Classification of RNA‐Seq data via Gaussian copulas

Abstract

RNA-sequencing (RNA-Seq) has become a preferred option to quantify gene expression, because it is more accurate and reliable than microarrays. In RNA-Seq experiments, the expression level of a gene is measured by the count of short reads that are mapped to the gene region. Although some normal-based statistical methods may also be applied to log-transformed read counts, they are not ideal for directly modelling RNA-Seq data. Two discrete distributions, Poisson distribution and negative binomial distribution, have been commonly used in the literature to model RNA-Seq data, where the latter is a natural extension of the former with allowance of overdispersion. Because of the technical difficulty in modelling correlated counts, most existing classifiers based on discrete distributions assume that genes are independent of each other. However, as we show in this paper, the independence assumption may cause non-ignorable bias in estimating the discriminant score, making the classification inaccurate. To this end, we drop the independence assumption and explicitly model the dependence between genes using a Gaussian copula. We apply a Bayesian approach to estimate the covariance matrix and the overdispersion parameter in negative binomial distribution. Both synthetic data and real data are used to demonstrate the advantages of our model.

qtQDA: quantile transformed quadratic discriminant analysis for high-dimensional RNA-seq data

“…These data sets are very common in the RNA-seq classification literature (see Witten, 2011;Tan, Petersen & Witten, 2014;Dong et al, 2016;Zhang, 2017). Using these data sets, we also compare the performance of qtQDA to a number of general machine learning classifiers and specialized RNA-seq classifiers (corresponding R packages used for our analysis are listed in brackets): For logistic regression, we use the GLMnet method proposed in Friedman, Hastie & Tibshirani (2010) since this is one of the best representatives of this approach.…”

“…We apply all methods as recommended in their documentation and any "tuning" parameters were chosen with the cross-validation tools provided in the corresponding software package or chosen with our own cross-validation. The Gaussian copula method of Zhang (2017) has no publicly available implementation.…”

“…As Sun & Zhao (2015) have suggested, since the presence of disease, and different disease types, leads to "rewiring" of genetic networks, and hence changes in gene associations, assuming a different covariance matrix for each class is likely to lead to better classifications. Finally, note that while the model specified by the process above is reminiscent of the Gaussian copula model of Zhang (2017), the two models are quite different.…”

“…As with negative binomial parameter estimation, this strategy is implemented using edgeR. Others have adopted essentially the same gene selection strategy, for example, NBLDA, SQDA, and the method of Zhang (2017).…”

“…However, this independence assumption is very unrealistic, since genes are typically involved in networks and pathways, implying that a particular gene's expression level is likely to be correlated with the expression level of other genes. Moreover, some have argued, for example, Zhang (2017), that the assumption of independence has a non-ignorable impact on our ability to classify: it causes bias in estimated discriminant scores, making classification inaccurate. Given this, some have focused on models for the data which incorporate dependence between genes.…”