[](https://travis-ci.org/alyssafrazee/ballgown)
# Introduction and Preprocessing
Ballgown is a software package designed to facilitate flexible differential expression analysis of RNA-Seq data. It also provides functions to organize, visualize, and analyze the expression measurements for your transcriptome assembly.
Before using the Ballgown R package, a few preprocessing steps are necessary:
1. RNA-Seq reads should be aligned to a reference genome.
2. A transcriptome should be assembled, or a reference transcriptome should be downloaded.
3. Expression for the features (transcript, exon, and intron junctions) in the transcriptome should be estimated in a Ballgown readable format.
Two sample pipelines for preprocessing are as follows:
1. **Pipeline 1:** _TopHat2_ (1) + _Stringtie_ (2,3)
1. _TopHat2_ [<a href="http://bioinformatics.oxfordjournals.org/content/25/9/1105.abstract">Trapnell et al. (2009)</a>] is built on the ultrafast short read mapping program _Bowtie_ and aligns RNA-Seq reads to a genome while identifying exonic splice junctions. Sample command:
` tophat2 -G reference.gff -o outputDirectory -p 6 referenceIndex reads `
2. _Stringtie_ [<a href="http://www.nature.com/nbt/journal/v33/n3/full/nbt.3122.html">M. Pertea et al. (2015)</a>] is a highly efficient assembler for RNA-Seq alignments using a novel network flow algorithm. It simultaneously assembles and quantifies expression levels for the features of the transcriptome in a Ballgown readable format (by using the option -B). One command to _Stringtie_ satisfies steps 2 and 3 above. Sample command: ` stringtie -B -G reference.gff -p 6 accepted_hits.bam -o stringtie.gff `
2. **Pipeline 2:** _TopHat2_ (1) + _Cufflinks_ (2) + _Tablemaker_ (3)
1. _Tophat2_ produces alignments as noted above.
2. _Cufflinks_ [<a href="http://dx.doi.org/10.1038/nbt.1621">Trapnell et al. (2010)</a>] also assembles transcriptomes from RNA-Seq data and quantifies their expression. Sample command:
` cufflinks -g reference.gff -o outputDirectory accepted_hits.bam `
3. _Tablemaker_ calls _Cufflinks_ to estimate feature expressions in a Ballgown readable format. _Tablemaker_ access and instructions can be found [here](https://github.com/leekgroup/tablemaker).
# Installation
Start R and run:
```r
if (!requireNamespace("BiocManager", quietly=TaRUE))
install.packages("BiocManager")
BiocManager::install("ballgown")
```
# Ballgown readable expression output
The files that _Stringtie_ and _Tablemaker_ produce for Ballgown to load is as follows:
* `e_data.ctab`: exon-level expression measurements. One row per exon. Columns are `e_id` (numeric exon id), `chr`, `strand`, `start`, `end` (genomic location of the exon), and the following expression measurements for each sample:
* `rcount`: reads overlapping the exon
* `ucount`: uniquely mapped reads overlapping the exon
* `mrcount`: multi-map-corrected number of reads overlapping the exon
* `cov` average per-base read coverage
* `cov_sd`: standard deviation of per-base read coverage
* `mcov`: multi-map-corrected average per-base read coverage
* `mcov_sd`: standard deviation of multi-map-corrected per-base coverage
* `i_data.ctab`: intron- (i.e., junction-) level expression measurements. One row per intron. Columns are `i_id` (numeric intron id), `chr`, `strand`, `start`, `end` (genomic location of the intron), and the following expression measurements for each sample:
* `rcount`: number of reads supporting the intron
* `ucount`: number of uniquely mapped reads supporting the intron
* `mrcount`: multi-map-corrected number of reads supporting the intron
* `t_data.ctab`: transcript-level expression measurements. One row per transcript. Columns are:
* `t_id`: numeric transcript id
* `chr`, `strand`, `start`, `end`: genomic location of the transcript
* `t_name`: Cufflinks-generated transcript id
* `num_exons`: number of exons comprising the transcript
* `length`: transcript length, including both exons and introns
* `gene_id`: gene the transcript belongs to
* `gene_name`: HUGO gene name for the transcript, if known
* `cov`: per-base coverage for the transcript (available for each sample)
* `FPKM`: Cufflinks-estimated FPKM for the transcript (available for each sample)
* `e2t.ctab`: table with two columns, `e_id` and `t_id`, denoting which exons belong to which transcripts. These ids match the ids in the `e_data` and `t_data` tables.
* `i2t.ctab`: table with two columns, `i_id` and `t_id`, denoting which introns belong to which transcripts. These ids match the ids in the `i_data` and `t_data` tables.
# Loading data into R
The default directory structure produced by _Stringtie_ and _Tablemaker_ should mirror the `extdata` folder in the Ballgown pacakge:
```
extdata/
sample01/
e2t.ctab
e_data.ctab
i2t.ctab
i_data.ctab
t_data.ctab
sample02/
e2t.ctab
e_data.ctab
i2t.ctab
i_data.ctab
t_data.ctab
...
sample20/
e2t.ctab
e_data.ctab
i2t.ctab
i_data.ctab
t_data.ctab
```
Data is loaded using the `ballgown` function.
If your data is stored in directories matching the above structure (one root folder, subfolders named by sample, and `.ctab` files in the subfolders), you can use the `dataDir` and `samplePattern` arguments to load the data. `samplePattern` takes a regular expressions specifying the subfolders that should be included in the ballgown object:
```r
library(ballgown)
data_directory = system.file('extdata', package='ballgown') # automatically finds ballgown's installation directory
# examine data_directory:
data_directory
```
```
## [1] "/Library/Frameworks/R.framework/Versions/3.1/Resources/library/ballgown/extdata"
```
```r
# make the ballgown object:
bg = ballgown(dataDir=data_directory, samplePattern='sample', meas='all')
bg
```
```
## ballgown instance with 100 transcripts and 20 samples
```
If your data is stored in a directory structure other than the one specified above, you can use the `samples` argument in the `ballgown` function: `samples` should be a vector (1-d array) with one entry per sample, where the entry gives the path to the folder containing that sample's `.ctab` files.
<!-- If you choose the `samples` option, you will also need to provide a vector called `sampleNames` that corresponds to `samples` and gives each sample a unique ID. Some example code to do this is:
```R
sample_IDs = c('oneSample', 'anotherSample', 'aThirdSample')
sample_paths = paste0('/home/', sample_IDs, '/ballgown')
sample_paths
## [1] "/home/oneSample/ballgown"
## [2] "/home/anotherSample/ballgown"
## [3] "/home/aThirdSample/ballgown"
bg = ballgown(samples=sample_paths, sampleNames=sample_IDs, meas='all')
```
-->
The result from either of these approaches is an object of class `ballgown` (named `bg` in these examples).
In the rest of this document, we use `bg` to refer to the first example, where samples are named `sample01` through `sample20`.
A note for large experiments (with many samples or with large genomes): loading the data might require a lot of time and memory. In these cases, it's often useful to do the data loading in non-interactive mode. More specifically, you could create a script called `load.R` that contains these lines:
```R
library(ballgown)
data_directory = system.file('extdata', package='ballgown')
bg = ballgown(dataDir=data_directory, samplePattern='sample', meas='all')
save(bg, file='bg.rda')
```
You could then run this script non-interactively using `R CMD BATCH`: from the command line, run:
```
R CMD BATCH load.R
```
This may take some time, but when it finishes, the file `bg.rda` will be saved in the current directory, and you can read it back into R using the `load()` function. Rda files are usually only a few Gb on disk, even for large experiments. It is also possible to load only a subset of all the expression measurements by changing the `meas` argument to the `ballgown` function. For example, to only load transcript-level FPKMs, set `meas = 'FPKM'` and to load average coverage values and read counts, set `meas=c('cov', 'rcount').`
See `?ballgown` for detailed information on creating Ballgown objects.
# Accessing assembly data
A `ballgown` object has six slots: `structure`, `expr`, `indexes`, `dirs`, `mergedDate`, and `meas`.
#### structure
The `structure` slot depends heavily on the `GenomicRanges` Bioconductor package (<a href="http://dx.doi.org/10.1371/journal.pcbi.1003118">Lawrence et al. (2013)</a>). The slot specifies the structure, i.e., genomic locations and relationships between exons, introns, and transcripts, of the transcriptome assembly. It is convenient to represent exons and introns as intervals and to represent transcripts as a set of intervals (exons), so assembled exons and introns are available as `GRanges` objects, and the assembled transcripts are available as a `GRangesList` object. This means that useful range operations, such as `findOverlaps` and `reduce`, are readily available for assembled features.
Exon, intron, and transcript structures are easily extracted from the main `ballgown` object:
```r
structure(bg)$exon
```
```
## GRanges object with 633 ranges and 2 metadata columns:
## seqnames ranges strand | id transcripts
## <Rle> <IRanges> <Rle> | <integer> <character>
## [1] 18 [24412069, 24412331] * | 12 10
## [2] 22 [17308271, 17308950] + | 55 25
## [3] 22 [17309432, 17310226] + | 56 25
## [4] 22 [18121428, 18121652] + | 88 35
## [5] 22 [18138428, 18138598] + | 89 35
## ... ... ... ... ... ... ...
## [629] 22 [51221929, 51222113] - | 3777 1294
## [630] 22 [51221319, 51221473] - | 3782 1297
## [631] 22 [51221929, 51222162] - | 3783 1297
## [632] 22 [51221929, 51222168] - | 3784 1301
## [633] 6 [31248149, 31248334] * | 3794 1312
## -------
## seqinfo: 3 sequences from an unspecified genome; no seqlengths
```
```r
structure(bg)$intron
```
```
## GRanges object with 536 ranges and 2 metadata columns:
## seqnames ranges strand | id
## <Rle> <IRanges> <Rle> | <integer>
## [1] 22 [17308951, 17309431] + | 33
## [2] 22 [18121653, 18138427] + | 57
## [3] 22 [18138599, 18185008] + | 58
## [4] 22 [18185153, 18209442] + | 59
## [5] 22 [18385514, 18387397] - | 72
## ... ... ... ... ... ...
## [532] 22 [51216410, 51220615] - | 2750
## [533] 22 [51220776, 51221928] - | 2756
## [534] 22 [51220780, 51221318] - | 2757
## [535] 22 [51221474, 51221928] - | 2758
## [536] 22 [51220780, 51221928] - | 2759
## transcripts
## <character>
## [1] 25
## [2] 35
## [3] 35
## [4] 35
## [5] 41
## ... ...
## [532] c(1294, 1297, 1301)
## [533] 1294
## [534] 1297
## [535] 1297
## [536] 1301
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengths
```
```r
structure(bg)$trans
```
```
## GRangesList object of length 100:
## $10
## GRanges object with 1 range and 2 metadata columns:
## seqnames ranges strand | id transcripts
## <Rle> <IRanges> <Rle> | <integer> <character>
## [1] 18 [24412069, 24412331] * | 12 10
##
## $25
## GRanges object with 2 ranges and 2 metadata columns:
## seqnames ranges strand | id transcripts
## [1] 22 [17308271, 17308950] + | 55 25
## [2] 22 [17309432, 17310226] + | 56 25
##
## $35
## GRanges object with 4 ranges and 2 metadata columns:
## seqnames ranges strand | id transcripts
## [1] 22 [18121428, 18121652] + | 88 35
## [2] 22 [18138428, 18138598] + | 89 35
## [3] 22 [18185009, 18185152] + | 90 35
## [4] 22 [18209443, 18212080] + | 91 35
##
## ...
## <97 more elements>
## -------
## seqinfo: 3 sequences from an unspecified genome; no seqlengths
```
#### expr
The `expr` slot is a list that contains tables of expression data for the genomic features. These tables are very similar to the `*_data.ctab` _Tablemaker_ output files. Ballgown implements the following syntax to access components of the `expr` slot:
```R
*expr(ballgown_object_name, <EXPRESSION_MEASUREMENT>)
```
where `*` is either e for exon, i for intron, t for transcript, or g for gene, and <EXPRESSION MEASUREMENT> is an expression-measurement column name from the appropriate `.ctab` file. Gene-level measurements are calculated by aggregating the transcript-level measurements for that gene. All of the following are valid ways to extract expression data from the `bg` ballgown object:
```r
transcript_fpkm = texpr(bg, 'FPKM')
transcript_cov = texpr(bg, 'cov')
whole_tx_table = texpr(bg, 'all')
exon_mcov = eexpr(bg, 'mcov')
junction_rcount = iexpr(bg)
whole_intron_table = iexpr(bg, 'all')
gene_expression = gexpr(bg)
```
Calculating the gene-level expression measurements can be slow for large experiments.
The `*expr` functions return matrices unless `meas = 'all'`, in which case some additional feature metadata is returned and the result is a `data.frame`.
#### indexes
The `indexes` slot of a ballgown object connects the pieces of the assembly and provides other experimental information. `indexes(bg)` is a list with several components that can be extracted with the `$` operator.
Perhaps most importantly, there is a component called `pData` that should hold a data frame of phenotype information for the samples in the experiment. This must be created manually. It is **very important** that the rows of pData are in the correct order. Each row corresponds to a sample, and the rows of pData should be ordered the same as the tables in the `expr` slot. You can check that order by running `sampleNames(bg)`. The `pData` component can be added during construction (you can pass a data frame to the `ballgown` function), or you can add it later:
```r
pData(bg) = data.frame(id=sampleNames(bg), group=rep(c(1,0), each=10))
```
The other components of `indexes` are the `e2t` and `i2t` tables described in the _Tablemaker_ section, as well as a `t2g` table denoting which transcripts belong to which genes. There is also a `bamfiles` component, designed to hold paths to the read alignment files for each sample. The `bamfiles` component isn't currently used by any ballgown functions, but it could come in handy for users of `RSamtools` or similar packages. Here are some examples of how to extract `indexes` components from ballgown objects:
```r
exon_transcript_table = indexes(bg)$e2t
transcript_gene_table = indexes(bg)$t2g
head(transcript_gene_table)
```
```
## t_id g_id
## 1 10 XLOC_000010
## 2 25 XLOC_000014
## 3 35 XLOC_000017
## 4 41 XLOC_000246
## 5 45 XLOC_000019
## 6 67 XLOC_000255
```
```r
phenotype_table = pData(bg)
```
#### other slots
The `dirs` slot gives full filepaths to _Tablemaker_ output:
```r
head(bg@dirs)
```
```
## sample01
## "/Library/Frameworks/R.framework/Versions/3.1/Resources/library/ballgown/extdata/sample01"
## sample02
## "/Library/Frameworks/R.framework/Versions/3.1/Resources/library/ballgown/extdata/sample02"
## sample03
## "/Library/Frameworks/R.framework/Versions/3.1/Resources/library/ballgown/extdata/sample03"
## sample04
## "/Library/Frameworks/R.framework/Versions/3.1/Resources/library/ballgown/extdata/sample04"
## sample05
## "/Library/Frameworks/R.framework/Versions/3.1/Resources/library/ballgown/extdata/sample05"
## sample06
## "/Library/Frameworks/R.framework/Versions/3.1/Resources/library/ballgown/extdata/sample06"
```
The `mergedDate` slot indicates when the `ballgown` object was created:
```r
bg@mergedDate
```
```
## [1] "Sun Feb 22 23:51:45 2015"
```
And the `meas` slot gives the expression measurements present in the object:
```r
bg@meas
```
```
## [1] "all"
```
# Plotting transcript structures
Visualization of the assembled transcripts is done with the `plotTranscripts` function. Transcripts or exons can be colored by expression level. This plot colors transcripts by expression level:
```r
plotTranscripts(gene='XLOC_000454', gown=bg, samples='sample12',
meas='FPKM', colorby='transcript',
main='transcripts from gene XLOC_000454: sample 12, FPKM')
```
It is also possible to plot several samples at once:
```r
plotTranscripts('XLOC_000454', bg,
samples=c('sample01', 'sample06', 'sample12', 'sample19'),
meas='FPKM', colorby='transcript')
```
You can also make side-by-side plots comparing mean abundances between groups (here, 0 and 1):
```r
plotMeans('XLOC_000454', bg, groupvar='group', meas='FPKM', colorby='transcript')
```
# Differential expression analysis
Ballgown provides a wide selection of simple, fast statistical methods for testing whether transcripts are differentially expressed between experimental conditions or across a continuous covariate (such as time).
The default statistical test in ballgown is a parametric F-test comparing nested linear models; details are available in the Ballgown manuscript (<a href="http://biorxiv.org/content/early/2014/03/30/003665">Frazee et al. (2014)</a>). These models are conceptually simialar to the models used by <a href="http://link.springer.com/chapter/10.1007%2F0-387-29362-0_23">Smyth (2005)</a> in the `limma` package. In `limma`, more sophisticated empirical Bayes shrinkage methods are used, and generally a single linear model is fit per feature instead of doing a nested model comparison, but the flavor is similar (and in fact, `limma` can easily be run on any of the data matrices in a `ballgown` object).
Ballgown's statistical models are implemented with the `stattest` function. Two models are fit to each feature, using expression as the outcome: one including the covariate of interest (e.g., case/control status or time) and one not including that covariate. An F statistic and p-value are calculated using the fits of the two models. A significant p-value means the model including the covariate of interest fits significantly better than the model without that covariate, indicating differential expression. We adjust for multiple testing by reporting q-values (<a href="http://dx.doi.org/10.1073/pnas.1530509100">Storey & Tibshirani (2003)</a>) for each transcript in addition to p-values: reporting features with, say, q < 0.05 means the false discovery rate should be controlled at about 5%.
`stattest` automatically handles two-group (e.g. case/control) comparisons, multi-group comparisons (e.g. comparison of several tissue types), and "timecourse" comparisons (with the scare quotes meaning that these comparisons are also applicable to continuous covariates that aren't time). For two- and multi-group comparisons, a significant result indicates that the feature is differentially expressed in at least one of the groups. For timecourse comparisons, significant results mean the feature has an expression profile that varies significantly over time (i.e., values of the continuous covariate) as opposed to being flat over time.
The example dataset `bg` contains two group labels, 0 and 1. We can test each transcript for differential expression with `stattest`:
```r
stat_results = stattest(bg, feature='transcript', meas='FPKM', covariate='group')
head(stat_results)
```
```
## feature id pval qval
## 1 transcript 10 0.01381576 0.10521233
## 2 transcript 25 0.26773622 0.79114975
## 3 transcript 35 0.01085070 0.08951825
## 4 transcript 41 0.47108019 0.90253747
## 5 transcript 45 0.08402948 0.48934813
## 6 transcript 67 0.27317385 0.79114975
```
The result is a data frame containing the feature tested, feature ids, and corresponding p- and q-values. See `?stattest` for further usage details.
#### timecourse experiments
For timecourse experiments, a smooth curve is fit to time (or the continuous covariate) using [natural splines](http://en.wikipedia.org/wiki/Spline_interpolation). The default degrees of freedom used for the spline model is 4, but this can be adjusted with the `df` option. The model for expression including these spline terms is compared to a model without any spline terms for the F-test. The results indicate which features' expression levels change significantly over time. For our example, we can define a "time" covariate and then demonstrate a typical call to `stattest` for a timecourse experiment:
```r
pData(bg) = data.frame(pData(bg), time=rep(1:10, 2)) #dummy time covariate
timecourse_results = stattest(bg, feature='transcript', meas='FPKM', covariate='time', timecourse=TRUE)
```
The timecourse option assumes that "time" in your study is truly continuous, i.e., that it takes several values along a time scale. If you have very few timepoints (e.g., fewer than 5), we recommend treating time as a categorical variable, since having very few values does not give much granularity for fitting a smooth curve using splines. You can do this by setting covariate equal to 'time' (or whatever your time variable is named) and simply leaving timecourse as FALSE, its default. If you don't have more timepoints than degrees of freedom in the spline model, a warning will be printed and time will be coerced to categorical.
#### adjusting for confounders
You can adjust for any or all variables in `pData` when testing for differential expression. Ballgown automatically adjusts for library size using the sum of all logged nonzero expression measurements below the 75th percentile of those measurements, for each sample. If you would like to adjust for other variables, just provide those confounders as the `adjustvars` argument to `stattest`:
```r
group_adj_timecourse_results = stattest(bg, feature='transcript', meas='FPKM', covariate='time',
timecourse=TRUE, adjustvars='group')
```
#### defining custom models
It is also possible to explicitly provide the design matrices for the models to be compared. For example, suppose we had sex and age information available, in addition to group and time, and we wanted to compare a model including all information (sex, age, group, time) to a model including only group and time. Code to do this with `ballgown` is:
```r
# create example data:
set.seed(43)
sex = sample(c('M','F'), size=nrow(pData(bg)), replace=TRUE)
age = sample(21:52, size=nrow(pData(bg)), replace=TRUE)
# create design matrices:
mod = model.matrix(~ sex + age + pData(bg)$group + pData(bg)$time)
mod0 = model.matrix(~ pData(bg)$group + pData(bg)$time)
# run differential expression tests:
adjusted_results = stattest(bg, feature='transcript', meas='FPKM', mod0=mod0, mod=mod)
head(adjusted_results)
```
```
## feature id pval qval
## 1 transcript 10 0.8242859 0.9755925
## 2 transcript 25 0.1985488 0.9725569
## 3 transcript 35 0.8114314 0.9755925
## 4 transcript 41 0.7647284 0.9755925
## 5 transcript 45 0.6497589 0.9755925
## 6 transcript 67 0.9775119 0.9874866
```
# Using alternative statistical methods
Ballgown's statistical methods for differential expression testing are straightforward and accurate (<a href="http://biorxiv.org/content/early/2014/03/30/003665">Frazee et al. (2014)</a>), but users may wish to use one of the many existing packages for differential expression. Ballgown's data structures make it easy to use table-based packages like limma (<a href="">Smyth (2005)</a>), limma Voom (<a href="http://dx.doi.org/10.1186/gb-2014-15-2-r29">Law et al. (2014)</a>), DESeq (<a href="http://dx.doi.org/10.1186/gb-2010-11-10-r106">Anders & Huber (2010)</a>), DEXSeq (<a href="http://dx.doi.org/10.1101/gr.133744.111">Anders et al. (2012)</a>), or EdgeR (<a href="http://dx.doi.org/10.1093/bioinformatics/btp616">Robinson et al. (2010)</a>) for differential expression analysis. A feature-by-sample expression table can be easily created with a `*expr` function and used directly as input to these or other differential expression packages.
# Simple transcript clustering
Sometimes several very similar transcripts are assembled for the same gene, which might cause expression estimates for those transcripts to be unreliable: statistically, it can very difficult or impossible to tell which of two very similar transcript a read came from. This means differential expression results might also be unreliable.
As a preliminary attempt at addressing this issue, Ballgown provides some simple transcript clustering functions. The idea is that similar assembled transcripts can be grouped together in clusters, and differential expression analysis could be performed on the cluster, whose expression measurement aggregates the expression estimates of the transcripts that compose it.
These functions measure the distance between transcripts using [Jaccard distance](http://en.wikipedia.org/wiki/Jaccard_index), where each transcript's "set" is the nucleotides included in its exons. Transcripts can be clustered using either _k_-means clustering or hierarchical clustering.
```r
clusterTranscripts(gene='XLOC_000454', gown=bg, k=2, method='kmeans')
```
```
## $clusters
## cluster t_id
## 1 2 1294
## 2 1 1297
## 3 2 1301
##
## $pctvar
## [1] 0.9117737
```
You can also visualize the transcript clusters:
```r
plotLatentTranscripts(gene='XLOC_000454', gown=bg, k=2, method='kmeans', returncluster=FALSE)
```
And you can calculate aggregate cluster expression measurements for some gene using `collapseTranscripts`. The `tab` result of `collapseTranscripts` can be passed to `stattest` as the `gowntable` argument, for differential expression analysis of the clusters:
```r
agg = collapseTranscripts(gene='XLOC_000454', gown=bg, k=2, method='kmeans')
stattest(gowntable=agg$tab, pData=pData(bg), feature='transcript_cluster',
covariate='group', libadjust=FALSE)
```
```
## feature id pval qval
## 1 transcript_cluster 1 0.3332238 0.6664477
## 2 transcript_cluster 2 0.6882119 0.6882119
```
This example clustered only three transcripts, but we imagine clustering could be useful when many more than three transcripts have been assembled for a single gene.
# References
- Simon Anders, Wolfgang Huber (2010). Differential Expression Analysis For Sequence Count Data. *Genome Biology* **11** R106-NA [10.1186/gb-2010-11-10-r106](http://dx.doi.org/10.1186/gb-2010-11-10-r106)
- Simon Anders, Alejandro Reyes, Wolfgang Huber (2012). Detecting Differential Usage of Exons From RNA-Seq Data. *Genome Research* **22** 2008-2017 [10.1101/gr.133744.111](http://dx.doi.org/10.1101/gr.133744.111)
- Alyssa C. Frazee, Geo Pertea, Andrew E. Jaffe, Ben Langmead, Steven L. Salzberg, Jeffrey T. Leek (2014). Flexible isoform-level differential expression analysis with Ballgown. *bioRxiv* [http://biorxiv.org/content/early/2014/03/30/003665](http://biorxiv.org/content/early/2014/03/30/003665)
- Charity W Law, Yunshun Chen, Wei Shi, Gordon K Smyth, (2014) Voom: Precision Weights Unlock Linear Model Analysis Tools For RNA-Seq Read Counts. *Genome Biology* **15** R29-NA [10.1186/gb-2014-15-2-r29](http://dx.doi.org/10.1186/gb-2014-15-2-r29)
- Michael Lawrence, Wolfgang Huber, Herve Pages, Patrick Aboyoun, Marc Carlson, Robert Gentleman, Martin T. Morgan, Vincent J. Carey, Andreas Prlic (2013). Software For Computing And Annotating Genomic Ranges. *Plos Computational Biology* **9** e1003118-NA [10.1371/journal.pcbi.1003118](http://dx.doi.org/10.1371/journal.pcbi.1003118)
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# Session Information
```r
sessionInfo()
```
```
## R version 3.1.1 (2014-07-10)
## Platform: x86_64-apple-darwin13.1.0 (64-bit)
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ballgown_1.0.1 knitr_1.8.2 colorout_1.0-3 devtools_1.6.1
##
## loaded via a namespace (and not attached):
## [1] annotate_1.44.0 AnnotationDbi_1.28.1
## [3] base64enc_0.1-2 BatchJobs_1.5
## [5] BBmisc_1.8 Biobase_2.26.0
## [7] BiocGenerics_0.12.1 BiocParallel_1.0.0
## [9] Biostrings_2.34.0 bitops_1.0-6
## [11] brew_1.0-6 checkmate_1.5.0
## [13] codetools_0.2-9 DBI_0.3.1
## [15] digest_0.6.4 evaluate_0.5.5
## [17] fail_1.2 foreach_1.4.2
## [19] formatR_1.0 genefilter_1.48.1
## [21] GenomeInfoDb_1.2.3 GenomicAlignments_1.2.1
## [23] GenomicRanges_1.18.3 grid_3.1.1
## [25] IRanges_2.0.0 iterators_1.0.7
## [27] lattice_0.20-29 limma_3.22.1
## [29] Matrix_1.1-4 mgcv_1.8-4
## [31] nlme_3.1-118 parallel_3.1.1
## [33] RColorBrewer_1.1-2 RCurl_1.95-4.5
## [35] Rsamtools_1.18.2 RSQLite_1.0.0
## [37] rtracklayer_1.26.2 S4Vectors_0.4.0
## [39] sendmailR_1.2-1 splines_3.1.1
## [41] stats4_3.1.1 stringr_0.6.2
## [43] survival_2.37-7 sva_3.12.0
## [45] tools_3.1.1 XML_3.98-1.1
## [47] xtable_1.7-4 XVector_0.6.0
## [49] zlibbioc_1.12.0
```
