FaStaNMF: a Fast and Stable Non-negative Matrix Factorization for Gene Expression.

Gene expression analysis of samples with mixed cell types only provides limited insight to the characteristics of specific tissues. In silico deconvolution can be applied to extract cell type specific expression, thus avoiding prohibitively expensive techniques such as cell sorting or single-cell sequencing. Non-negative matrix factorization (NMF) is a deconvolution method shown to be useful for gene expression data, in part due to its constraint of non-negativity. Unlike other methods, NMF provides the capability to deconvolve without prior knowledge of the components of the model. However, NMF is not guaranteed to provide a globally unique solution. In this work, we present FaStaNMF, a method that balances achieving global stability of the NMF results, which is essential for inter-experiment and inter-lab reproducibility, with accuracy and speed. Results: FaStaNMF was applied to four datasets with known ground truth, created based on publicly available data or by using our simulation infrastructure, RNAGinesis. We assessed FaStaNMF on three criteria - speed, accuracy, and stability, and it favorably compared to the standard approach of achieving reproduceable results with NMF. We expect that FaStaNMF can be applied successfully to a wide array of biological data, such as different tumor/immune and other disease microenvironments.

Examining the rare disease assumption used to justify HWE testing with control samples.

Many statistical methods for analyzing genetic data, such as those used in genome-wide association studies, assume Hardy-Weinberg Equilibrium (HWE). Therefore, to use such methods, one must check whether the HWE assumption is valid. For a case-control study, researchers have recognized that Hardy Weinberg proportions will be distorted if the marker being tested happens to be associated with the disease. To alleviate this problem, many studies carry out HWE testing on controls only. A number of papers in the literature have justified this practice by making the rare disease assumption without providing rigorous theoretical basis for this justification. Even though many of the diseases studied today are common, whether it is justifiable to use controls to test for HWE when the disease is indeed rare remains an outstanding issue. In this study, we address the rare disease assumption as well as potential problems associated with testing for HWE using controls only, regardless of the prevalence of the disease. We carried out theoretical derivations and numerical studies; the latter were performed using simulated genotypes as well as data from the 1000 Genomes Project. The results from our study are striking: the type I error can be severely inflated, regardless of whether the disease being investigated is rare or common. This study shows that, based on the common practice of using controls only to test for HWE, many genetic variants will be discarded erroneously, wasting valuable information and hindering the ability to detect disease-associated variants.