Efficient Variant Set Mixed Model Association Tests for Continuous and Binary Traits in Large-Scale Whole-Genome Sequencing Studies

Abstract

With advances in whole-genome sequencing (WGS) technology, more advanced statistical methods for testing genetic association with rare variants are being developed. Methods in which variants are grouped for analysis are also known as variant-set, gene-based, and aggregate unit tests. The burden test and sequence kernel association test (SKAT) are two widely used variant-set tests, which were originally developed for samples of unrelated individuals and later have been extended to family data with known pedigree structures. However, computationally efficient and powerful variant-set tests are needed to make analyses tractable in large-scale WGS studies with complex study samples. In this paper, we propose the variant-set mixed model association tests (SMMAT) for continuous and binary traits using the generalized linear mixed model framework. These tests can be applied to large-scale WGS studies involving samples with population structure and relatedness, such as in the National Heart, Lung, and Blood Institute's Trans-Omics for Precision Medicine (TOPMed) program. SMMATs share the same null model for different variant sets, and a virtue of this null model, which includes covariates only, is that it needs to be fit only once for all tests in each genome-wide analysis. Simulation studies show that all the proposed SMMATs correctly control type I error rates for both continuous and binary traits in the presence of population structure and relatedness. We also illustrate our tests in a real data example of analysis of plasma fibrinogen levels in the TOPMed program (n = 23,763), using the Analysis Commons, a cloud-based computing platform.

Keywords: TOPMed; generalized linear mixed model; population structure; rare variants; relatedness; variant set association test; whole-genome sequencing.

Figure 1

Map of Spatially Continuous Populations from Which Genotypes Were Simulated Based on the Coalescent Model (A) Map for a single-cohort simulation study: the top left 10 × 10 grid formed population 1, and the rest formed population 2. (B) Map for a meta-analysis simulation study: scenario A studies were unrelated individuals sampled from population 1 only; scenario B studies were related individuals sampled from specific regions in population 1 and population 2; scenario C studies were unrelated individuals sampled from specific regions in population 1 and population 2; and scenario D studies were related individuals sampled from specific regions in population 2 only.

Figure 2

Quantile-Quantile Plots of SMMAT-B, SMMAT-S, SMMAT-O, and SMMAT-E in the Analysis of 10,000 Samples in Single-Cohort Studies with Both Population Structure and Cryptic Relatedness, under the Null Hypothesis of No Genetic Association (A) Continuous traits in linear mixed models. (B) Binary traits in logistic mixed models.

Figure 3

Quantile-Quantile Plots of SMMAT-B, SMMAT-S, SMMAT-O, and SMMAT-E in the Meta-analysis of 12 Studies with a Total Sample Size of 12,000, under the Null Hypothesis of No Genetic Association (A) Continuous traits in linear mixed models, all studies in the same group. (B) Binary traits in logistic mixed models, all studies in the same group. (C) Continuous traits in linear mixed models, scenario A, B, C, and D studies in four separate groups. (D) Binary traits in logistic mixed models, scenario A, B, C, and D studies in four separate groups.

Figure 4

Empirical Power of Linear Mixed Model-Based SMMAT-B, SMMAT-S, SMMAT-O, SMMAT-E, and GLMM-MiST in Continuous Trait Analysis of 2,000, 5,000, and 10,000 Samples (A–C) 10% causal variants with 100% (A), 80% (B), or 50% (C) negative effects. (D–F) 20% causal variants with 100% (D), 80% (E), or 50% (F) negative effects. (G–I) 50% causal variants with 100% (G), 80% (H), or 50% (I) negative effects. Effect sizes were simulated using the same parameter in each row, but different across rows.

Figure 5

Empirical Power of Logistic Mixed Model-Based SMMAT-B, SMMAT-S, SMMAT-O, SMMAT-E, and GLMM-MiST in Binary Trait Analysis of 2,000, 5,000, and 10,000 Samples (A–C) 10% causal variants with 100% (A), 80% (B), or 50% (C) negative effects. (D–F) 20% causal variants with 100% (D), 80% (E), or 50% (F) negative effects. (G–I) 50% causal variants with 100% (G), 80% (H), or 50% (I) negative effects. Effect sizes were simulated using the same parameter in each row, but different across rows.

Figure 6

TOPMed Fibrinogen Level SMMAT Analysis Results via a Heteroscedastic Linear Mixed Model on Rare Variants with MAF < 5% in Non-overlapping 4 kb Sliding Windows on Chromosome 4 (n = 23,763) (A) Quantile-quantile plot. (B) p values on the log scale versus physical positions of the windows on chromosome 4 (build hg38).