypes when such nonlinearity exists. We show that DeepNull can substantially improve phenotype prediction. In addition, we show that DeepNull achieves results similar to a standard GWAS when the effect of covariate on the phenotype is linear and can significantly outperform a standard GWAS when the covariate effects are nonlinear. DeepNull is open source and is available for download from GitHub or installation via PyPI.

By Farhad Hormozdiari and Andrew Carroll – Genomics team in HealthAI


This blog summarizes the work of the following Google contributors, who we would like to thank: Zachary R. McCaw, Thomas Colthurst, Ted Yun, Nick Furlotte, Babak Alipanahi, and Cory Y. McLean. In addition, we would like to thank Alkes Price, Babak Behsaz, and Justin Cosentino for their invaluable comments and suggestions.