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.