MultipleBeta t-TestsofDifferentialTranscrip ......Multiple Beta t-Tests of Differential Transcription of mRNAs Between Two Conditions with Small Samples 7 306 59209 UCRC chr22 + 30165939

1Other Bioconductorpackages with similaraims are edgeR, bay-Seq, DESeq and DE-Seq2

Multiple Beta t-Tests of Differential Transcrip-tion of mRNAs Between Two Conditions withSmall Samples

Yuan-De [email protected]

April 27, 2020

Abstract

A major task in the analysis of count data of RNA reads from RNA-Seq is the detection ofdifferentially expressed genes or isoforms. The count data are presented as a matrix consistingof RNA isoform annotation and the number of reads. Analogous analyses also arise for otherassay types, such as comparative ChIP-Seq. The MBttest provides a powerful method totest for differential expression by use of the beta distribution and gene- or isoform-specificvariable ρ to control fudge effect due to small sample size. 1. This vignette explains the useof the package. For more detail of the statistical method, please see our paper [8].

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Data Preparation and Input . . . . . . . . . . . . . . . . . . . . . 2

3 Simulation for Calculating omega Value . . . . . . . . . . . . . . 3

3.1 Step1: Simulate null count data . . . . . . . . . . . . . . . . . . 3

3.2 Step2: Perform multiple beta t-tests . . . . . . . . . . . . . . . . 4

3.3 Step3: Calculate omega value . . . . . . . . . . . . . . . . . . . 4

4 Normalize the count data . . . . . . . . . . . . . . . . . . . . . . 8

5 Perform Multiple Beta t-Tests on The Real Data . . . . . . . . . 8

6 Session Info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

http://bioconductor.org/packages/edgeR

http://bioconductor.org/packages/baySeq


http://bioconductor.org/packages/DESeq

http://bioconductor.org/packages/DESeq2


http://bioconductor.org/packages/MBttest

Multiple Beta t-Tests of Differential Transcription of mRNAs Between Two Conditions with Small Samples

1 Introduction

This vignette is intended to give a rapid introduction to the commands used in implementingnew beta t-test methods of evaluating differential expression in high-throughput sequencingdata by means of the MBttest package. For fuller details on the methods being used, consultTan et al (2015) [8] .

We assume that we have count data from a set of sequencing or other high-throughputexperiments, arranged in an array such that except gene annotation information and id, eachcolumn describes a library and each row describes RNA tag or isoform for which data havebeen acquired. For example, the rows may correspond to the different sequences observed ina sequencing experiment. The data then consists of the number of each sequence observedin each sample. We wish to determine which, if any, rows of the data correspond to somepatterns of differential expression across the samples.

TheMBttest uses new beta t-test method to identify differential expression for each row. Thisapproach introduces a gene- or isoform-specific variable, called ρ, into t-statistics to controlfudge effect resulted from small samples. It has higher work efficiency than existing methodsfor identifying differential expressions of genes or isoforms either by inflating t-values withρ > ω a threshold or by shrinking those with ρ < ω [8] when number of replicate librariesin each condition is small, for example, equal to or less than 6.

Different from the exiting methods such as baySeq [2], edgeR Exact test [6] and[7], edgeRGLM [5] and [7], DESeq [1] and DESeq2 [4], etc, MBttest requires performance of simulationto determine threshold ω before running program mbetattest. MBttest provides negativebinomial simulation program to generate null count data without inputting arguments. Usershould repeat five or more simulations, perform program smbettest to produce null resultsand calculate ω using the method given in our paper [8].

2 Data Preparation and Input

We begin by loading the MBttest package.

> library(MBttest)

MBttest requires data file contain two parts: Annotation information and count data. Infor-mation consists of tagid, geneid, gene name, chromosome id, DNA strand, etc. Informationcolumns are in left side. The count datasheet has at least one column for geneid or tagid(isoformid). The data contain two conditions each having several replicate libraries andmust be in right side. Here is an example :

> data(jkttcell)

> jkttcell[1:10,]

tagid geneid name chr strand pos anno Jurk.NS.A Jurk.NS.B Jurk.NS.C

1 54 58998 COMT chr22 + 19956542 sg 66.80 43.48 4.65

2 111 59029 CRKL chr22 + 21308033 tu-ce 68.75 63.94 66.46

3 171 59104 SLC2A11 chr22 + 24227723 sg 2.86 2.67 8.15

4 231 59157 ADRBK2 chr22 + 26118985 tu 12.88 8.45 8.59

5 242 59164 SRRD chr22 + 26887904 sg 62.54 59.88 83.27

6 265 59184 HSCB chr22 + 29153206 tu 4.02 2.07 6.85

2






http://bioconductor.org/packages/DESeq







7 306 59209 UCRC chr22 + 30165939 sg 516.71 594.71 83.84

8 327 59212 MTMR3 chr22 + 30426495 tu 4.08 3.99 2.93

9 445 59310 NCF4 chr22 + 37274056 sg 0.00 1.30 0.03

10 472 59321 CYTH4 chr22 + 37711384 sg 4.40 1.60 0.12

Jurk.48h.A Jurk.48h.B Jurk.48h.C

1 32.99 25.49 14.68

2 80.42 63.89 72.48

3 12.95 12.70 8.81

4 13.13 35.34 9.78

5 54.99 51.15 66.61

6 9.66 4.02 5.87

7 254.81 142.26 156.72

8 10.38 14.23 6.85

9 71.26 25.89 11.73

10 37.61 18.54 16.64

User also may use R function (head) to display the data with top 6 lines:

> head(jkttcell)

tagid geneid name chr strand pos anno Jurk.NS.A Jurk.NS.B Jurk.NS.C

1 54 58998 COMT chr22 + 19956542 sg 66.80 43.48 4.65

2 111 59029 CRKL chr22 + 21308033 tu-ce 68.75 63.94 66.46

3 171 59104 SLC2A11 chr22 + 24227723 sg 2.86 2.67 8.15

4 231 59157 ADRBK2 chr22 + 26118985 tu 12.88 8.45 8.59

5 242 59164 SRRD chr22 + 26887904 sg 62.54 59.88 83.27

6 265 59184 HSCB chr22 + 29153206 tu 4.02 2.07 6.85

Jurk.48h.A Jurk.48h.B Jurk.48h.C

1 32.99 25.49 14.68

2 80.42 63.89 72.48

3 12.95 12.70 8.81

4 13.13 35.34 9.78

5 54.99 51.15 66.61

6 9.66 4.02 5.87

If the datasheet is .csv file, user can use R function (read.csv) to input data into R Consoleor RStudio. If the datasheet is txt file, user can use R function read.delim or read.table toload data into R Consoleor RStudio. After loading data, user should check the data inputted.jkttcell shows an example. In this example, 7 columns in the left side are information forpoly(A) sites. The count data are listed in the right side.

3 Simulation for Calculating omega Value

Before performing mbetattest on the real data, user needs simulation to determine ω value.There are three steps for doing so:

3.1 Step1: Simulate null count data

Use the following function to generate null simulation data

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simulat(yy, nci, r1, r2, p, q, A)

whereyy is real data.r1 and r2 are replicate numbers in conditions 1 and 2.p is proportion of genes differentially expressed in m genes, default value is 0.q is proportion of genes artificial noise. Its default value is 0.A is effect value. Its default value is 0. nci : column number of information of data.Here is an example:

> sjknull1<-simulat(yy=jkttcell[1:500,], nci=7,r1=3,r2=3,p=0, q=0.2)

The example dataset is jkttcell. It has 7 columns for alternative poly(A) site information.Two conditions are resting and stimulation. Each has 3 replicate libraries, r1=3 and r2=3.Since this is null simulation, we set p=0 and q=0.2 for artificial noise. With the same readdata and parameters, you can generate a set of 4-6 null datasets: sjknull2, · · · , sjknull6 forcalculating ω value.

3.2 Step2: Perform multiple beta t-tests

Use function smbetattest to perform multiple beta t-test with ρ =1 on the simulated nulldata:

smbetattest(X, na, nb,alpha)

whereX=simulated data.na and nb are numbers of replicate libraries in conditions 1 and 2.alpha is probabilistic threshold. User can set alpha=0.05 or 0.01.The example is

> mysim1<-smbetattest(X=sjknull1,na=3,nb=3,alpha=0.05)

Save them to .csv files using write.csv. After performing smbetattest on each simulatednull dataset, user would have results recorded in a file like simulatedNullData1Result.csv andopen it with excel.

In symbol column, mbeta t-test gives test result: symb= "-" means that a gene or a tag isnot chosen while symb= "+" indicates that the gene or isoform is found to be differentiallyexpressed.

In this example, 12 genes would be found to be falsely positive.

3.3 Step3: Calculate omega value

Here is a demo for calculating omega(since we can’t use greek letter omega in R function, weuse W to represent omega). In Figure 3, red highlighted column is rho column. We copiedthe ρ values of these 12 genes into another empty column and sorted them from the smallestto the largest. Then we gave sequence numbers from 1 to 12 corresponding to ρ-values andcalculate q-value for each ordered ρ value:

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Figure 1: This is an example showing the results obtained by smbetattest from simulated null dataColumn A is row number, geneid is set in simulation, and geneid.1 is original geneid.

We chose the 10th ρ value (1.09166) as the first W value because the 11th rho value hasq-value > 0.85. Repeat this process in 4-6 simulated null datasets and we took the averagedW value as ω value in the real data.

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Figure 2: The row number in column A in Figure 1 was deletedTo show explicitly, we here hided geneid (for simulation), tagid column and selected rows are genes thatwere identified to be differentially expressed.

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Figure 3: Demo for calculating W

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4 Normalize the count data

As a second processing step, we need to estimate the effective library size. This step is alsocalled normalization, even though it may not make the count data be of normal distribution.If the counts of expressed genes in one condition are, on average, twice as high as in another(because the library was sequenced twice as deeply), the size factor for the first conditionshould be twice higher than the second one, then differential analysis would give error results.For this reason, we must make all libraries have the same size before performing any statisticalmethod. For doing so, user can the function estimateSizeFactors of package DESeq [1] ortextbfDESeq2 [4] to estimate the size factors from the count data or use the following simplemethod to normalize the the count data: In excel sheet, use function sum to calculate sizesof all libraries, and then use excel function average to calculate averaged library size. Thelast step is to use the following equation to convert the original count data to new countdata with the same library size:

Yik =yijN̄

Nj1

2

wherei = 2, · · · , n(number of genes or isofoms) in rows in a sheet, j = nci+ 1, · · · , nci+ c wherec = na+ nb and nci is column number of annotation information; k = nci+ c+ 2 + j; Nj

is size of library j and N̄ is mean of sizes over all libraries; yij is original count of RNA readsin row i and column j.

5 Perform Multiple Beta t-Tests on The Real Data

Suppose the data have been normalized so that all libraries have the same size. After obtainingW value, user can use the function and the real data to perform mbeta t-test: mbetat

test(X,na,nb,W , alpha, file) where X is real data. In our current example, X=jkttcell. naand nb are respectively numbers of replicate libraries in conditions 1 and 2. For jktcell data,na = nb = 3. W is omega value. According to our calculation above step, W = 1. alphais the probabilistic threshold. You can set alpha=0.05 or 0.01 or the other values; file is csvfile for saving the results. The example is

> res<-mbetattest(X=jkttcell[1:1000,],na=3,nb=3,W=1,alpha=0.05,file="jurkat_NS_48h_tag_mbetattest.csv")

mbetattest has two output results: one is saved in csv file and the other is dat for maplotand for heatmap. The package MBttest has this result obtained the whole data. We hereload it for making MAplot:

> data(dat)

> head(dat)

tagid geneid name chr strand pos anno Jurk.NS.A Jurk.NS.B Jurk.NS.C Jurk.48h.A

1 83344 58782 MX1 chr21 + 42831139 sg 0 0.00 0.00 29.61

2 197313 56792 CD22 chr19 + 35838262 sg 0 0.45 3.81 96.33

3 202264 53072 CD19 chr16 + 28950664 sg 0 0.00 0.00 37.65

4 232007 37653 BASP1 chr5 + 17276943 sg 0 0.55 1.31 63.15

5 301820 46661 HBB chr11 - 5246697 sg 0 0.00 0.00 4.52

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6 368151 51057 TCL1A chr14 - 96176393 sg 0 1.03 5.15 153.51

Jurk.48h.B Jurk.48h.C beta_t rho symb

1 0.48 0 0 0 -

2 8.07 0 0 0 -

3 0.52 0 0 0 -

4 0.58 0 0 0 -

5 39.52 0 0 0 -

6 9.93 0 0 0 -

> maplot(dat=dat,r1=3,r2=3,TT=350,matitle="MA plot")

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MA plot

log(mean)

t−va

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Figure 4: ’MA’-plot of t-value against log mean over all replicate libraries across two conditionsThe isoforms who were given differential transcripts in simulation had absolute larger t-values that werehighlighted in red than the threshold given in multiple tests. Those who were given no differential expres-sion had very small absolute t-values close to zero labeled in black across long means. Here threshold fortruncating t-values is set to be 350, since none of absolute t-values are over 350, the MAplot is an outlineMAplot in which red and black dots are not explicitly seen.

> maplot(dat=dat,r1=3,r2=3,TT=50,matitle="MA plot")

myheatmap has multiple options: both-side, row and column cluster trees with distance meth-ods: "euclidean", "pearson", "spearman", and "kendall" correlation coefficients and colorlabel with "redgreen", "greenred", "redblue", "bluered" or "heat.colors" and angles for genes

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2 4 6 8 10

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MA plot

log(mean)

t−va

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Figure 5: ’MA’-plot of t-value against log mean over all replicate libraries across two conditionsTo explicit display the t-values across log mean, absolute t-values >= 50 were truncated. One can explic-itly see that truly differential transcripts in simulation had absolute larger t-values that were highlightedin red than the threshold given in multiple tests and those who had no differential expressions had verysmaller absolute t-values that were labeled in black than the threshold.

or isoforms in row and cases (conditions) in column. User can use default without anychoice like (Figure 6) which has tree="both" for both-side tree, or choose tree="column"like (Figure 8) if columns are species or cancer cases or not choose tree with tree="none"(see (Figure 7)). User may change heatmap color with colors, for example, in (Figure 8), wechose colors="redblue". If user find that default column name or row name does no havegood angles, then user can adjust them with rwangle (row angle) or clangle(column angle).rwangle and clangle values are from 0 to 90.

> myheatmap(dat=dat,r1=3,r2=3,maptitle="Jurkat T-cell heatmap2")

> myheatmap(dat=dat,r1=3,r2=3,tree="none",maptitle="Jurkat T-cell heatmap3")

> myheatmap(dat=dat,r1=3,r2=3,colrs="redblue", tree="column",

+ method="pearson", maptitle="Jurkat T-cell heatmap")

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Jurk.NS.B

Jurk.NS.A

Jurk.NS.C

Jurk.48h.A

Jurk.48h.C

Jurk.48h.B1310012866119391216412457115891246812604125271161712890132941303312185130681161311649120771219011684127191216912888123341291913157133071151111683122801270311813125491234612116125251274812139114691311412187120521256012955122211311612951127911218111523127541200612590122951247512552131151273511946131351314412897122111198313013129711214812605125431254412842129921251312989117641298513385133861294212891133531276512638131711217411869115851190811556121201167012458124521241112609131021300812570126001186413154123771190912957126881219312235125111250512383123971223112055129651250912180118401248912854122611236612095122361188312112131531216313006122821272413103131331277112215119781324013091131231273212043124511219212064119961224712574125801148912963120541291213042121321278112626123221254712463118311197012792126681266411887115251240213025121001150311819114641265312344114781236312817122331237611961121041221912053128711313413086116481219511823129861217312766125351275512198121301244712678120011175712496122511295312314120911213112325116411235411714123171223712242121681260212396128371249512869118411205911678126141257212393124981265811628116891294813295126521322912143129071319412778129491322512491126811309312265132881300211933128191236412784128121242212682125931308113090124491250612954130211240912453125121241812814118551290212762117431246512153125241167612340126101164312546131751274713176131861303912700124561282512804125871339311787133771229712137133051173511926117311215712101123011216011758118531297612339120131265513184126271198911812116091147213076116271148411792122941179912945129991301211911127101309212256120691156512107115041306913032131901329213287123891297813168131411235312118127491258512042124621220111580121751202412413124451202112777125731200513409117241221412956128021305712455122491233611976118431248411877118101165212381115281170312482126371225412608118011294712750123601148012633125531193811919133601292912158126711184911871119671231812663115941264811741122711179412908133471311113130132351272912178128981208411536118991305811637129831240812270118761189011992128361282912279125751151312450115861168812106119491247011934115291168011692122261221612400124481296212641130431321912820132991315213227132221320213234128111332012714122901287713306117551218912444132091258812852132701288313112131981235812599133331310913323132961312813402125361256211705118701167712204129401170113014127941267611532118961271111727127831289512307123041262511993126181248612878114771224512725122001237411772132891298412504130841240612967128011222313404131221302913035131321270713304128351324813205133591316913164126671306113203115541178611856123231199412545125031165311501116581147012635119301259712460117821203712579124201261511566124431269612646124781180512025114881167913048116151145912268119811270112414122091145712651117781183712362124161272212937132241318211793126431305112266123241307012548115881279312296124691300511604128221157012018125101209312086116061244212559126231273612126119651263412439128991309412145130951267912844118081151211833122931255412227125951229112136120901240312057123781207312569119211246712004119411283112742129771232712348128301311713075131931331412964129961316512394126951288712399114671244011674127451215212715119321267312601125611201112941127201273412995129211217612905133381292813046119681281512584132061293212029121821255012607127441183412537124611205611880115811214712299127281154512612131191290313104129181172211779120671297513275116181297413183131721293111910124071333613357131241333412165130541320013322128181328312243133511338713382133761299413383126241202813408132451299013064127171339713216133561333713370127971272613187132041334213345134061321513257133031331013355121081203613335129011317713236132311332812821126401226411473124251302012708115871310512886119311336712272128601334013281123471312113007125321233012697132581185812033131071272712154129911297213261125831326712746131401211312743122071316612151130091323812832131611337213242132511308013388133541328513315133301339513380121841230013143130271159112186123801238711700127851210212197119511181711973124641222012040126541188612276120091182112051131391192412499133081232112687123521247711816120991222212979119451268011736119871286812202116201266011535121621185111756117801212511486116341192212426124731266611483123331212312156115411189811986118791190612218117081227511492121291176111697120781175012768128261267411508122741269013110124311251913327131201275811814130381186112853123131306512741129351298013358124011289611977123841337113155127981178412103120961253311997124151231512492123321293612507132761327313331133481221212694128271161212208132651310812319123371340513221131881181813375132531324412166118381259812311130031199912167115791231211763122841287611775126751190212481125421182812454124371290613018121271289412230116511248712760122381297311982121421222912149126161257812427115491252311547129501244113368132841340113274132301228112704122061251711895114811288012526126591173411593125001288511962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Jurkat T−cell heatmap2

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Cou

nt

Figure 6: The heatmap has both-side trees and displays explicitly differential expression betweenstimulating and restMost of genes were up-expressed by stimulation but a small part of genes were down-expressed. The treein column divides columns into two groups: NS and 48h. The tree in row is tree of differentially expressedgenes and also divide genes in row into two big groups.

11


Jurk.NS.B

Jurk.NS.A

Jurk.NS.C

Jurk.48h.A

Jurk.48h.C

Jurk.48h.B1310012866119391216412457115891246812604125271161712890132941303312185130681161311649120771219011684127191216912888123341291913157133071151111683122801270311813125491234612116125251274812139114691311412187120521256012955122211311612951127911218111523127541200612590122951247512552131151273511946131351314412897122111198313013129711214812605125431254412842129921251312989117641298513385133861294212891133531276512638131711217411869115851190811556121201167012458124521241112609131021300812570126001186413154123771190912957126881219312235125111250512383123971223112055129651250912180118401248912854122611236612095122361188312112131531216313006122821272413103131331277112215119781324013091131231273212043124511219212064119961224712574125801148912963120541291213042121321278112626123221254712463118311197012792126681266411887115251240213025121001150311819114641265312344114781236312817122331237611961121041221912053128711313413086116481219511823129861217312766125351275512198121301244712678120011175712496122511295312314120911213112325116411235411714123171223712242121681260212396128371249512869118411205911678126141257212393124981265811628116891294813295126521322912143129071319412778129491322512491126811309312265132881300211933128191236412784128121242212682125931308113090124491250612954130211240912453125121241812814118551290212762117431246512153125241167612340126101164312546131751274713176131861303912700124561282512804125871339311787133771229712137133051173511926117311215712101123011216011758118531297612339120131265513184126271198911812116091147213076116271148411792122941179912945129991301211911127101309212256120691156512107115041306913032131901329213287123891297813168131411235312118127491258512042124621220111580121751202412413124451202112777125731200513409117241221412956128021305712455122491233611976118431248411877118101165212381115281170312482126371225412608118011294712750123601148012633125531193811919133601292912158126711184911871119671231812663115941264811741122711179412908133471311113130132351272912178128981208411536118991305811637129831240812270118761189011992128361282912279125751151312450115861168812106119491247011934115291168011692122261221612400124481296212641130431321912820132991315213227132221320213234128111332012714122901287713306117551218912444132091258812852132701288313112131981235812599133331310913323132961312813402125361256211705118701167712204129401170113014127941267611532118961271111727127831289512307123041262511993126181248612878114771224512725122001237411772132891298412504130841240612967128011222313404131221302913035131321270713304128351324813205133591316913164126671306113203115541178611856123231199412545125031165311501116581147012635119301259712460117821203712579124201261511566124431269612646124781180512025114881167913048116151145912268119811270112414122091145712651117781183712362124161272212937132241318211793126431305112266123241307012548115881279312296124691300511604128221157012018125101209312086116061244212559126231273612126119651263412439128991309412145130951267912844118081151211833122931255412227125951229112136120901240312057123781207312569119211246712004119411283112742129771232712348128301311713075131931331412964129961316512394126951288712399114671244011674127451215212715119321267312601125611201112941127201273412995129211217612905133381292813046119681281512584132061293212029121821255012607127441183412537124611205611880115811214712299127281154512612131191290313104129181172211779120671297513275116181297413183131721293111910124071333613357131241333412165130541320013322128181328312243133511338713382133761299413383126241202813408132451299013064127171339713216133561333713370127971272613187132041334213345134061321513257133031331013355121081203613335129011317713236132311332812821126401226411473124251302012708115871310512886119311336712272128601334013281123471312113007125321233012697132581185812033131071272712154129911297213261125831326712746131401211312743122071316612151130091323812832131611337213242132511308013388133541328513315133301339513380121841230013143130271159112186123801238711700127851210212197119511181711973124641222012040126541188612276120091182112051131391192412499133081232112687123521247711816120991222212979119451268011736119871286812202116201266011535121621185111756117801212511486116341192212426124731266611483123331212312156115411189811986118791190612218117081227511492121291176111697120781175012768128261267411508122741269013110124311251913327131201275811814130381186112853123131306512741129351298013358124011289611977123841337113155127981178412103120961253311997124151231512492123321293612507132761327313331133481221212694128271161212208132651310812319123371340513221131881181813375132531324412166118381259812311130031199912167115791231211763122841287611775126751190212481125421182812454124371290613018121271289412230116511248712760122381297311982121421222912149126161257812427115491252311547129501244113368132841340113274132301228112704122061251711895114811288012526126591173411593125001288511962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DE

gen

es

Jurkat T−cell heatmap3

−1 0 1

Value

010

00


Cou

nt

Figure 7: The heatmap did not give trees on both sides, but the heatmap is the same with (Figure 6)

12


Jurk.NS.C

Jurk.NS.A

Jurk.NS.B

Jurk.48h.A

Jurk.48h.B

Jurk.48h.C1168412169127191233412888129191315711511133071164912077121901289013294116131303312185130681158912457119391216412866131001246812604116171252712180125091296512055122311223512511125051238312397121931268812377131541190912957124111245211864130081257012600126091310212748121161252512346125491181312703116831228012052121871311411469121391314412211128971198312971130131194613135125521273513115121811279112951125601295512221131161152312295124751275412006125901251312992121481260512842125431254411670124581212011556119081217413171115851186912942133861338512985117641298912638127651289113353116761234012610116431254612593126821242212812124491308113090130211240912453125061295412418125121185512814117431246512153125241276212902116891162812658123931249812572126141167812059123641278412948132951193312819130021226513288124911268113093129071265212143132291277813194129491322512132130421205412912114891296311831124631232212547126261278111970127921188712664126681152512402122471257412580119961206412192120431245113240119781221512732130911312312163131531300612282127241277113103131331188312112120951223612261123661285411840124891147812344121001302511464126531150311819116411232511841124951286912837123961260212168122421223712317117141235412314129531209112131121981275512173129861253512766122511175712496121301244712001126781196112104120531221912233123761236312817118231219511648130861287113134114721307611609118121162711484117921294511799122941299913012130921191112710120691225611504130691156512107130321319013287132921238912978123531314113168125851211812749120421220112462117311210112157121601230112976117581185311989126271201312339126551318411926117351213713305122971339311787133771245612825125871280412700130391317512747131761318611652124821170312637126081225412381115281193811919133601267111849129291215812947118011263312553127501236011480126631231811967118711159412648117941227111741118771181011976124841184312175115801340911724125731200512413120241277712445120211233612249130571245512214129561280211572130531160011773114751180212776123421239111815117891230811716123351207212205126191193511732119181188512596122671199812672121791177111940123061160212879120451154812224117831208212015116551202012859127791256811942127531242911881117021252812529125141233112041114981272312240122531249011897121211155311990119641192713180114621285512564116591303011552129241292512049127821237912958116681253911537120971285812430120601207611493125201279512515116561195312105115951176212329127301237312048125711166611690127331239812589122861195213228130441312612828130881275713290132501263213271133411331912959125911339413398132801319913125132691313113344133181321012194133811324613233123031324113016131631340712966132931339213067129001332113220130041328613384133461280312677116011223912857119951253011633121101307212030129141241211770127401237013096128471269912840127691207913099124851230513118130661337312882128731276312508126701214411575123751311312875133261297012476131811335011768129971258612636124801245912320128061277013087128461273712012122031277413074125341208011752133091157312385127311222512649123021213811985115621235512738119501261112066128341273912135128051182612863119141279012371121461225912258128811241011980115991222811972116671228312350118061225712884126441161412171119121204611605124211241711578116941292611944125761205012809127161268412150115841153412662118391287412522125511191312014114941210911872117971263012960126201325211777129341151412538119741322613136131011298113106125631234313060127181304111706133611243212428120711249713085130001275612435122981308312292130561268913150129461319712260131851263913237133291275912909131511217713390128621217212889123611326212058132231325513282130781261313254132561209813218131591303113302131781319613311127021339612848124051196913162131451329813195132631295212683120031302612892133741324913352127521192813015127961294412357129611316713363131371290412241132721302812772121591293312943120081266512483134031325913399133321317313174132911317013369133131289313213129101204413232129171319213201128381327812751128001326013098121551162212068115261278711809119481156813149119841298212557123591337913079126471219113019128561238811754117961239212262128331262812622129201278813001123091171811709115301150012922128651256711905118031203211630122631162612326114821254012705126911216113138117591262112285118441161012351115961149011889117071228712250124881191512341130591305013217129381303413017119231291313055128721278613207131601317912987115461330112565130621272112423130891280713156130521292312824127641327913266120071336213189119431234911577130241223212789132681251612556121701239011468127991213313023122441307712434129391286413343125011284913349130821307313297125211312912911127121336613325133001323913364133391299313211132431326413389129691285011650124361315813037118111232811646121401195811824114761236912775126421281012502130971292712474122771249312780127091231612839132771314213071132141337813011122131260613212126861263112424130451228812419116231146112531119631255512278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DE

gen

es

Jurkat T−cell heatmap

−1 0 1

Value

010

00


Cou

nt

Figure 8: This heatmap was labeled with red and blue and gave column trees

13


6 Session Info

> sessionInfo()

R version 4.0.0 (2020-04-24)

Platform: x86_64-pc-linux-gnu (64-bit)

Running under: Ubuntu 18.04.4 LTS

Matrix products: default

BLAS: /home/biocbuild/bbs-3.11-bioc/R/lib/libRblas.so

LAPACK: /home/biocbuild/bbs-3.11-bioc/R/lib/libRlapack.so

locale:

[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8

[4] LC_COLLATE=C LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8

[7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C

[10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:

[1] stats graphics grDevices utils datasets methods base

other attached packages:

[1] MBttest_1.16.0 gtools_3.8.2 gplots_3.0.3

loaded via a namespace (and not attached):

[1] Rcpp_1.0.4.6 digest_0.6.25 bitops_1.0-6 evaluate_0.14

[5] KernSmooth_2.23-17 rlang_0.4.5 gdata_2.18.0 rmarkdown_2.1

[9] BiocStyle_2.16.0 tools_4.0.0 xfun_0.13 yaml_2.2.1

[13] compiler_4.0.0 BiocManager_1.30.10 caTools_1.18.0 htmltools_0.4.0

[17] knitr_1.28

References

[1] Anders S, Huber W (2010) Differential expression analysis for sequence count data.Genome Biol 11: R106.

[2] Thomas J. Hardcastle and Krystyna A. Kelly (2010) baySeq: Empirical BayesianMethods For Identifying Differential Expression In Sequence Count Data. BMCBioinformatics.

[3] Thomas J. Hardcastle (2015) Generalised empirical Bayesian methods for discovery ofdifferential data in high-throughput biology. bioRχv preprint.

[4] Love MI, Huber W, Anders S (2014) Moderated estimation of fold change anddispersion for RNA-Seq data with DESeq2. bioRxiv doi:10.1101/002832.

[5] McCarthy DJ, Chen Y, Smyth GK (2012) Differential expression analysis of multifactorRNA-Seq experiments with respect to biological variation. Nucleic Acids Res,2012, 40:4288-4297.

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[6] Robinson MD, Smyth GK (2008) Small-sample estimation of negative binomialdispersion, with applications to SAGE data. Biostatistics 2008, 9: 321-332.

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[8] Yuan-De Tan. Anita M. Chandler, Arindam Chaudhury, and Joel R. Neilson(2015) APowerful Statistical Approach for Large-scale Differential Transcription Analysis. PlosOne. 2015 DOI: 10.1371.

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MultipleBeta t-TestsofDifferentialTranscrip ......Multiple Beta t-Tests of Differential Transcription of mRNAs Between Two Conditions with Small Samples 7 306 59209 UCRC chr22 + 30165939