Sparse latent factor regression models for genome-wide and epigenome-wide association studies

Association of phenotypes or exposures with genomic and epigenomic data faces important statistical challenges. One of these challenges is to account for variation due to unobserved confounding factors, such as individual ancestry or cell-type composition in tissues. This issue can be addressed with penalized latent factor regression models, where penalties are introduced to cope with high dimension in the data. If a relatively small proportion of genomic or epigenomic markers correlate with the variable of interest, sparsity penalties may help to capture the relevant associations, but the improvement over non-sparse approaches has not been fully evaluated yet. Here, we present least-squares algorithms that jointly estimate effect sizes and confounding factors in sparse latent factor regression models. In simulated data, sparse latent factor regression models generally achieved higher statistical performance than other sparse methods, including the least absolute shrinkage and selection operator and a Bayesian sparse linear mixed model. In generative model simulations, statistical performance was slightly lower (while being comparable) to non-sparse methods, but in simulations based on empirical data, sparse latent factor regression models were more robust to departure from the model than the non-sparse approaches. We applied sparse latent factor regression models to a genome-wide association study of a flowering trait for the plant Arabidopsis thaliana and to an epigenome-wide association study of smoking status in pregnant women. For both applications, sparse latent factor regression models facilitated the estimation of non-null effect sizes while overcoming multiple testing issues. The results were not only consistent with previous discoveries, but they also pinpointed new genes with functional annotations relevant to each application.