Linear mixed models have attracted considerable recent attention as a powerful and effective tool for accounting for population stratification and relatedness in genetic association tests. However, existing methods for exact computation of standard test statistics are computationally impractical for even moderate-sized genome-wide association studies. To deal with this several approximate methods have been proposed. Here, we present an efficient exact method that makes these approximations unnecessary in many settings. This method is roughly n times faster than the widely-used exact method EMMA, where n is the sample size, making exact genome-wide association analysis computationally practical for large numbers of individuals.

Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling in genome-wide association studies. These two approaches make very different assumptions, so are expected to perform well in different situations. However, in practice, for a given dataset one typically does not know which assumptions will be more accurate. Motivated by this, we consider a hybrid of the two, which we refer to as a “Bayesian sparse linear mixed model” (BSLMM) that includes both these models as special cases. We address several key computational and statistical issues that arise when applying BSLMM, including appropriate prior specification for the hyper-parameters and a novel Markov chain Monte Carlo algorithm for posterior inference. We apply BSLMM and compare it with other methods for two polygenic modeling applications: estimating the proportion of variance in phenotypes explained (PVE) by available genotypes, and phenotype (or breeding value) prediction. For PVE estimation, we demonstrate that BSLMM combines the advantages of both standard LMMs and sparse regression modeling. For phenotype prediction it considerably outperforms either of the other two methods, as well as several other large-scale regression methods previously suggested for this problem. Software implementing our method is freely available from http://stephenslab.uchicago.edu/software.html.

Multivariate linear mixed models (mvLMMs) are powerful tools for testing SNP associations with multiple correlated phenotypes while controlling for population stratification in genome-wide association studies. We present computationally-efficient algorithms for fitting mvLMMs and computing likelihood ratio tests that improve on existing approximate methods in i) computation speed, ii) power/p value calibration, iii) ability to deal with more than two phenotypes. We illustrate these features on real and simulated data.

Identifying genes that display spatial expression pattern in spatially resolved transcriptomic studies is an important first step towards characterizing the spatial transcriptomic landscape of complex tissues. Here, we developed a statistical method, SPARK, for identifying such spatially expressed genes in data generated from various spatially resolved transcriptomic techniques. SPARK directly models spatial count data through the generalized linear spatial models. It relies on newly developed statistical formulas for hypothesis testing, providing effective type I error control and yielding high statistical power. With a computationally efficient algorithm based on penalized quasi-likelihood, SPARK is also scalable to data sets with tens of thousands of genes measured on tens of thousands of samples. In four published spatially resolved transcriptomic data sets, we show that SPARK can be up to ten times more powerful than existing methods, revealing new biology in the data that otherwise cannot be revealed by existing approaches.

Spatial transcriptomic studies are becoming increasingly common and large, posing important statistical and computational challenges for many analytic tasks. Here, we present SPARK-X, a non-parametric method for rapid and effective detection of spatially expressed genes in large spatial transcriptomic studies. SPARK-X not only produces effective type I error control and high power but also brings orders of magnitude computational savings. We apply SPARK-X to analyze three large datasets, one of which is only analyzable by SPARK-X. In these data, SPARK-X identifies many spatially expressed genes including those that are spatially expressed within the same cell type, revealing new biological insights.

Many spatially resolved transcriptomic technologies do not have single-cell resolution but measure the average gene expression for each spot from a mixture of cells of potentially heterogeneous cell types. Here, we introduce a deconvolution method, conditional autoregressive deconvolution (CARD), that combines cell type–specific expression information from single-cell RNA sequencing (scRNA-seq) with correlation in cell type composition across tissue locations. Modeling spatial correlation allows us to borrow the cell-type composition information across locations, improving accuracy of deconvolution even with a mismatched scRNA-seq reference. CARD can also impute cell type compositions and gene expression levels at unmeasured tissue locations, enable the construction of a refined spatial tissue map with a resolution arbitrarily higher than that measured in the original study, and perform deconvolution without a scRNA-seq reference. Applications to four datasets including a pancreatic cancer dataset identified multiple cell types and molecular markers with distinct spatial localization that define the progression, heterogeneity, and compartmentalization of pancreatic cancer.

Gene-by-environment (GxE) interactions determine common disease risk factors and biomedically relevant complex traits. However, quantifying how the environment modulates genetic effects on human quantitative phenotypes presents unique challenges. Environmental covariates are complex and difficult to measure and control at the organismal level, as found in GWAS and epidemiological studies. An alternative approach focuses on the cellular environment using in vitro treatments as a proxy for the organismal environment. These cellular environments simplify the organism-level environmental exposures to provide a tractable influence on subcellular phenotypes, such as gene expression. Expression quantitative trait loci (eQTL) mapping studies identified GxE interactions in response to drug treatment and pathogen exposure. However, eQTL mapping approaches are infeasible for large-scale analysis of multiple cellular environments. Recently, allele-specific expression (ASE) analysis emerged as a powerful tool to identify GxE interactions in gene expression patterns by exploiting naturally occurring environmental exposures. Here we characterized genetic effects on the transcriptional response to 50 treatments in five cell types. We discovered 1455 genes with ASE (FDR < 10%) and 215 genes with GxE interactions. We demonstrated a major role for GxE interactions in complex traits. Genes with a transcriptional response to environmental perturbations showed sevenfold higher odds of being found in GWAS. Additionally, 105 genes that indicated GxE interactions (49%) were identified by GWAS as associated with complex traits. Examples include GIPR-caffeine interaction and obesity and include LAMP3-selenium interaction and Parkinson disease. Our results demonstrate that comprehensive catalogs of GxE interactions are indispensable to thoroughly annotate genes and bridge epidemiological and genomewide association studies.

Epistasis, commonly defined as the interaction between multiple genes, is an important genetic component underlying phenotypic variation. Many statistical methods have been developed to model and identify epistatic interactions between genetic variants. However, because of the large combinatorial search space of interactions, most epistasis mapping methods face enormous computational challenges and often suffer from low statistical power due to multiple test correction. Here, we present a novel, alternative strategy for mapping epistasis: instead of directly identifying individual pairwise or higher-order interactions, we focus on mapping variants that have non-zero marginal epistatic effects—the combined pairwise interaction effects between a given variant and all other variants. By testing marginal epistatic effects, we can identify candidate variants that are involved in epistasis without the need to identify the exact partners with which the variants interact, thus potentially alleviating much of the statistical and computational burden associated with standard epistatic mapping procedures. Our method is based on a variance component model, and relies on a recently developed variance component estimation method for efficient parameter inference and p-value computation. We refer to our method as the “MArginal ePIstasis Test”, or MAPIT. With simulations, we show how MAPIT can be used to estimate and test marginal epistatic effects, produce calibrated test statistics under the null, and facilitate the detection of pairwise epistatic interactions. We further illustrate the benefits of MAPIT in a QTL mapping study by analyzing the gene expression data of over 400 individuals from the GEUVADIS consortium.