 Breast Cancer GeneExpression Miner v5.0 (bcGenExMiner v5.0)   
Glossary
[
Published annotated data ][
Published transcriptomic data ][
Intrinsic molecular subtype classification ][
Data preprocessing ]
[
Statistical analyses ][
Survival statistical tests ][
Graphic illustrations ]
Published annotated data:

The following inclusion criteria for selection of transcriptomic data were used:
 invasive carcinomas,
 metastasisfree at diagnosis,
 freshfrozen tumour macrodissection (no microdissection, no formalinfixed paraffinembedded, no biopsy [expect for TCGA]),
 no neoadjuvant therapy before tumour collection,
 minimum number of patients per cohorts: 35,
 no duplicate sample inside and between datasets, filtering:
. by sample ID and,
. by a threshold of Pearson correlation ‹ 0.99 which is used to avoid duplicate data,
 female breast cancer.

Ver^{1}  Reference  No. patients  ER  PR  HER2  Nodal status  Histo. type  PTS  SBR  NPI  AOL  Age diagn.  Ki67  P53  BRCA  SSPs  SCMs  IC  Event status  IHC  seq  GES  DMFS  OS  DFS  Healthy  4.5  GTEx et al. 2019  92                                            Total for healthy: 92  Tumouradjacent  4.5  TCGA et al. 2012  104                                            Total for tumouradjacent: 104  Tumour  4.3  TCGA et al. 2012  743  717  713  505  690  701  737        743      729    732  743  743    41  95  131  4.3  Saal et al. 2015  3 273  3 073  2 940  3 151  3 180      3 212  3 114    3 273  1 550          3 270  3 273      336  336  4.3  Brueffer et al. 2018  405  405  405  405        405        405          405  405          5.0  Jiang et al. 2016  358  358  358  358  356  334    295  322    358  358        215      235      358  5.0  Jézéquel et al. 2023  48  48  48  48  48  46  46  48  48    48  48        8        3    4  Total for tumour: 4827   5 023  4 601  4 464  4 467  4 274  1 081  783  3 960  3 484  0  4 422  2 361  0  729  0  955  4 418  4 421  235  44  431  829 
 ^{a} ER status determined by means of transcriptomics data (Affymetrix™ probe: 205225_at) in case of a lack of IHC data.
See Kenn et al.
 ^{b} NPI score could be computed only for node negative patients

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Published transcriptomic data:

The following inclusion criteria for selection of transcriptomic data were used:
 invasive carcinomas,
 metastasisfree at diagnosis,
 freshfrozen tumour macrodissection (no microdissection, no formalinfixed paraffinembedded, no biopsy [expect for TCGA]),
 no neoadjuvant therapy before tumour collection,
 minimum number of patients per cohorts: 35,
 no duplicate sample inside and between datasets, filtering:
. by sample ID and,
. by a threshold of Pearson correlation ‹ 0.99 which is used to avoid duplicate data,
 female breast cancer.

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Intrinsic molecular subtypes classification:
Table 1: Intrinsic molecular subtyping methods

MSP 
No. genes in MSP 
Reference 
Platform correspondence 
R script reference 
Statistics 
Subtypes 
Sorlie's SSP 
500 
Sorlie et al, 2003 
Gene symbols; probes median (if multiple probes for a same gene) 
Weigelt et al, 2010 
Nearest centroid classifier; highest correlation coefficient between patient profile and the 5 centroids 
Basallike, HER2E, Luminal A, Luminal B, Normal breastlike 
Hu's SSP 
306 
Hu et al, 2006 
PAM50 SSP 
50 
Parker et al, 2009 
SCMOD1 
726 
Desmedt et al, 2008
Wirapati et al, 2008 
subtype.cluster function, R package genefu 
Mixture of three gaussians; use of ESR1, ERBB2 and AURKA modules 
ER/HER2, HER2E, ER+/HER2 low proliferation, ER+/HER2 high proliferation 
SCMOD2 
663 
SCMGENE 
3 
Table 2: Intrinsic molecular subtyping of 16 854 breast cancer patients
included in bcGenExMiner v5.0 according to 6 molecular subtype predictors.
A DNA microarrays (n = 11 831). B RNAseq (n = 5 023).
(RSSPC: robust SSP classification based on patients classified in the same subtype with the three SSPs;
RSCMS: robust SCM classification based on patients classified in the same subtype with the three SCMs;
RIMSPC: robust intrinsic molecular subtype predictors classification based on patients classified in the same subtype with the six MSPs)

A 
MSP  Basallike  HER2E  Luminal A  Luminal B  Normal breastlike  unclassified  No  %  No  %  No  %  No  %  No  %  No  %  Sorlie's SSP  1 636  15.0  1 313  12.0  3 257  29.8  1 250  11.4  1 454  13.3  2 013  18.5  Hu's SSP  2 510  23.0  983  9.0  2 658  24.3  2 006  18.4  1 662  15.2  1 104  10.1  PAM50 SSP  2 171  19.9  1 623  14.9  3 130  28.7  2 096  19.2  1 325  12.1  578  5.2  RSSPC  1 482    444    1 631    404    709        
MSP  ER/HER2  HER2E  ER+/HER2 low proliferation  ER+/HER2 high proliferation    unclassified  No  %  No  %  No  %  No  %      No  %  SCMOD1  2 067  18.9  1 372  12.6  3 382  31.0  3 037  27.8      1 065  9.7  SCMOD2  2 194  20.1  1 440  13.2  3 250  29.8  2 919  26.7      1 120  10.2  SCMGENE  3 099  28.4  1 599  14.6  2 895  26.5  2 470  22.6      860  7.9  RSCMC  1 488    788    2 031    1 624             RIMSPC  1 227    267    915    265             B 
MSP  Basallike  HER2E  Luminal A  Luminal B  Normal breastlike  unclassified  No  %  No  %  No  %  No  %  No  %  No  %  Sorlie's SSP  582  13.2  605  13.7  1 503  34  625  14.1  789  17.8  317  7.2  Hu's SSP  954  21.6  396  9.0  1 126  25.4  935  21.1  869  19.7  141  3.2  PAM50 SSP  783  17.7  693  15.7  1 343  30.4  966  21.9  602  13.5  34  0.8  RSSPC  544    199    708    210    410        
MSP  ER/HER2  HER2E  ER+/HER2 low proliferation  ER+/HER2 high proliferation    unclassified  No  %  No  %  No  %  No  %      No  %  SCMOD1  584  13.2  343  7.8  1 877  42.4  1 617  36.6      0  0.0  SCMOD2  617  14.0  397  9.0  1 801  40.7  1 606  36.3      0  0.0  SCMGENE  616  13.9  406  9.2  1 838  41.6  1 561  35.3      0  0.0  RSCMC  525    290    1 500    1 209             RIMSPC  482    135    504    202            
Figure 1: Intrinsic molecular subtyping of 16 854 breast cancer patients
included in bcGenExMiner v5.0 according to 6 intrinsic molecular subtype predictors by comparison of source of data: DNA microarrays (outer circles) vs. RNAseq (inner circles).
A 3 single sample predictors and the robust SSP classification (intersection).
B 3 subtype clustering models and the robust SCM classification (intersection).
C Robust RIMSPC classification (robust intrinsic molecular subtype predictors classification based on patients classified in the same subtype with the six MSPs).
 A 
Sorlie's SSP  Hu's SSP  PAM50 SSP  RSSPC  Legend     

Basallike 

HER2E 

Luminal A 

Luminal B 

Normal breastlike 

unclassified 

  B 
SCMOD1  SCMOD2  SCMGENE  RSCMC  Legend     

ER/HER2 

HER2E 

ER+/HER2 low prolif. 

ER+/HER2 high prolif. 

  C 
   RIMSPC  Legend     

Basallike 

HER2E 

Luminal A 

Luminal B 


Legend

MSP:  molecular subtype predictor (SSPs + SCMs)  No.:  number of patients  RIMSPC:  robust intrinsic molecular subtype predictors classification based on patients classified in the same subtype with the six molecular subtype predictors (3 SSPs + 3 SCMs)  RSCMC:  robust SCM classification based on patients classified in the same subtype with the three SCMs  RSSPC:  robust SSP classification based on patients classified in the same subtype with the three SSPs  SCM:  Subtype clustering model (SCMOD1, SCMOD2 or SCMGENE)  SSP:  single sample predictor (Sorlie's, Hu's or PAM50) 


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Data preprocessing:
1 DNA microarrays data
1.1 Affymetrix® preprocessing:
Before being log2transformed, Affymetrix™ raw CEL data were MAS5.0normalised (Microarray Affymetrix™ Suite 5.0)
using the Affymetrix Expression Console™,
except for Affymetrix™ Gene 1.0 ST which were preprocessed using robust multiarray analysis (RMA) algorithme
from Affy Bioconductor package ^{a}.
1.2 NonAffymetrix preprocessing:
Data have been downloaded as they were deposited in the public databases.
When patient to reference ratio and its log2transformation were not already calculated,
we performed the complete process.
1.3 Merging data:
Finally, in order to merge data from all studies and create pooled cohorts,
we converted all studies data, except triplenegative breast cancer (TNBC) subtypes, cohorts to a common scale (median equal to 0
and standard deviation equal to 1 ^{b}). For TNBC cohorts, ComBat ^{c} method was used.


2 RNAseq data
2.1 TCGA preprocessing:
2.1.1 All analyses except nature of tissues:
RNASeq dataset were downloaded from the TCGA database (Genomic Data Commons Data Portal).
Alignment was performed using STAR twopass method, and counts were normalized using the FPKM normalization method ^{d}
(see protocol here).
FPKM values were log2transformed using an offset of 0.1 in order to avoid undefined values.
2.1.2 Nature of the tissue:
To carry out analyses according to the nature of tissue, we used already processed RNAseq data collected by the TCGA.
TPM values were downloaded from GEO via accession number GSM1536837 (tumour) and GSM1697009 (tumouradjacent).
As detailed on GEO website, reads were aligned against hg19 and quantified using the Rsubread package ^{e}.
FPKM values were obtained with with R open source packages edgeR and limma. TPM normalization from the FPKM values.
Once downloaded, gene expression datasets were log2 transformed using an offset of 1.
2.2 GTEx preprocessing:
We used a dataset that contains gene expression values for healthy tissues (no history of cancer, ie reduction mammoplasty) from the GTEx project.
The FPKM values available from GEO (accession number GSE86354) were initially processed and normalized using Rsubread package ^{e} and hg19 as reference genome, as for TCGA.
We converted all FPKM gene expression data to TPM data using the formula below:
An offset of 1 was added to the TPM values prior to log2 transformation.
2.3 SCANB (GSE81540) preprocessing:
We used the Sweden Cancerome Analysis Network – Breast (SCANB) ^{f} database.
RNAseq reads were mapped to the hg19 human genome with tophat2 and normalized in FPKM with cufflinks2 pipeline.
Then log2transformed with an offset of 0.1.
2.4 Merging data:
Finally, in order to merge all studies data and create pooled cohorts,
we converted studies data to a common scale (median equal to 0
and standard deviation equal to 1 ^{b}).
For the analysis of nature of the tissue, standardization is not required since RNAseq raw reads files from different data sources were processed
and normalized with the Rsubread package ^{e}, and aligned to the same reference genome UCSC hg19 with the same pipeline.
For TNBC cohorts, ComBat ^{c} method was used.

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Statistical analyses:
Several types of analyses are available: correlation analyses, expression analyses and prognostic analyses,
all of which have different subtypes.

Correlation analyses


Gene correlation targeted analysis:
Pearson's correlation coefficient is computed with associated pvalue for each pair of genes based on eight different populations:
 all patients pooled together,
 patients with positive or negative oestrogen receptor (ER) status,
 patients with positive or negative progesterone receptor (PR) status,
 patients with ER and PR combinations statuses,
 PAM50 molecular subtyped patients,
 RIMSPC molecular subtyped patients,
 basallike (as defined by PAM50) and triplenegative (as defined by immunohistochemistry [IHC]) patients and the intersection of the 2 latter populations,
 and finally triplenegative breast cancer subtypes patients.
Results are displayed in a correlation map, where each cell corresponds to a pairwise correlation
and is coloured according to the correlation coefficient value, from dark blue (coefficient = 1) to dark red (coefficient = 1).
Pearson's pairwise correlation plots are also computed to illustrate each pairwise correlation.
Gene correlation exhaustive analysis:
Pearson's correlation coefficient is computed, with associated pvalue, between the chosen gene
and all other genes that are present in the database, based on eight different populations: see list in "Gene correlation targeted analysis" section.
Genes with correlation above 0.40 in absolute value and with associated pvalue less than 0.05 are retained and the genes with best correlation coefficients are displayed
in two different tables: one for the first 50 (or less) positive correlations, one for the first 50 (or less) negative ones.
The lists with all genes fulfilling criteria of correlation coefficient above 0.40 in absolute value and associated pvalue less than 0.05 can be downloaded from the results page.


Gene Ontology analysis:
As a complement to this "screening" analysis, an analysis is performed to find Gene Ontology enrichment terms.
This analysis focuses on significantly under or overrepresented terms present in the list of genes most positively correlated with the chosen gene, including itself,
in the list of genes most negatively correlated with the chosen gene and in the union of these two lists.
For each term of each of the Gene Ontology trees (biological process, molecular function and cellular component), comparison is done between
the number of occurrences of this term in the "target list", i.e. the number of times this term is directly linked to a gene,
and the number of occurrences of this term in the "gene universe" (all of the genes that are expressed in the database) by means of Fisher's exact test.
Terms with associated pvalues less than 0.01 are kept.
Gene correlation analysis by chromosomal location:
Pearson's correlation coefficient is computed, with associated pvalue,
between the chosen gene and genes located around the chosen gene (up to 15 up and 15 down) on the same chromosome,
based on eight different populations: see list in "Gene correlation targeted analysis" section.
Pearson's pairwise correlation plots
are also performed to illustrate correlation of each gene with the chosen one.
Targeted correlation analysis (TCA):
As a complement, results of gene correlation analysis for genes selected via the "TCA" column can be displayed.
Targeted correlation analysis ("TCA" button), which aims at evaluating the robustness of clusters, is proposed:
correlation analyses are automatically computed between all possible pairs of genes that compose a selected cluster.

Expression analyses


Targeted expression analysis:
Once the analysis criteria have been chosen (data source, gene / Probe set to be tested, clinical criterion (criteria) to test the gene against),
the distribution of the gene in the available population (all cohorts with availability of required information pooled together)
according to the population splitting criterion (criteria) is illustrated by
box and whisker,
bee swarm,
violin and
raincloud plots.
To assess the significance of the difference in gene distributions in between the different groups, a Welch's test is performed,
as well as DunnettTukeyKramer's tests when appropriate.


Exhaustive expression analysis:
Box and whisker,
bee swarm,
violin and
raincloud plots are displayed, along with Welch's (and DunettTukeyKramer's) tests
for every possible population splitting criteria for a unique gene.
Customised expression analysis:
Similarly to targeted analysis, distribution of a chosen gene is compared in between groups, but here, the groups are defined based on another gene:
the population (all cohorts with both gene values available pooled together) is split according to the expression level(s) of the latter gene.

Prognostic analyses


Timetoevent endpoints or event:
The Timetoevent endpoints (or event) used for survival analyses are:
 "distant metastasisfree survival" (DMFS): first pejorative event represented by distant relapse,
 "overall survival" (OS): first pejorative event represented by death,
 "diseasefree survival" (DFS): first pejorative event represented by any relapse or death.
Targeted prognostic analysis:
Once the analysis criteria have been chosen (data source, gene / Probe Set to be tested,
nodal, oestrogen receptor and progesterone receptor statuses of the cohorts to be explored, event, on which survival analysis will be based, and splitting criterion for the gene),
the prognostic impact of the gene is evaluated on all cohorts pooled by means of univariate
Cox proportional hazards model, stratified by cohort,
and illustrated with a KaplanMeier curve.
Cox results are displayed on the curve. In case of more than 2 groups, detailed Cox results (pairwise comparisons) are given in a separate table.
In order to minimize unreliability at the end of the curve, the 15% of patients with the longest followup are not plotted ^{a}.
To evaluate independent prognostic impact of gene(s) relative to
the wellestablished clinical markers NPI ^{b} and AOL ^{c} (10year overall survival) and to proliferation score ^{d},
adjusted Cox proportional hazards models are performed on pool's patients with available data.
Exhaustive prognostic analysis:
Univariate Cox proportional hazards model and
KaplanMeier curves
are performed on each of the 27 possible pools corresponding to every combination of population (nodal, oestrogen receptor and progesterone receptor status)
for each event criteria (DMFS, OS and DFS)
to assess the prognostic impact of the chosen gene / Probe Set, discretised according to the splitting criterion selected.
Results are displayed by event criteria and population, and are ordered by pvalue (smallest to largest).


Molecular subtype prognostic analysis:
Patients are pooled according to their molecular subtypes, based on three single sample predictors (SSPs)
and three subtype clustering models (SCMs), and on three supplementary robust molecular subtype classifications
consisting on the intersections of the 3 SSPs and/or of the 3 SCMs classifications:
only patients with concordant molecular subtype assignment for the 3 SSPs (RSSPC),
for the 3 SCMs (RSCMC), or for all predictors (RIMSPC), are kept. Univariate Cox proportional analysis
and KaplanMeier curves are performed after choosing
data source, gene / Probe Set, molecular subtype populations, kind of event and discretised according to the splitting criterion selected.
TNBC/Basallike prognostic analysis:
Univariate Cox proportional hazards analyses
and KaplanMeier curves
are performed, for the chosen gene / Probe Set, discretised according to the splitting criterion selected
for allevent criteria (DMFS, OS and DFS),
on Basallike (BL) patients (PAM50), on triplenegative breast cancer (TNBC) patients (IHC) and on patients both TNBC and BL.
TNBC subtypes prognostic analysis:
Univariate Cox proportional hazards analyses and
KaplanMeier curves
are performed, for the chosen gene / Probe Set, discretised according to the splitting criterion selected
for allevent criteria (DMFS, OS and DFS),
on the four triplenegative breast cancer (TNBC) subtyped patients (IHC):
 LAR: luminal androgen receptor;
 MLIA: mesenchymallike immunealtered;
 BLIA: basallike immuneactivated;
 BLIS: basallike immunesuppressed.
More details about TNBC subtypes classification :
Jézéquel et al. Breast Cancer. 2024 May 22.

Nota bene:
 When working with gene symbols and in case of multiple probesets for
the same gene, probeset value median is taken as unique value for the gene.
 KaplanMeier curves will not be computed in populations with less than 5 patients.

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Statistical tests:
Correlation statistical tests


Pearson correlation
 The coefficient:
Pearson correlation coefficient, also known as the Pearson's product moment correlation coefficient and denoted by r, measures the linear dependence (correlation)
between two variables (e.g. genes).
It is obtained by the formula r = cov(G_{1},G_{2}) / (std(G_{1})*std(G_{2})),
where cov(G_{1},G_{2}) is the covariance between the variables G_{1} and G_{2} and std denotes the standard deviation of each variable.
r values can vary from 1 to 1. A negative r means that when the first variable increases, the second one decreases,
a postive r means that both variables increase or decrease simultaneously.
The greater the r in absolute value, the stronger the linear dependence between the two variables, with the extreme values of 1 or 1 meaning a perfect linear dependence
between the two variables, in which case, if the two variables are plotted, all data points lie on a line.


 The associated pvalue:
Along with the Pearson correlation coefficient, one can test if this coefficient is different from 0, knowing that the statistic
t = r*√(n2)/√(1r^{2}) follows a Student distribution with (n2) degrees of freedom, n being the number of values.
The pvalue associated with the Pearson correlation coefficient permits thus to know if a linear dependence exists between the two variables.
Note that one has to be careful when interpreting pvalue associated with Pearson correlation coefficient: a significant pvalue means that a linear dependence
exists between two variables but does not mean that this linear dependence is strong; for example, a coefficient of 0.05 with 1600 data points is associated
with a significant pvalue (p = 0.046) but one can certainly not conclude that there is a strong linear dependence between the two variables !

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Expression statistical tests


Geneexpression comparisons
To evaluate the difference of gene's expression among the different population groups, Welch's test is used in between the groups.
Moreover, when there are at least three different groups and Welch's pvalue is significant (indicating that gene's expression
is different in between at least two subpopulations), DunnettTukeyKramer's test is used for twobytwo comparisons
(this test permits to know the significativity level but does not give a precise pvalue).


Optimal discretisation
In customised analyses, when choosing "optimal" as the splitting criterion for discretisation, gene / Probe Set is split according to
all percentiles from the 20th to the 80th, with a step of 5, and the cutoff giving the best pvalue (Welch's test) is kept.

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Prognostic statistical tests


Optimal discretisation
In prognostic analyses, when choosing "optimal" as the splitting criterion for discretisation,
gene / Probe Set is split according to


all percentiles from the 20th to the 80th, with a step of 5, and
the cutoff giving the best pvalue (Cox model) is kept.


Cox model
 Aim of the Cox model:
Cox model is a regression model to express the relation between a covariate,
either continuous (e.g. G gene) or ordered discrete (e.g. SBR grade), and the risk
of occurrence of a certain event (e.g. metastatic relapse).
Its simplified formula for G gene can be written as follows:
h(t,g) = h0(t)*exp(ß.g), where h is the hazard function of the event occurrence at time t,
dependent on the value g of G and h0(t) is the positive baseline hazard function,
shared by all patients.
ß is the regression coefficient associated with G, the parameter one wants to evaluate.
 Interpretation of Cox model results:
There are two particularly interesting results when building a Cox model: the pvalue
associated with ß, which tells us whether the covariate (e.g. gene) has a significant
impact on the eventfree survival (if the pvalue is less than a certain threshold,
usually 5%) and the hazard ratio (HR) (equal to exp(ß)), sometimes summed up by its “way”
(sign of ß).


The HR, which is really interesting when the pvalue is significant,
is actually a risk ratio of an event occurrence between patients with regards
to their relative measurements for the gene under study. To be more specific,
the HR corresponds to the factor by which the risk of occurrence of
the event is multiplied when the risk factor increases by one unit:
h(t,G+1) = h(t,G)*exp(ß).
The "way" of this HR permits therefore to know how the gene will generally affect
the patients eventfree survival.
For example, saying that parameter ß associated with the gene G under study is negative
(thus exp(ß) < 1) means that the greater the value of G, the lower the risk of event:
if A and B are two patients such as A's G value gA is greater than B's G value gB,
then one can say that patient A has a lower risk of metastatic relapse than patient B:
gA > gB, ß < 0
⇒ ß.gA < ß.gB
⇒ exp(ß.gA) < exp(ß.gB)
⇒ h0(t)*exp(ß.gA) < h0(t)*exp(ß.gB), that is, h(t, gA) < h(t, gB).

KaplanMeier curves
 The KaplanMeier estimator:
KaplanMeier method, also known as the productlimit method, is a nonparametric method
to estimate the survival function S(t) (= Pr(T > t): probability of having a survival
time T longer than time t) of a given population. It is based on the idea that being alive
at time t means being alive just before t and staying alive at t.
Suppose we have a population of n patients, among whom k patients have experienced
an event (metastastic relapse or death for instance) at distinct times
t1 < t2 < ... < tm
(m=k if all events occurred at different times). For each time ti, let ni designs
the number of patients still at risk just before ti, that is patients who have not
yet experienced the event and are not censored, and let ei designs the number of
events that occurred at ti. The eventfree survival probability at time ti, S(ti),
is then the probability S(ti1) of not experiencing the event before time ti
(at time ti1) multiply by the probability (niei)/ni of not experiencing the event
at time ti (which by definition of ti corresponds to the probability of not experiencing
the event during the interval between ti1 and ti): S(ti) = S(ti1) x (niei)/ni.
The KaplanMeier estimator of the survival function S(t) is thus the cumulative product:


 The curve:
The KaplanMeier survival curve, i. e. the plot of the survival function, permits to
visualize the evolution of the survival function (estimate). The curve is shaped like
a staircase, with a step corresponding to events at the end of each [ti1; ti[ interval.
Tick marks on each curve indicate censored observation.
The illustration of the KaplanMeier survival estimator by the KaplanMeier survival
curve becomes especially interesting when there are different groups of patients
(e.g. according to different treatments or different values of biological markers)
and one wants to compare their relative eventfree survival. The different survival
curves are then plotted together and can be visually compared.
The colour palette used for the curve is from R package viridis ^{a},
it permits to keep the colour difference when converted to black and white scale
and is designed to be perceived by readers with the most common form of color blindness.
 Reliability of the estimation:
Caution must be taken concerning the interpretation of the survival curve,
especially at the end of the survival curve: the censored patients induce a loss
of information and reduce the sample size, making the survival curve less reliable;
the end of the curve is obviously particularly affected. For our analyses, in order
to minimize unreliability at the end of the curve, the 15% of patients with
the longest eventfree survival or followup are not plotted ^{a}.

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Graphic illustrations:
Correlation graphic illustrations


Correlation map
A correlation map illustrates pairwise correlations among a given group of genes.
A correlation map is a square table where each line and each column represent a gene.
Each cell represents a mathematical relation between two genes and is coloured according to the value of the Pearson correlation coefficient between these two genes,
from dark blue (coefficient = 1) to dark red (coefficient = 1).
Cells from the diagonal of the correlation map represents "interaction" of a gene with itself and are coloured in black.


Pairwise correlation plot
On a correlation plot, the leastsquares regression line is plotted along with the data points to illustrate the correlation between two given genes.
Pairwise correlation hexagonal bins
For hexbin ^{a} correlation plots, an R Package with binning and plotting functions for hexagonal bins is used.


Expression graphic illustrations


Box and whisker, bee swarm, violin and raincloud plots
Box and whisker plots permit to graphically represent descriptive statistics of a continuous variable (e.g. gene):
the box goes from the lower quartile (Q1) to the upper quartile (Q3), with an horizontal line marking the median.
At the bottom and the top of the box, whisker indicates the distance between the Q1, respectively Q3,
and 1.5 times the interquartile range, that is: Q11.5*(Q3Q1) and Q3+1.5*(Q3Q1).
Bee swarm is a onedimensional scatter plot similar to stripchart, except that wouldbe overlapping points are separated such that each is visible
(package beeswarm^{a}).
Violin plot combines the kernel probability density plot and box and whisker plot.
Density curves are plotted symmetrically on both sides of the box and whisker plot.


Raincloud plot is a combination of splithalf violin, raw jittered data points, and box and whisker plot ^{b}.
Box and whisker, bee swarm, violin and raincloud plots permit to visually compare distributions of a gene among the different population groups.

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