## 1. Introduction

### 1.1 Motivation for Developing Oncomix

The advent of large, well-curated databases, such as the genomic data commons, that contain RNA sequencing data from hundreds of patient tumors has made it possible to identify oncogene candidates solely based off of patterns present in mRNA expression data. Oncomix is the first method developed to identify oncogenes in a visually-interpretable manner from RNA-sequencing data in large cohorts of patients.

Oncomix is an R package for identifying oncogene candidates based off of 2-component Gaussian mixture models. It estimates parameters using the expectation maximization procedure as implemented in the R package mclust. This tutorial will demonstrate how to identify oncogene candidates from a set of mRNA sequencing data. We start by loading the package:

#devtools::install_github("dpique/oncomix", build_vignettes=T)
library(oncomix)

### 1.2 Distribution of Oncogene mRNA Expression

We first explore the idea of what the distribution of gene expression values for a oncogene should look like. It is known that oncogenes such as ERBB2 are overexpressed in 15-20% of all breast cancer patients. In addition, oncogenes should not be expressed in normal tissue. Based on this line of reasoning, we formulate a model for the distribution of oncogene mRNA expression values in a population of both tumor (teal curves) and normal (red-orange curves) tissue:

library(ggplot2)
oncoMixIdeal()

The x-axis represents mRNA expression values, with lower values toward the left and larger values (i.e. higher expression) toward the right. The y axis represents density. The teal curves represent the best-fitting Gaussian probability distribution (PD) over expression values from a single gene obtained from multiple tumor samples. The red-orange curves represent the PD over expression values from the same gene obtained from multiple adjacent normal tissue samples. This mixture model is applied once to the tumor data and again (separately) to the adjacent normal data, hence the 4 curves.

The advantage of applying a 2-component mixture model is that we are able to capture biologically-relevant clusters of gene expression that may naturally exist in the data. Otherwise, we might represent our data with just a single curve sitting in the middle of what really are 2 distinct clusters. Visually, we see that for a theoretical oncogene, there is a subgroup of tumors that overexpresses this gene relative to normal tissue.

### 1.3 Comparison of Oncomix to Existing Differential Expression Methods

We now conceptually compare oncomix to the techniques employed by traditional differential expression analysis (e.g. Student’s t-test, as employed by limma, or DESeq2). These existing approaches make strong assumptions – namely, that the data from a particular group are well-described by distributions with mass concentrated around a central value (such as a ‘mean’). If we were to use one of these approaches on a large dataset, our assumption would be that oncogenes are overexpressed in every tumor sample compared to normal tissue. This assumption can be visualized below:

oncoMixTraditionalDE()

The red-orange curve represents the gene expression values from the adjacent normal data, and the teal curve represents the gene expression values from the tumor data. Note, however, that the goal for a DE analysis using existing methods (such as limma) would be to find genes that maximize the difference between these two curves. This approach does not represent our knowledge of how oncogenes are expressed in a population of individuals – that is, highly expressed in a subset of patient tumors, and lowly expressed in adjacent normal tissue.

## 2. Identifying Oncogene Candidates

### 2.1 Loading Example Data and Exploring the mixModelParams Object

Now, we will load an example dataset that contains expression values for 700 mRNA isoforms obtained from paired samples of breast tumor (exprTumIsof) and adjacent normal(exprNmlIsof) breast tissue from 113 patients in the Genomic Data Commons. We will fit the mixture model using the oncomix function mixModelParams, which takes dataframes that contain patients as rows and mRNA isoforms/genes as columns. The number of columns (genes) should be the same between both dataframes, though the number of rows can vary.

data(exprNmlIsof, exprTumIsof, package="oncomix")

##look at the matrix of mRNA expression data from adjacent normal samples
dim(exprNmlIsof)
## [1] 700 113
exprNmlIsof[1:5, 1:5] 
##            TCGA-A7-A0CE-11A TCGA-A7-A0CH-11A TCGA-A7-A0D9-11A TCGA-A7-A0DB-11A
## uc001qoa.2         1.972887        2.4877508         1.534429         2.787777
## uc002jyg.1         1.488236        0.9886728         3.363712         3.301014
## uc011lsc.1         5.939032        6.7117641         5.210523         5.664385
## uc004cpd.1         1.816706        1.6479322         1.295284         1.537309
## uc011mgy.1         1.573477        1.3371375         2.027953         2.070035
##            TCGA-A7-A0DC-11A
## uc001qoa.2         1.821897
## uc002jyg.1         3.127924
## uc011lsc.1         5.433401
## uc004cpd.1         1.533831
## uc011mgy.1         2.431077
##look at the matrix of mRNA expression data from tumors
dim(exprTumIsof)
## [1] 700 113
exprTumIsof[1:5, 1:5] 
##            TCGA-A7-A0CE-01A TCGA-A7-A0CH-01A TCGA-A7-A0D9-01A TCGA-A7-A0DB-01A
## uc001qoa.2        1.2399803         1.780444         1.704665         2.390934
## uc002jyg.1        3.1547083         3.503748         2.432818         2.638793
## uc011lsc.1        5.2938539         5.622610         9.029952         6.077302
## uc004cpd.1        0.8499161         1.803169         2.518515         1.735324
## uc011mgy.1        0.6849480         2.081580         3.343087         1.546985
##            TCGA-A7-A0DC-01A
## uc001qoa.2         2.310899
## uc002jyg.1         1.893164
## uc011lsc.1         7.636221
## uc004cpd.1         1.882874
## uc011mgy.1         2.415372
##fits the mixture models, will take a few minutes
mmParams <- mixModelParams(exprNmlIsof, exprTumIsof)
head(mmParams)
##                   nMu1       nMu2        nVar      nPi1      tMu1     tMu2
## uc002jxc.2 1.250068025 1.83147135 0.116400229 0.7967701 1.7371897 4.285259
## uc001jrg.2 0.006952803 0.01324544 0.005531848 0.5003037 0.1113493 1.625321
## uc003aab.2 0.985454390 1.59242262 0.087878646 0.4896663 2.0035574 4.522943
## uc004cmb.2 0.385483412 0.87309050 0.046609881 0.6731112 1.1691973 3.389940
## uc002jfu.2 0.382007855 0.45789679 0.558312339 0.5189438 0.5591093 2.645615
## uc001lcs.1 0.600357282 1.45153880 0.178300764 0.6373414 0.3463322 2.934114
##                 tVar      tPi1 deltaMu2   deltaMu1        SI     score
## uc002jxc.2 0.4368186 0.5943046 2.453788  0.4871217 1.0000000 1.4134475
## uc001jrg.2 0.1074420 0.7913964 1.612076  0.1043965 1.0000000 1.3947057
## uc003aab.2 0.6200912 0.7359520 2.930521  1.0181030 1.0000000 1.2044477
## uc004cmb.2 0.5000264 0.7992164 2.516849  0.7837139 1.0000000 1.1864992
## uc002jfu.2 0.3309116 0.6385413 2.187718  0.1771014 0.9911504 1.1114688
## uc001lcs.1 0.5330532 0.5976110 1.482575 -0.2540251 0.8849558 0.9072978

The object returned by mixModelParams is a dataframe with rows corresponding to genes and 12 columns containing mixture model parameters. The rows are sorted according to the score column, with the first row containing the highest oncomix score (defined below). The meaning of the dataframe columns are described below:

• nMu1 = the mean ($$\mu$$) of the Gaussian curve with the smaller mean fit to the adjacent normal expression data (referred to as Mode 1).
• nMu2 = the mean ($$\mu$$) of the Gaussian curve with the larger mean fit to the adjacent normal expression data (referred to as Mode 2).
• nVar