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Decision Making Associa ion Rules o Recogni ion o
Di e en ial Gene Exp ession P ofiles
Con e ence Pape inLec u e No es in Compu e Science · Sep embe 2006
DOI: 10.1007/11875581_135·Sou ce: DBLP
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Decision Making Associa ion Rules o Recogni ion o
Di e en ial Gene Exp ession P o iles
C. Rubio-Escude o1, Co al del Val1, O. Co dón1,2, and I. Zwi 1,3
1 Depa men o Compu e Science and A i icial In elligence, Uni e si y o G anada, Spain
2 Eu opean Cen e o So Compu ing, Mie es, Spain
3 Howa d Hughes Medical Ins i u e, Washing on Uni e si y School o Medicine, S . Louis, MO
{c ubio, del al, oco don, zwi }@decsai.ug .es
Abs ac . The apid de elopmen o me hods ha selec o e /unde exp essed
genes om RNA mic oa ay expe imen s ha e no ye sa is ied he need o
ools ha iden i y di e en ial p o iles ha dis inguish be ween expe imen al
condi ions such as ime, ea men and pheno ype. We e alua e se e al mic oa -
ay analysis me hods and s udy hei pe o mance, inding ha none o he
me hods alone iden i ies all obse able di e en ial p o iles, no subsumes he
esul s ob ained by he o he me hods. The e o e, we p opose a machine lea n-
ing based me hodology ha iden i ies and combines he abili ies o mic oa ay
analysis me hods o ecognize di e en ial p o iles. We encode he esul s o his
me hodology in decision making associa ion ules able o decide which me hod
o me hod-agg ega ion is op imal o e ie e a se o genes exhibi ing a common
p o ile. These solu ions a e op imal in he sense ha hey cons i u e pa ial o -
de ed subse s o all me hod-agg ega ions bounded by he mos speci ic and he
mos sensi i e a ailable solu ion. This me hodology was success ully applied o
a s udy o in lamma ion and hos esponse o inju y da a se de i ed om he
analysis o longi udinal blood mic oa ay p o iles o human olun ee s ea ed
wi h in a enous endo oxin compa ed o placebo. Ou app oach was able o un-
co e a cohesi e se o di e en ially exp essed genes and no el membe s ex-
hibi ing p e iously s udied di e en ial p o iles. This guideline se es as a
means o suppo decisions on new mic oa ay p oblems.
1 Backg ound
Ad ances in molecula biology and compu a ional echniques pe mi he sys ema ical
s udy o molecula p ocesses ha unde lie biological sys ems [1]. Pa icula ly, mi-
c oa ay echnology has e olu ionized mode n biomedical esea ch by i s capaci y o
moni o changes in RNA abundance o housands o genes simul aneously [2].
To add ess he s a is ical challenge o analyzing hese la ge da a se s, new me hods
ha e eme ged ([3], [4], [5], [6], [7]). Howe e , he e is a dea h o compu a ional
me hods o acili a e unde s anding o di e en ial gene exp ession p o iles (e.g., p o-
iles ha change o e ime and/o o e ea men s and/o o e pa ien s) and o decide
which is he mos eliable me hod o iden i y di e ences ac oss p o iles.
We de elop a de ailed e alua ion o he pe o mance o se e al commonly used
s a is ical me hods o iden i y di e en ial exp ession p o iles. We ound ha he ap-
plica ion o hese me hods e u n di e en esul s applied o e he same se o da a:
he me hods do no iden i y all obse able di e en ial p o iles (genes exhibi ing a
common beha io h oughou expe imen al condi ions). Mo eo e , none o he me h-
ods subsume he esul s ob ained by he o he me hods.
Ou s udy e eals how some me hods a e able o ecognize some di e en ial p o-
iles and no o he s and ha some o he no e ie ed p o iles migh con ain signi i-
can genes o he expe imen unde s udy. The e o e, we p opose a me hodology ha
combines he p ope ies o each me hod in o a se o decision making associa ion
ules ([8], [9], [10]) de o ed o disco e op imal agg ega ions o mic oa ay analysis
me hods in an e o o iden i y di e en ial gene exp ession p o iles. The associa ion
ules allow use s o que y o he mos app op ia e me hod o agg ega ion o hem o
e ie e signi ican genes based on he di e en ial p o iles hey exhibi .
To c ea e such se o decision associa ion ules we pe o m he ollowing s eps
o e a se o mic oa ay gene exp ession da a (Fig. 1). Fi s , we ex ac om he da a
se all genes which beha e in a di e en way om one expe imen al condi ion o he
o he s (i.e., genes ha change o e ime, ea men s and pheno ype). We apply se e al
classical mic oa ay analysis me hods (T-Tes s [11], Pe mu a ion Tes s [6], Analysis
o Va iance [5] and Repea ed Measu es ANOVA [12]). Second, we c ea e a da abase
con aining dis inc ypes o di e en ial p o iles o e ime, expe imen and subjec s
om p e iously eco e ed genes.
DIFFERENTIALLY
EXPRESSED
GENES
MICROARRAY
RAW DATA
MICROARRAY
PREPROCESSED
DATA
PREPROCESSING
(1)
(4)
IDENTIFICATION
OF DIFFERENTIAL
PROFILES
DIFFERENTIAL
EXPRESSION
PROFILES
METHOD
EVALUATION
SCALING
(2)
IDENTIFICATION
OF DIFF.
EXPRESSED
GENES
(6)
PREDICTION
QUERY PROFILES
+
MICROARRAY
DATA
(OPTIONAL)
METHOD
SELECTION
(5)
CREATION OF
METHOD ASS.
RULES
METHOD
ASSOCIATION
RULES
(3)
ASSOCIATION
OF STATISTICAL
METHODS
LATTICE
OF METHOD
ASSOCIATIONS
STATISTICAL
METHODS
CONCEPTUAL
CLUSTERING
PROFILE
IDENTIF.
PROFILE
PRUNING
NORMALIZING
Fig. 1. G aphical ep esen a ion o he me hodology. The squa ed boxes ep esen he phases o
he me hodology, he ound co ne ed boxes co espond o he inpu /ou pu da a a each s ep,
and he ellipses he ope a ions pe o med a each phase.
Thi d, we c ea e decision making associa ion ules, whe e he an eceden s a e di -
e en ial p o iles and he consequen s a e me hods o agg ega ions o hem capable o
iden i y he p o iles. Fou h, we a ange he associa ion ules in o a la ice, whe e he
ules a e o de ed om he mos gene al ( op) o he mos speci ic solu ion (bo om).
We use his s uc u e o e alua e he pe o mance o he ules by analyzing hei
speci ici y, sensi i i y and cos , applying mul iobjec i e op imiza ion echniques.
Fi h, we use a selec ed se o op imal ules as a amewo k o suppo new decisions
abou he applicabili y o mic oa ay analysis me hods o e ie e di e en ial gene
exp ession p o iles.
2 Resul s
The esul s a e ob ained om he applica ion o ou p ocedu e o a da a se de i ed
om longi udinal blood exp ession p o iles o human olun ee s ea ed wi h in a e-
nous endo oxin compa ed o placebo. The mo i a ion o hese expe imen s is o p o-
ide insigh o he hos esponse o inju y as pa o a La ge-scale Collabo a i e
Resea ch P ojec sponso ed by he Na ional Ins i u e o Gene al Medical Sciences
(www.glueg an .o g) [13]. Analysis o he se o gene exp ession p o iles ob ained
om his expe imen is complex, gi en he numbe o samples aken and a iance due
o ea men , ime, and subjec pheno ype. The e o e, we belie e his p oblem is ypi-
cal and in o ma i e as a mic oa ay case s udy. The da a we e acqui ed om blood
samples collec ed om eigh no mal human olun ee s, ou ea ed wi h in a enous
endo oxin (i.e., pa ien s 1 o 4) and ou wi h placebo (i.e., pa ien s 5 o 8). Comple-
men a y RNA was gene a ed om ci cula ing leukocy es a 0, 2, 4, 6, 9 and 24 hou s
a e he i. . in usion and hyb idized wi h GeneChips® HG-U133A 2.0 om A y-
me ix Inc., which con ains 22216 p obe se s, analyzing he exp ession le el o 18400
ansc ip s and a ian s, including 14500 well-cha ac e ized human genes.
2.1 Accu acy o he S a is ical Me hods
We in es iga e he pe o mance o se e al commonly used s a is ical me hods in iden-
i ying di e en ial exp ession p o iles ha change o e ime, ea men s and pheno-
ype. We name T-Tes as 1
M, T-Tes conside ing ime as 2
M, Pe mu a ion Tes
as 3
M, Pe mu a ion Tes conside ing ime as 4
M, ANOVA o e ea men as 5
M,
ANOVA o e ime as 6
M, ANOVA o e ea men and ime as 7
M, RMANOVA
o e ea men as 8
M, RMANOVA o e ime as 9
Mand RMANOVA o e ea men
and ime as 10
M, whe e conside ing ime e e s o he ac ha he es s ha e been
speci ically applied o ind di e ences be ween ime poin s. Fo ou se o da a, we
ound ha hese me hods do no iden i y all obse able dis inc p o iles. Mo eo e ,
none o hem subsumes he esul s ob ained by o he me hods (Table 1). Di e en
me hods e ie e di e en amoun s o p obe se s (e.g., he applica ion o 1
Mo e he
mic oa ay da ase e ie es 962 genes as di e en ially exp essed, whe eas 5
M e-
ie es 1734 genes, and 3
M
e ie es 612 genes). The conco dance a es be ween he
se s o genes e ie ed also a ies widely, indica ing ha none o he me hods sub-
sumes he o he s (Table 1)(e.g., om he genes e ie ed by 3
M, only 31.11% a e
also e ie ed by 5
M, and 52.29% by 1
M.
2.2 S a is ical Me hods and Di e en ial P o iles
We ound ha he e is a ela ionship be ween he s a is ical me hods and he di e en-
ial p o iles hey a e able o iden i y, ha ing di e en ial p o iles iden i ied by some
me hods and no by o he s. This ype o ela ion is wha we encode in he se o deci-
sion making associa ion ules ha we ob ain om he applica ion o ou me hodology.
In ou pa icula p oblem, he e a e genes highly ela ed wi h he in lamma ion p ob-
lem which exhibi p o iles ha would no be e ie ed applying some o he classic
mic oa ay analysis me hods indi idually. Tha is he case o p obe se 206011_a ,
which is ela ed in beha io and in unc ion (apop osis- ela ed cys eine pep idase) o
p obe se s 211367_s_a and 211368_s_a (Fig. 2(a)), s a ed as ele an o he in-
lamma ion p oblem in [13]. Fo hese pa icula p obe se , he isola ed applica ion o
classical me hods such as 1
Mo 3
M wi h ei he de aul p- alue o alse disco e y,
a e, depending on wha each me hod uses, would no e ie e such p obe se as di -
e en ially exp essed. The same si ua ion applies o p obe se s 202076_a and
210538_s_a , ela ed bo h in beha io and in unc ion (inhibi o o apop osis p o ein 2
and 1 espec i ely) (Fig. 2(b)).
Table 1. In e sec ion o he esul s be ween me hods ecognizing di e en ially exp essed
genes. The numbe in each cell ep esen s he a io o coincidence be ween genes e ie ed by
he s a is ical me hod in he column and in he ow ela i e o he o al numbe o genes eco -
e ed by he me hod in he ow RowColumnRow /)(( ∩).
% 1
M2
M3
M 4
M 5
M6
M7
M 8
M9
M10
M
1
M -- 92.20 52.29 75.05 96.48 69.23 85.55 70.06 61.33 50.52
2
M56.06 -- 34.07 57.84 85.27 59.54 71.11 62.64 50.57 42.98
3
M 82.19 88.07 -- 96.24 94.77 57.35 78.75 72.87 56.86 46.73
4
M67.22 85.19 54.84 -- 95.16 55.49 73.65 70.20 51.49 42.83
5
M55.20 77.80 33.45 58.94 -- 50.28 66.72 66.38 46.42 38.93
6
M59.04 83.51 31.11 52.84 77.30 -- 89.63 56.56 60.64 49.38
7
M58.36 79.79 34.18 56.10 82.05 71.70 -- 62.34 57.23 49.07
8
M 57.36 84.34 37.96 64.17 95.96 54.30 74.80 -- 49.62 40.51
9
M62.10 84.21 36.63 58.21 84.74 72.00 84.95 61.36 -- 72.31
10
M 59.56 83.34 35.05 56.37 82.72 68.26 84.80 58.34 84.19 --
In con as , some o he a ailable me hods e ie e p o iles ha do no di e be-
ween he conside ed expe imen al condi ions. Fo example, ANOVA, pe haps based
on he iola ion o s a is ical cons ain s ([14]), e ie es a 43% o genes lacking an
obse able change wi h he de aul pa ame e alues. The inc ease o he speci ici y
o hese pa ame e s gene a es se e e e ec s on he sensi i i y o o he ue changes.
These indings e eal ha he e a e desi ed and undesi ed di e en ial p o iles
e med posi i e and nega i ely, espec i ely. Fo example, some p o iles exhibi ing
simila ly a anged pa e ns bu shi ed o e ime may be ele an o a speci ic ex-
pe imen bu no o o he . In addi ion, we also ound ha me hods applied o mi-
c oa ay p o iles a e ocused on iden i ying di e ences among exp ession pa e ns
o e ea men and/o ime since biological eplica es a e a e aged in he same ex-
pe imen al g oup. Howe e , we migh also need o de ec di e ences among subjec s.
We c ea e a da abase wi h all possible di e en ial p o iles de i ed om genes e-
ie ed in ou in lamma ion p oblem by all a ailable me hods (i.e., 28 di e en ial p o-
iles). This da abase con ains di e en ial p o iles ha can be labeled as posi i e o
nega i e acco ding o hei in e es o be e ie ed o a pa icula s udy. To alida e
biologically hese p o iles we calcula e he coincidence he coincidence be ween ou
e ie ed di e en ial p o iles and ex e nal in o ma ion p o ided by he Gene On ology
da abase ([15]) showing ha genes sha ing beha iou a e ela ed in unc ion ([16]).

1000
2000
3000
4000
5000
PAT1 PAT2 PAT3 PAT4
(a)
1000
2000
3000
4000
5000
PAT1 PAT2 PAT3 PAT4
(b)
Fig. 2. P obe se s in blue a e s a ed as ele an o he in lamma ion p oblem in ([13]). P obe
se s in ed a e de ec ed by applica ion o ou me hodology bu no by applying some classical
mic oa ay analysis me hods indi idually. In (a) he p obe se in ed, 206011_a , is ela ed o
p obe se s 211367_s_a and 211368_s_a (blue) bo h in exp ession h oughou ime and in unc-
ion (apop osis- ela ed cys eine pep idase). In (b) we see he same si ua ion be ween 202076_a
in ed and 210538_s_a in blue, which ha e co ela ed le el o exp ession h oughou ime and
sha e hei unc ion (inhibi o o apop osis p o ein 2 and 1 espec i ely).
The empo al exp ession da a in ou da abase can be a e aged o sequen ially ep e-
sen ed o each biological eplica e. O iginally, he da abase was buil based on he in-
lamma o y esponse pa e ns, which is based on a e y obus mic oa ay expe imen
([13]). Now, i is being upda ed wi h expe imen s p o ided om di e en sou ces
such as he Ven ila o Associa ed Pneumonia (unpublished esul s).
The applica ion o ou me hodology o he da abase o di e en ial p o iles allowed
he op imal e ie al o he desi ed di e en ial p o iles. Fo example, i we we e in e -
es ed in p obe exhibi ing any o 27 o he p o iles in he da abase and no exhibi ing
one o he p o iles, we a e able o do applying 65 MM ∪wi h speci ici y and sensi i -
i y le els o 94% and 92% espec i ely. In Fig. 3 we show he me hod-agg ega ions
om he op imal ules o e ie e indi idually each o he 28 p o iles in ou da abase.
Fig. 3. Mic oa ay analysis me hods a e able o e ie e some di e en ial p o iles and no o h-
e s. Rows co espond o me hod-agg ega ions using he union ope a o and columns o each o
he 28 indi idual di e en ial p o iles om ou example. The colo ing scheme co esponds o
he sensi i i y in e ie ing he di e en ial p o ile: om g een, he lowes , o black, he highes .
M6.M9.M10
M6.M10
M5.M6.M7.M8.M10
M5.M6
M4.M6.M8.M10
M4.M6.M10
M3.M8
M3.M4
M2.M6.M9
M2.M5.M6.M7.M8.M10
M2.M5
M2.M4.M7.M8.M10
M2.M4.M5.M6.M7.M10
M2.M3.M10
M10
M1.M6.M9
M1.M4.M6.M7.M8
M1.M4
M1.M2
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Ou app oach also eco e s p obe se s wi h ela ed beha io o o he p obe se s
wi h al eady known p o iles which migh ha e ela ed unc ionali ies ([16]). Fo in-
s ance, p obe se 206011_a is ela ed in beha io and in unc ion (apop osis- ela ed
cys eine pep idase) o p obe se s 211367_s_a and 211368_s_a (Fig. 2(a)), s a ed as
ele an o he in lamma ion p oblem in [13]. Fo hese pa icula p obe se , he iso-
la ed applica ion o classical me hods such as 1
Mo 3
M wi h he de aul p- alue and
alse disco e y a e would no e ie e such p obe se as di e en ially exp essed. We
e ie e such p obe se applying he ule ha implies he me hod agg ega-
ion 107MM ∪ wi h alues (1, 0.25, 0.8) o sensi i i y, speci ici y and cos espec-
i ely. The same si ua ion applies o p obe se s 202076_a and 210538_s_a , ela ed
bo h in beha io and in unc ion (inhibi o o apop osis p o ein 2 and 1 espec i ely)
(Fig. 2(b)). I is e ie ed applying he ule o me hods 63 MM ∪wi h alues (0.93,
0.35, 0.8).
In addi ion, he ep esen a ion used in he in lamma ion p oblem (Fig. 4) allows us
o independen ly examine he gene beha io in each subjec , helping o unco e indi-
idual endencies among biological eplica es ha could ep esen condi ions no p e-
iously conside ed such as gende o age (e.g., di e en ial p o ile #15 (Fig. 5), whe e
some o he p obe se s om pa ien 1 exhibi a e y di e en beha io han he es o
he pa ien s).
We illus a e he ob ained associa ion ules o P o ile #19 om ou da abase (Ta-
ble 2) and he Pa e o-op imal on o he h ee objec i es co esponding o he se-
lec ed ules (Fig. 6).
Fig. 4. P o ile #19: he exp ession p o iles ha e been ep esen ed sepa a ely o each subjec he
expe imen al g oup and pa ien s a e a anged indi idually
3 Me hods
Mos machine lea ning echniques a e applied o mine in o da ase s o disco e con-
cep s in ol ing objec s which sha e a common me hodological amewo k, e en
hough hey employ dis inc me ics, heu is ics o p obabili y in e p e a ions ([17],
[18]): (1) iden i ica ion o a da abase, di e en da a ypes can be e icien ly o ganized
by aking ad an age o a na u ally occu ing s uc u e o e ea u e space. (2) lea ning
ules om he da abase, sea ching h ough he ea u e space o po en ial ela ionships
5000
10000
HOUR
02469240246924 0246924 0246924
PAT1 PAT2 PAT3 PAT4
5000
10000
HOUR
0246924 02924 0246924 0246924
PAT5 PAT6 PAT7 PAT8
0 2 4 6 9 24
5000
10000
0 2 4 6 9 24
5000
10000
among da a, and ei he e u ning he bes one ound o an op imal sample o hem. This
lea ning p ocess would esul in he gene a ion o many ules wi h small ex en , as i is
easie o explain o ma ch small da a subse s han hose ha cons i u e a signi ican
po ion o he da ase . Fo his eason, any success ul me hodology should also con-
side addi ional c i e ia ([19]) o ex ac b oade o mo e comp ehensi e ules as a mul-
iobjec i e op imiza ion p oblem, based on hei speci ici y, sensi i i y and cos as a
measu es o he ule quali y. (3) In e ence, whe e new obse a ions can be p edic ed
om p e iously lea ned ules by using classi ie s ha op imize hei ma ching o he
ules based on dis ance ([18]) o p obabilis ic me ics ([20], [21]).
We p opose a me hod, inspi ed on concep ual clus e ing and op imiza ion ech-
niques ([9], [10], [17]), ha iden i ies a da abase o gene p o iles ha change hei ex-
p ession o e ime and/o o e ea men s and/o o e subjec s, lea ns associa ions
ules and make decisions abou he mic oa ay analysis me hod o he bes agg ega-
ion o me hods capable o de ec ing a desi ed se o di e en ial p o iles, and inally
uses hese ules o make decisions based on new si ua ions (Fig.1).
0.5
1
1.5
2
2.5 x 10
4
PAT1 PAT2 PAT3 PAT4
0.5
1
1.5
2
2.5 x 10
4
PAT5 PAT6 PAT7 PAT8
Fig. 5. P o ile #15: pa ien 1 beha es di e en han pa ien s 2, 3 and 4 o he ea men g oup
Table 2. Se o decision making associa ion ules gene a ed o e ie e P o ile #19. The axes
(X,Y,Z) ep esen he numbe o me hods, speci ici y and sensi i i y o each o he 35 solu ions
gene a ed.
RULES Sensi i i y Speci ici y Cos
R1:IF
x1
IS (
PTPC
)19 THEN
Z1
IS
M1
0.878378 0.0675676 0.9
R2:IF
x1
IS (
PTPC
)19 THEN
Z2
IS
M2
0.972973 0.045512 0.9
R3:IF
x1
IS (
PTPC
)19 THEN
Z3
IS
M7
0.905405 0.0475177 0.9
R4:IF
x1
IS (
PTPC
)19 THEN
Z4
IS
M1
∩
M2
0.864865 0.0721533 0.8
R5:IF
x1
IS (
PTPC
)19 THEN
Z5
IS
M2
∪
M10
1 0.0430733 0.8
R7:IF
x1
IS (
PTPC
)19 THEN
Z7
IS
M1
∩
M10
0.594595 0.090535 0.8
R8:IF
x1
IS (
PTPC
)19 THEN
Z8
IS
M2
∩
M7
0.891892 0.0538776 0.8
R9:IF
x1
IS (
PTPC
)19 THEN
Z9
IS
M3
∩
M9
0.472973 0.100575 0.8
R10:IF
x1
IS (
PTPC
)19 THEN
Z10
IS
M3
∩
M10
0.405405 0.104895 0.8
R11:IF
x1
IS (
PTPC
)19 THEN
Z11
IS
M1
∩
M2
∩
M7
0.797297 0.0732919 0.7
R12:IF
x1
IS (
PTPC
)19 THEN
Z12
IS
M1
∩
M2
∩
M9
0.662162 0.0853659 0.7
R13:IF
x1
IS (
PTPC
)19 THEN
Z13
IS
M1
∩
M3
∩
M7
∩
M10
0.459459 0.112211 0.6
R14:IF
x1
IS (
PTPC
)19 THEN
Z14
IS
M3
∩
M6
∩
M9
∩
M10
0.364865 0.135 0.6
R15:IF
x1
IS (
PTPC
)19 THEN
Z15
IS
M1
∩
M3
∩
M6
∩
M9
∩
M10
0.364865 0.140625 0.6
R16:IF
x1
IS (
PTPC
)19 THEN
Z16
IS
M1
∩
M3
∩
M4
∩
M6
∩
M9
∩
M10
0.364865 0.141361 0.4
3.1 Iden i ica ion o he Da abase
Ou da abase is composed o di e en ial p o iles ob ained om he p obe se s di e -
en ially exp essed e ie ed om he exp ession da ase s. The p obe se s a e ob ained
using se e al classical mic oa ay analysis me hods. These me hods include S uden ’s
T-Tes p oposed in [11], wi h a ian s ha dis inguish changes in he abundance o
RNA occu ing no only o e ea men bu also o e ime; Pe mu a ion Tes de-
sc ibed in ([6]), also including a ime app oach; Analysis o Va iance desc ibed in
([5]); and Longi udinal Da a app oach using Repea ed Measu es Analysis o Va iance
desc ibed in ([12]).
Fig. 6. Pa e o- on ep esen a ion o he se o ules gene a ed o e ie e P o ile #19. The axes
(X,Y,Z) ep esen he numbe o me hods, speci ici y and sensi i i y o each o he 35 solu ions
gene a ed.
The p obe se s iden i ied by he s a is ical me hods se e as a means o c ea e di -
e en ial exp ession p o iles (i.e., se s o genes wi h coo dina e changes in RNA
abundance) exp essed om one expe imen al condi ion o he o he s (i.e., p obe se s
ha change o e ime, ea men s and pheno ype). We g oup sepa a ely p obe se s o
di e en expe imen al condi ions, ea men and PT con ol PC by applying he K-
means clus e ing algo i hm ([22]), which akes h ee inpu pa ame e s: i s , numbe
o esul ing clus e s K, which is es ima ed by applica ion o he Da ies-Bouldin alid-
i y index ([23]); second, he simila i y measu e applied, Euclidean dis ance, which
yields he bes esul s in he clus e ing o his p oblem and hi d, he ini ializa ion
s a egy, andom gene a ion o he clus e cen oids.
Pa icula ly, in ou in lamma ion p oblem, we conside he empo al exp ession
da a sequen ially ep esen ed o each biological eplica e (i.e., pa ien s in he same
expe imen al g oup) ins ead o a e aging hem o unco e pheno ype di e ences.
We iden i y di e en ial p o iles by applying a coincidence index (CI) based on he
hype geome ic dis ibu ion (p- alue <0.05), which de e mines he s a is ical signi i-
cance o o e lap be ween pai wise p o ile associa ion in ea men and con ol condi-
ions ([16]):
)/
0
(1),( ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
∑=⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−= h
g
qn
hq
p
qq
h
C
P
T
PCI (1)
ha gi es he chance p obabili y o obse ing a leas p candida es om a se T
Po
size h wi hin ano he se C
Po size n, in a uni e se o g candida es. The e o e, p obe
se s belonging o a clus e in ea men , T
P, can i in mo e han one clus e in con ol,
Z
X
Y