Abstract
DNA methylation and gene expression are interdependent and both implicated in cancer development and progression, with many individual biomarkers discovered. A joint analysis of the two data types can potentially lead to biological insights that are not discoverable with separate analyses. To optimally leverage the joint data for identifying perturbed genes and classifying clinical cancer samples, it is important to accurately model the interactions between the two data types. Here, we present EBADIMEX for jointly identifying differential expression and methylation and classifying samples. The moderated t-test widely used with empirical Bayes priors in current differential expression methods is generalised to a multivariate setting by developing: (1) a moderated Welch t-test for equality of means with unequal variances; (2) a moderated F-test for equality of variances; and (3) a multivariate test for equality of means with equal variances. This leads to parametric models with prior distributions for the parameters, which allow fast evaluation and robust analysis of small data sets. EBADIMEX is demonstrated on simulated data as well as a large breast cancer (BRCA) cohort from TCGA. We show that the use of empirical Bayes priors and moderated tests works particularly well on small data sets.
Funding source: Independent Research Fund Denmark
Award Identifier / Grant number: 7016-00379
Funding source: Sapere Aude
Award Identifier / Grant number: 12-126439
Funding source: Innovation Fund Denmark
Award Identifier / Grant number: 10-092320/DSF
Funding statement: This study was supported by Independent Research Fund Denmark, Grant Number: 7016-00379, Sapere Aude, Grant Number: 12-126439 and Innovation Fund Denmark, Grant Number: 10-092320/DSF.
Appendix
A Statistical notes
A.1 Huber Loss
To limit the influence of a single data type (expression or methylation), when performing classification, we use the Huber Loss instead of the log-density.
If
The Huber-loss function L(x) is linear when x is more than k standard deviations away from μ.
We use k = 2.5 in our data analyses.
A.2 Normalization
Let Rgi denote the raw read count for gene g in sample i. The read counts are scaled by a sample-specific factor and then log-transformed,
We implement two normalization strategies, namely total count (TC) and upper-quartile (UQ). In TC normalization we normalize with the total library size of the specific sample, i.e.
In UQ normalization we set Ki equal to the upper-quartile of the set
A.3 Filtering
We filter out lowly-expressed genes using a method outlined in Ding et al. (2015). For all genes we compute a specified quantile (by default the median, q = 0.5). Typically, a large group of genes display low median expression (Supplementary Figure S6). Based on a histogram we could dichotomize into two groups by manually setting a threshold. The selection of this threshold can be aided by fitting a two component normal mixture to the data: The genes having a posterior probability of belonging to the lowly expressed class larger than a half are not considered in subsequent analysis.
A.4 Kullback-Leibler divergence
Kullback-Leibler divergence can be used as an alternative ranking criterion to p-values. The Kullback-Leibler divergence between two normal distributions
More generally, for a multivariate normal, we have
B R-package
All functionality of EBADIMEX is implemented as an R-package. The package, with accompanying tutorial, is available at https://github.com/TobiasMadsen/EBADIMEX.
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Supplementary Material
The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/sagmb-2018-0050).
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