 Breast Cancer GeneExpression Miner v4.5 (bcGenExMiner v4.5)   
Glossary
[
Published annotated data ][
Published genomic 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,
 freshfrozen tumour macrodissection (no microdissection, no biopsy),
 no neoadjuvant therapy before tumour collection,
 minimum number of patients: 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^{2}  PR^{2}  HER2^{2}  Nodal status  Histo. type^{3}  SBR  NPI  AOL  Age diagn.^{4}  P53  SSPs  SCMs  Event status  IHC  seq  GES  DMFS  OS  DFS  Healthy      0                                    Total for healthy: 0  Tumouradjacent      0                                    Total for tumouradjacent: 0  Tumour  1.0  Van de Vijver et al. 2002  295  295  41    295    41  40^{b}    41        295  295  101  79  122  1.0  Sotiriou et al. 2003  99  99      99  99  99  99  99  99        90  99  30  45  53  1.0  Ma et al. 2004  59  59  59  55  52  59  59  52  52  59        59  59      27  1.0  Minn et al. 2005  82  82  82  76  82          82        82  82  27    27  1.0  Pawitan et al. 2005  159  159^{a}          147            159  159  159  40  40  50  1.0  Wang et al. 2005  286  286      286                  286  286  107    107  1.0  Weigelt et al. 2005  50  50      50    50  21^{b}    50        50  50  13  10  13  1.0  Bild et al. 2006  158  158^{a}                        158  158    50  50  1.0  Chin et al. 2006  112  112  112  78  112    107  46^{b}    112  80      99  112  21  35  42  1.0  Ivshina et al. 2006  249  245      240    249  159^{b}    249  247    249  249  249      89  1.0  Desmedt et al. 2007  198  198      198  184  196  196  196  198        198  198  62  56  91  1.0  Loi et al. 2007  267  261  87    261    208  123^{b}    267      267  266  267  66    88  1.0  Minn et al. 2007  58  58                        58  58  11    11  1.0  Naderi et al. 2007  135  133      129    134  129  128  135        127  135    47  65  1.0  Anders et al. 2008  75  71  70    75  74  64  64  61  75        75  75  14    14  1.0  Chanrion et al. 2008  151  139  139    146  139  144  134  124  151        139  151  46  41  55  1.0  Loi et al. 2008  77  77  77    77    58  30^{b}    77      77  77  77  10    13  1.0  Calabrò et al. 2009  139  136  136  49  103          139        116  139    63  96  1.0  Jézéquel et al. 2009  252  239  236  203  252    252  252  252  252            65  47  68  1.1  Schmidt et al. 2008  200  200^{a}      200    200  200            200  200  46    46  1.1  Zhang et al. 2009  136  136  136    136                  136  136  20    20  3.1  Chin et al. 2007  171  170      170    170  170    171        152  171  38  57  56  3.1  Zhou et al. 2007  54  54      54          54        54  54  9    9  3.1  Desmedt et al. 2009  55  55  55  45  55    55      55      55  55  55      55  3.1  Jönsson et al. 2010  346  335  332        226              346      151  151  3.1  Li et al. 2010  115  115  115  115  115  103  115  64^{b}    115      115  115  115  14    14  3.1  Sircoulomb et al. 2010  55  47  47  37  45  33  47      49  29    55  55  55  17    17  3.1  Buffa et al. 2011  216  216      216    191  191    216        216  216  82    82  3.1  Dedeurwaerder et al. 2011  85  84    85  85  85  85  29^{b}    85      85  85  85      36  3.1  Filipits et al. 2011  277  277    277                    276  277  58    58  3.1  Hatzis et al. 2011  309  304  303  309  309    286      309        309  309  65    65  3.1  Kao et al. 2011  296  296^{a}      296          296      296  296  296  63  62  73  3.1  Sabatier et al. 2011  239  237  237  224  233  211  233      238  175    239  239  239      74  3.1  Wang et al. 2011  149  149  149  149  148  147  149  148    149        149  149      10  3.1  Kuo et al. 2012  51  51  51  51  51  51  47      51        51  51  12    12  3.1  Nagalla et al. 2013  41  40  38  39  41    39  39  36  41        41  41  14  10  14  4.3  expO et al. 2005  298  210  209  198  257  289  252  39^{b}    298      298  298  298        4.3  Yau et al. 2007  47  47  47    43          47        47  47        4.3  Parris et al. 2010  94  94  94  94  94  80  75  75    93        93  94    44  45  4.3  Symmans et al. 2010  43  43      42                  43  43  71    71  4.3  Heikkinen et al. 2011  174                          172  174  34  27  34  4.3  Sabatier et al. 2011  71  71  71  19  26          44      71  71  71        4.3  Curtis et al. 2012  1 980  1 937  1 980  1 980  1 980  1 830  1 892  1 875    1 980    1 980    1 978  1 980  602  1 143  1 235  4.3  Guedj et al. 2012  536  515  514  390  438  427  517      523  239    536  536  536  119    119  4.3  Servant et al. 2012  343        337  318  339      343  97      343  343  119    119  4.3  Clarke et al. 2013  104  101      104    104  45^{b}    104      104  104  104  48  35  48  4.3  Larsen et al. 2013  183  183  183  183    169  157      183        182  183        4.3  Castagnoli et al. 2014  53  53  53  53  53    53      53        53  53  23    23  4.3  Fumagalli et al. 2014  56  56  56  56  54  52  56  54    55      56  56  56        4.3  Merdad et al. 2014  45  38  38  38    40  38      45        45  45        4.3  Terunuma et al. 2014  55  55  12  12  55    48  24^{b}    55  55      55  55    19  19  4.3  Burstein et al. 2015  66  66  66  49    64  47      63      66  66  66        4.3  Michaut et al. 2016  104  88  92  89  104  95  96  83    103        104  104  26  20  32  4.3  Biermann et al. 2017  53  52  52  53  42          53        53  53        4.5  Bos et al. 2009  204  56  56  56                              4.5  Silver et al. 2010  75  35  35  35                              4.5  Burstein et al. 2015  198  198  198  198                              4.5  Jézéquel et al. 2015  107  107  107  107                              4.5  Jézéquel et al. 2019  131  131  131  131                              Total for tumour: 10716   10 716  9 759  6 496  5 533  8 240  4 549  7 325  4 381  948  7 857  922  1 980  2 728  9 657  9 403  2 093  2 081  3 618 
 ^{1} Version of bcGenExMiner webtool
 ^{2} ER, PR and HER2 status determined by immunohistochemistry (IHC)
 ^{3} Histological types
 ^{4} Age at diagnosis
 ^{a} ER status determined by means of genomics 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 genomic data:

The following inclusion criteria for selection of transcriptomic data were used:
 invasive carcinomas,
 freshfrozen tumour macrodissection (no microdissection, no biopsy),
 no neoadjuvant therapy before tumour collection,
 minimum number of patients: 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

Molecular subtypes predictor (MSP) 
No. genes in MSP 
Reference 
Platform correspondence 
R script reference 
Statistics 
Subtypes 
Single sample predictor (SSP) 
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 
Subtype clustering model (SCM) 
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 14 713 breast cancer patients
included in bcGenExMiner v4.4 according to 6 molecular subtype predictors.
A DNA microarrays (n = 10 001). B RNAseq (n = 4 712).
(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  1 453  14.5  1 182  11.8  2 934  29.3  1 142  11.4  1 313  13.1  1 977  19.8  Hu's SSP  2 277  22.8  879  8.8  2 422  24.2  1 840  18.4  1 500  15  1 083  10.8  PAM50 SSP  1 954  19.5  1 477  14.8  2 811  28.1  1 944  19.4  1 257  12.6  558  5.6  RSSPC  1 306    388    1 439    366    651        
MSP  ER/HER2  HER2E  ER+/HER2 low proliferation  ER+/HER2 high proliferation    unclassified  No  %  No  %  No  %  No  %      No  %  SCMOD1  1 867  18.7  1 156  11.6  3 104  31  2 809  28.1      1 065  10.6  SCMOD2  1 965  19.6  1 117  11.2  2 966  29.7  2 682  26.8      1 271  12.7  SCMGENE  2 790  27.9  1 400  14  2 586  25.9  2 202  22      1 023  10.2  RSCMC  1 288    690    1 827    1 490             RIMSPC  1 055    231    828    242             B 
MSP  Basallike  HER2E  Luminal A  Luminal B  Normal breastlike  unclassified  No  %  No  %  No  %  No  %  No  %  No  %  Sorlie's SSP  625  13.3  641  13.6  1 595  33.8  667  14.2  839  17.8  345  7.3  Hu's SSP  1 022  21.7  421  8.9  1 200  25.5  1 001  21.2  923  19.6  145  3.1  PAM50 SSP  832  17.7  736  15.6  1 433  30.4  1 029  21.8  639  13.6  43  0.9  RSSPC  583    208    748    226    435        
MSP  ER/HER2  HER2E  ER+/HER2 low proliferation  ER+/HER2 high proliferation    unclassified  No  %  No  %  No  %  No  %      No  %  SCMOD1  630  13.4  365  7.7  1 986  42.2  1 731  36.7      0  0.0  SCMOD2  667  14.2  416  8.8  1 913  40.6  1 716  36.4      0  0.0  SCMGENE  781  16.6  2 360  50.1  838  17.7  733  15.6      0  0.0  RSCMC  551    150    661    465             RIMSPC  513    72    192    66            
Figure 1: Intrinsic molecular subtyping of 14 713 breast cancer patients
included in bcGenExMiner v4.4 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  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  SSP:  single sample predictor 


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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 all studies data and create pooled cohorts,
we converted all studies data, except tripleNegative breast cancer (TNBC), 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).
We used the RNAseq expression level read counts data produced by HTSeq and normalized using the FPKM normalization method ^{d} .
FPKM values was 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 RNAseq data collected by the TCGA processed and normalized using the Rsubread package ^{e}.
TPM values were downloaded from GEO via accession number GSM1536837 (tumour) and GSM1697009 (tumouradjacent).
All 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.
FPKM values available from GEO (accession number GSE86354) were processed and normalized using Rsubread package ^{e}.
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.

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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, beeswarm, 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, beeswarm, 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 subtypes populations, kind of event and discretised according to the splitting criterion selected.
Basallike/TNBC 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 all event criteria (DMFS, OS and DFS),
on Basallike (BL) patients (PAM50), on TripleNegative breast cancer (TNBC) patients (IHC) and on patients both BL and TNBC.

Nota bene:
 When working with gene symbols and in case of multiple probesets for
the same gene, probeset values 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.


Expression graphic illustrations


Box and whisker, beeswarm, 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).
Beeswarm 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, beeswarm, violin and raincloud plots permit to visually compare distributions of a gene among the different population groups.

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