A Join Spa io empo al Di e en ial Exp ession Modeling
o Exposu e E ec s in Spa ial T ansc ip omics Da a
Osa u Augus ine Egbon1,2 and Benedic Anchang1,2
1Na ional Ins i u e o En i onmen al Heal h Sciences (NIEHS/NIH), Du ham, NC 27709, Uni ed S a es
2Na ional Cance Ins i u e, Be hesda, MD 20892, Uni ed S a es
Abs ac
Di e en ial exp ession analysis in spa ial ansc ip omics da a is impo an o iden i ying local-
ized biological p ocesses and spa ially s uc u ed gene egula ion. While nume ous me hods ha e
been de eloped o iden i ying di e en ially exp essed genes (DEGs) in con en ional single-cell
RNA-seq da a, app oaches ha explici ly accoun o spa ial and empo al con ex emain sca ce. A
majo challenge in spa ial DEG analysis is he spa ial misalignmen be ween issue sec ions unde
con ol and pe u bed condi ions, which ende s coo dina e-based compa isons un eliable. To ad-
d ess his gap, we de eloped Spa ialDENe , a amewo k ha iden i ies DEGs in spa ially s uc u ed
single-cell da a by inco po a ing spa ial in o ma ion h ough a hie a chical ne wo k-based model.
This app oach accoun s o spa ial con ounding and le e ages issue a chi ec u e o align biological
signals ac oss condi ions. We alida ed Spa ialDENe h ough simula ion s udies and compa a i e
benchma ks wi h exis ing popula me hods. Ou indings demons a e ha Spa ialDENe p o ides
a powe ul and in e p e able al e na i e o spa ial ansc ip omics analysis and may in o m he
de elopmen o a ge ed he apies.
Key Wo ds: Bayesian in e ence, Ne wo k model, Di e en ial exp ession analysis, Gaussian Ma ko
Random Field, Ze o-in la ion.
1 In oduc ion
Spa ial ansc ip omics echnologies a e inc easingly popula o in es iga ing he spa ial a chi ec u e
o issues, unco e ing cell-cell in e ac ions, and analyzing gene exp ession pa e ns in si u wi h high
esolu ion1,2. Howe e , conduc ing Di e en ial Exp ession (DE) analysis o iden i y di e en ially
exp essed genes (DEG) be ween wo biological condi ions on spa ial ansc ip omics da a p esen s
signi ican challenges due o i s high dimensionali y, noise, spa si y, and spa ial s uc u e.
Me hods o DE analysis in s udying biological a ia ions a he single-cell le el a e eme ging
quickly. Fo ins ance, he popula ly used me hods include DESeq23, EdgeR4, Lima5, MAST6,
Zinbwa e7, among o he s. Howe e , mos o hese me hods do no accoun o spa ial a ia ion, an
impo an sou ce o biological and echnical a iabili y ha can con ound di e en ial exp ession
analysis esul s8. Exis ing s a is ical and compu a ional me hods8–13 o analyzing spa ially esol ed
1
single-cell da a a e pa icula ly designed o iden i y spa ially a iable genes (SVGs), and no adequa e
a en ion has been gi en o iden i ying DEGs be ween con ol and ea men scena ios in spa ially
esol ed single-cell da a.
To add ess his conce n, we p oposed a s a is ical amewo k, Spa ialDENe (Sp ial Di e en ial
Exp ession Analysis h ough Ne wo k), o iden i y di e en ial exp ession genes be ween con ol and
pe u bed condi ions while co ec ing o spa ial con ounding (SC). Spa ialDENe add esses h ee
main analy ical conce ns in spa ially esol ed single-cell da a. Fi s ly, Spa ialDENe adjus s o he
SC issue h ough spa ial hie a chical modeling. This me hod allows he accu a e es ima ion o he
impac o a speci ic ea men on cells a e con olling o he spa ial e ec s. Secondly, spa ially
esol ed single-cell da a is associa ed wi h spa ial misalignmen due o he non-longi udinal and non-
homologous na u e o he da a ac oss samples. Tha is, he spa ial coo dina es change om issue
samples o samples. To add ess his conce n, Spa ialDENe le e ages ne wo k models o map
cellula spa ial neighbo hoods be ween mul iple issues un o a la en space, c ea ing a uni ied spa ial
ield o adjus ing o SC and iden i ying DEGs. Las ly, Spa ialDENe accoun s o he spa si y in
he exp ession da a. The ze os due o spa si y can a ise om echnical limi a ions in he sequencing
p ocess o e lec ue biological absences o gene exp ession o speci ic cells. Dis inguishing
be ween hese wo sou ces o ze os is c i ical o accu a e in e p e a ion. Spa ialDENe u ilizes a
wo-pa (coun and ac i a ion) ze o-in la ed model o accoun o excess ze os.
The emainde o his pape is o ganized as ollows. We i s b ie ly desc ibe he s a is ical ame-
wo k o Spa ialDENe and i s ex ension o accommoda e ze o-in la ed da a. We hen benchma k
he amewo k wi h popula ly used di e en ial exp ession analysis me hods h ough a simula ion
s udy. Finally, we conclude wi h a summa y o ou con ibu ions and po en ial di ec ions o u u e
esea ch.
2 S a is ical F amewo k
2.1 Backg ound o di e en ial analysis amewo k
In single-cell DE analysis, he gene al amewo k adop ed by exis ing me hods can be desc ibed
as ollows. Le 𝑌𝑔𝑠 be he obse ed exp ession le el (e.g., ead coun ) o gene 𝑔in cell 𝑠, whe e
𝑔=1, . . . , 𝐺 and 𝑠=1, . . . , 𝑆. A gene alized linea model (GLM) is ypically used o model gene
exp ession as:
𝑌𝑔𝑠 ∼NB(𝜇𝑔𝑠, 𝜙𝑔),(1)
whe e NB deno es a Nega i e Binomial dis ibu ion, 𝜇𝑔𝑠 is he expec ed exp ession le el o gene 𝑔
in cell 𝑠,𝜙𝑔is a gene-speci ic dispe sion pa ame e . The pa ame e 𝜇𝑔𝑠 is hen linked o co a ia es
2
h ough a log-linea model gi en as
log(𝜇𝑔𝑠)=𝛽𝑔0+log(𝑙𝑠) +𝑐𝑠𝛽𝑔1+x⊤
𝑠𝜷𝑔,(2)
whe e 𝑙𝑠is a size ac o o lib a y size no maliza ion o cell 𝑠,𝛽0is he model in e cep , 𝑐𝑠∈ {0,1}
is he ea men indica o , wi h e ec size 𝛽1,x𝑠is a ec o o co a ia es o adjus o obse ed
con ounding a iables, and 𝜷𝑔is a co esponding ec o o eg ession coe icien s o gene 𝑔.
To es o di e en ially exp essed genes be ween con ol and ea men condi ions, we de ine he
hypo hesis (Hypo hesis 1) o a speci ic gene 𝑔as
𝐻0:𝛽𝑔1=0 s. 𝐻1:𝛽𝑔1≠0,(3)
whe e 𝛽𝑔1is he coe icien co esponding o he condi ion o in e es .
In single-cell spa ially esol ed da a wi h genes exhibi ing spa ial a ia ion and ze o in la ion,
Hypo hesis 1 becomes p oblema ic and inapp op ia e o inding di e en ial exp ession genes in
single-cell analysis.
2.2 Spa ialDENe : The p oposed amewo k
To add ess he abo e conce n, we p oposed a uni ied amewo k ha add esses spa ial con ounding,
spa ial misalignmen , he empo al e olu ion o gene exp ession, and ze o-in la ion p oblems in
single-cell spa ially esol ed da a.
2.2.1 Response model
Conside a scena io whe e we ha e p e-p ocessed single-cell exp ession da a collec ed o e ime.
Le 𝑌𝑔𝑠𝑡, 𝑠 =1,2, ..., 𝑆;𝑔=1,2, ..., 𝐺,𝑡=1,2, ..., 𝑇 be a gene exp ession coun a spa ial loca ion
deno ed by 𝑠a ime 𝑡 o gene 𝑔.𝑆is he o al numbe o spo s/cells ac oss all issues. No e he e ha
he cell index 𝑠p e iously de ined as a cell is now ede ined as a spo index 𝑠in spa ial ansc ip omics
da a. We assume ha
𝑌𝑔𝑠𝑡 |𝛽𝑔0, 𝛽𝑔1,𝜷𝑔∼NB(𝜇𝑔𝑠𝑡 , 𝜙𝑔),
log(𝜇𝑔𝑠𝑡)=𝛽𝑔0+log(𝑙𝑠𝑡 ) +𝑐𝑠𝑡 𝛽𝑔1+x⊤
𝑠𝑡 𝜷𝑔+𝜓𝑔𝑠𝑡,
(4)
whe e 𝜓𝑔𝑠𝑡 is a spa io empo al la en a ia ion used o adjus o spa ial con ounding in he gene
exp ession da a, 𝑙𝑠𝑡 is he size ac o , 𝑐𝑠𝑡 ∈ {0,1}is he condi ion indica o o spa ial poin 𝑠a ime
𝑡. The di e en ial genes a e hen iden i ied using Hypo hesis 1.
In s anda d spa ial s a is ical modeling, whe e he spa ial loca ion domain emains ixed, 𝜓𝑔𝑠𝑡
in Equa ion (4) can be easily es ima ed by assuming a Gaussian Ma ko andom ield (GMRF)
p io dis ibu ion. Howe e , in single-cell analysis, he spa ial domain ( issue sample) dissocia es
du ing da a collec ion and hus, di e en issues a e used in he ea men and con ol condi ions,
3
causing spa ial misalignmen due o non-homologous issue samples. To add ess his challenge, we
model 𝜓𝑔𝑠𝑡 using a Ne wo k-Based-GMRF p io dis ibu ion, which is discussed in he subsequen
subsec ion.
2.2.2 De i ing ne wo k-based-GMRF
To de ine a ne wo k-based Gaussian Ma ko Random Field (GMRF) p io o modeling spa io em-
po al la en e ec s, we in oduce a amewo k ha cons uc s a dynamic cell-neighbo hood ne wo k
o e a spa ial domain, in o med by gene exp ession summa ies14.
Le Ddeno e a egula spa ial domain o a speci ic issue sample, such ha 𝑠∈ D. Fo each ime
𝑡o a speci ic issue sample, he domain D𝑡⊂ D is non-linea ly pa i ioned in o non-o e lapping
spa ial egions 𝐷𝑖𝑡 ,𝑖=1,2, ..., 𝐼, called a node, such ha
D𝑡=
𝐼𝑡
Ø
𝑖=1
𝐷𝑖𝑡 , 𝐷𝑖𝑡 ∩𝐷𝑖′𝑡=∅ o 𝑖≠𝑖′.(5)
Fo each pa i ion 𝐷𝑖𝑡 , we calcula e a ep esen a i e cen oid using a summa y s a is ic, such as he
mean exp ession o he p incipal componen s (PCs) de i ed om he gene exp ession da a. Suppose
he educed gene exp ession space consis s o 10 PCs; o each pa i ion 𝐷𝑖𝑡 , we compu e he mean
alue o each PC ac oss all cells wi hin ha pa i ion. Consequen ly, each 𝐷𝑖𝑡 is ep esen ed by a
ec o o 10 mean alues, co esponding o he 10 PCs. The numbe o nodes is chosen o esul in
op imal p ecision. We hen de ine a cell-neighbo hood ne wo k Tby connec ing each node 𝐷𝑖𝑡 o i s
𝑘-nea es neighbo s based on cen oid p oximi y. Fo mally, de ine an undi ec ed g aph T=(G,E),
whe e Gis he se o nodes (pa i ions ac oss all 𝑡) and Eis he se o edges, such ha (𝑖, 𝑡)∼(𝑗, 𝑡′)
i and only i 𝐷𝑗𝑡′is among he 𝑘nea es neighbo s o 𝐷𝑖𝑡 based on cen oid dis ance. Fo example,
i he e exis s a o al o 1000 non-o e lapping pa i ions o D, he ne wo k Twill ha e 1000 nodes
(#G=1000), indica ing ha each cell/spo belongs o only one o he 1000 nodes. Gi en he nodes
in G, he Ne wo k Tis used o inco po a e he spo /cell in e ac ion and dependencies in o med by
he ela ionship be ween he cell’s exp ession s a us ac oss all he genes.
To ob ain he ne wo k-based GMRF, suppose ne wo k Thas 𝑛nodes, wi h 𝜓𝑔𝑖𝑡 ∈R ep e-
sen ing he node la en e ec o node 𝑖a ime 𝑡. Le 𝝍𝑔𝑡 =(𝜓𝑔1𝑡, 𝜓𝑔2𝑡, ..., 𝜓𝑔𝑛𝑡 )𝑇and 𝝍𝑔=
(𝝍𝑔1,𝝍𝑔2, ..., 𝝍𝑔𝑇 )𝑇. We assumed a Gaussian Ma ko Random Field (GMRF) on he la en a i-
ables 𝜓𝑔𝑖𝑡 , which cap u es he ne wo k s uc u e. Le N𝑖be he collec ion o all he index se s o
nodes ha ing an edge wi h node 𝑖on ne wo k T, hen he ne wo k-based GMRF is de ined as
𝜓𝑔𝑖𝑡 |𝝍−𝑖
𝑔,N𝑖∼𝑁Í𝑗∈N𝑖𝜓𝑔 𝑗𝑡
#N𝑖
,1
#N𝑖𝜏𝑔,(6)
whe e #N𝑖is he o al numbe o nodes connec ed o node 𝑖.𝝍−𝑖
𝑔is 𝝍𝑔bu excluding componen
𝜓𝑔𝑖𝑡 om he ec o . Equa ion (6) shows ha he expec ed alue o he la en a iable in node 𝑖is
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he a e age o he alues o he la en a iables ep esen ing he nodes connec ed o node 𝑖, and he
a iance is scaled by he numbe o edges o node 𝑖. The equa ion cap u es he dependency be ween
he nodes ac oss he ne wo k. Fo example conside a ne wo k T=(G,E) such ha he node se is
G={1,2,3,4,5}and edge se E={1∼3,1∼2,2∼3,2∼4,3∼4,3∼5}, whe e 𝑖∼𝑗indica es
ha node 𝑖is connec ed o node 𝑗on he ne wo k. The e o e, N1={2,3},N2={1,3,4},N3=
{1,2,4,5},N4={2,3},N5={3}. The join dis ibu ion o he ne wo k-based-GMRF o he la en
a iable 𝝍𝑔|𝜏𝑔∼𝑁(0,𝚺(𝜏𝑔)), whe e 𝚺(𝝉𝑔)=(𝜏𝑔Q)−1and Qis a s uc u ed ma ix ha cap u es
he spa ial s uc u e gi en in Equa ion (6), which is de ined as
𝑄𝑖𝑖′=







|N𝑖|,i 𝑖=𝑖′,
−1,i 𝑗∈ N𝑖,
0,o he wise.
(7)
2.2.3 Ze o-In la ion join model
A se ious conce n wi h single-cell da a is i s spa si y. The exp ession con ains excessi e ze os ha
can bias mos modeling app oaches, especially in e p e able models. As a esul , i is impo an
o accoun o hese ze oes in he modeling amewo k o di e en ia e be ween ue ze oes and
biological ze os. To add ess his conce n, we adop ed a “ wo-pa " modeling echnique. In he i s
pa , we model he ac i a ion p ocess o gene 𝑔 h ough a logis ic model. We model he p obabili y
ha a speci ic gene is ac i a ed (exp essed) o no . In he second s ep, he ex en o ac i a ion is
modeled h ough a di e en s anda d p obabili y model.
Ma hema ically, de ine a new a iable 𝑍𝑔𝑠𝑡 such ha
𝑍𝑔𝑠𝑡 =(1i 𝑌𝑔𝑠𝑡 >0,
0o he wise. (8)
Thus, o a gi en gene 𝑔, we assume ha 𝑍𝑔𝑠𝑡 ∼Be noulli(𝜋𝑔𝑠𝑡), whe e 𝜋𝑔𝑠𝑡 deno es he p obabili y
o obse ing non-ze o exp ession. Mo eo e , we de ine ano he a iable 𝑉𝑔𝑠𝑡 =𝑌𝑔𝑠𝑡 only i 𝑍𝑔𝑠𝑡 =1,
and 𝑉𝑔𝑠𝑡 is modeled using a ze o- unca ed nega i e binomial dis ibu ion.
We de ine 𝜓𝑔𝑖𝑡 as he la en e ec associa ed wi h node 𝑖a ime 𝑡. Each spo 𝑠is assigned
o a node 𝑖(𝑠), and hus he spo -le el e ec is gi en by 𝜓𝑔𝑠𝑡 =𝜓𝑔,𝑖(𝑠),𝑡 . The ull model o he
Spa ialDENe is gi en as
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𝑍𝑔𝑠𝑡 |.∼Be noulli(𝜋𝑔𝑠𝑡),
log 𝜋𝑔𝑠𝑡
1−𝜋𝑔𝑠𝑡 =𝛼𝑔0+𝑐𝑠𝑡 𝛼𝑔1+x𝑇
𝑠𝑡 𝜶𝑔+𝜓𝑔𝑖𝑡 , 𝑠 ∈node 𝑖
𝑉𝑔𝑠𝑡 |.∼Nega i eBinomial(𝜇𝑔𝑠𝑡, 𝜙𝑔),
log(𝜇𝑔𝑠𝑡 )=𝛽𝑔0+log(𝑙𝑠𝑡 ) +𝑐𝑠𝑡 𝛽𝑔1+x𝑇
𝑠𝑡 𝜷𝑔+𝜓𝑔𝑖𝑡 ,
𝝍𝑔∼𝑁0,𝚺(𝜏𝑔),
(𝛼𝑔0, 𝛼𝑔1,𝜶𝑔, 𝛽𝑔0, 𝛽𝑔1,𝜷𝑔)𝑇∼𝑀𝑉𝑁(0,104I),
𝚲∼𝑃(𝚲),
(9)
whe e 𝜋𝑔𝑠𝑡 is he p obabili y ha a speci ic gene 𝑔is biologically ac i a ed. Each spo 𝑠belongs
o a node 𝑖(𝑠). Thus, in he linea p edic o e m, 𝜓𝑔𝑖𝑡 is included h ough 𝜓𝑔,𝑖(𝑠)𝑡, which is sha ed
be ween he bina y and he coun componen s. As p e iously de ined, 𝜓𝑔𝑖𝑡 adjus s o he spa ial
con ounding in he ac i a ion componen o he model using he ne wo k-based-GMRF. 𝚲is a ec o
o hype pa ame e s, 𝚲=(𝜏𝑔, 𝜙𝑔)𝑇and 𝑃(𝚲)is he p io dis ibu ion o 𝚲. We assigned log-
gamma p io o 𝜙𝑔,log(𝜙𝑔) ∼ 𝑙𝑜𝑔 −𝐺𝑎𝑚𝑚𝑎(1,0.00005). We adop ed he PC p io dis ibu ion
o 𝜏𝑔, which is among he mos widely used p io dis ibu ions due o i s obus ness. The PC p io
dis ibu ion o 𝜏=𝜏𝑔is gi en as
𝜋(𝜏)=𝜆
2𝜏−3/2exp −𝜆 𝜏−1/2, o 𝜏 > 0,(10)
whe e 𝜆=−log 𝛼
𝑢, such ha 𝑃(1
√𝜏> 𝑢)=𝛼. The p io is ully speci ied i 𝑢and 𝛼a e ixed o
known, which can be in o ma i ely de i ed om he empi ical da a.
3 Simula ion s udy
We conduc ed a simula ion s udy o benchma k Spa ialDENe wi h commonly used me hods in
he li e a u e. To simula e he gene exp ession da a, we adop ed a ze o in la ed nega i e binomial
dis ibu ion. To simula e he spa ially andom e o , we adop ed a Gaussian bump model. The da a
gene a ion model is gi en as
xcoo d ∼uni o m(0,1)
ycoo d ∼uni o m(0,1)
𝑓𝑔(𝑠, 𝑡)=exp −2𝑡((xcoo d −0.5)2+ (ycoo d −0.5)2)
log(𝜇𝑔𝑠𝑡)=𝛽𝑔0+𝑐𝑠𝑡 𝛽𝑔1+𝑓𝑔(𝑠, 𝑡)
𝑍𝑔𝑠𝑡 ∼Be noulli(𝜋𝑔𝑠𝑡)
𝑌𝑔𝑠𝑡 =(0i 𝑍𝑔𝑠𝑡 =0,
NB(𝜇𝑔𝑠𝑡 , 𝜙𝑔)i 𝑍𝑔𝑠𝑡 =1.
(11)
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whe e xcoo d and ycoo d ep esen he spa ial coo dina es o each loca ion, and 𝑓𝑔(𝑠, 𝑡)deno es
he spa ially a ying e o e m, which can po en ially con ound he es ima ion o 𝛽𝑔1. The e o is
highe owa ds he cen e o he domain and ades away owa ds he edges. We assumed an e ec
size o 𝛽𝑔1=[2,4], 𝑔 =1,2, ..., 𝐺 be ween he ea men and con ol condi ions. We delibe a ely
in oduced his spa ial e o o e alua e how e ec i ely he ne wo k-based model cap u es spa ial
s uc u e, wi hou di ec ly simula ing om he ne wo k-based GMRF.
To simula e he di e en ially exp essed genes, we se 𝑐𝑠𝑡 =1in he ea men condi ion and
𝑐𝑠𝑡 =0in he con ol condi ion. To simula e non-di e en ially exp essed genes, we se 𝛽𝑔1=0 o
bo h ea men and con ol. In he simula ion, 𝜋𝑔𝑠𝑡 =0.6,∀𝑔, 𝑠, 𝑡.𝛽0was ixed o 1and he dispe sion
pa ame e 𝜏𝑔=𝜙𝑔=1,∀𝑔.
Gi en he simula ed da a, we compa e Spa ialDENe wi h commonly used di e en ial analysis
me hods in he li e a u e. Speci ically, we conside ed DESeq23, EdgeR4, Limma5, MAST6, and
monocle315. Figu e 1a shows he andomly selec ed spa ial loca ion wi h he spa ial domain (0,1)2.
Using 𝑓(𝑠, 𝑡), he igu e shows ha he spa ial pa e n exhibi s highe in ensi y mo ing close o he
cen e o he spa ial domain. This indica es ha genes ha a e mo e exp essed in he cen e egion
end o be ela i ely mo e a ec ed by spa ial con ounding issues. Using he spa ial e ec 𝑓(𝑠, 𝑡)in
he s ochas ic ep esen a ion in Equa ion (11), di e en ially and non-di e en ially exp essed genes
a e simula ed. Figu e 1b shows he Spa ialDENe ep esen a ion o he spa ial domain. Each node
is a clus e o neighbo ing poin s, and he size o he ne wo k de e mines he numbe o neighbo ing
spa ial loca ions p esen in he da a. La ge nodes ha e a highe numbe o spa ial loca ions. The
g aph is colo ed by he node-a e aged simula ed spa ial e ec .
(a) (b)
Spa ialDENe
EdgeR
DESeq2
MAST
Monocol3
False Disco e y Ra e
Powe
(c)
Figu e 1: Simula ion s udy: (a) The simula ed spa ial con ounding a iable dis ibu ed ac oss (0,1)
in bo h x and y axes. (b) The ne wo k ep esen a ion o he simula ed spa ial egion. (c) The powe
agains alse disco e y a es o he compe ing models.
We simula ed 1000 genes in o al. O hose, 100 (10%) di e en ially exp essed genes be ween
con ol and ea men condi ions we e simula ed. The plo o he powe agains he alse disco e y
a e be ween Monocle 3, MAST, DESeq2, EdgeR, and spa ialDENe is shown in Figu e 1c. The
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powe and he FDR we e compu ed using
Powe =𝑇 𝑃
𝑇𝑃 +𝐹𝑁 ,FDR =𝐹𝑃
𝑇𝑃 +𝐹𝑃 ,(12)
whe e 𝑇𝑃 is ue posi i e, 𝐹𝑃 is alse posi i e, and 𝐹𝑁 is alse nega i e. The esul s showed ha
DESeq2 achie ed a powe o 0.80 a an FDR o 0.005, pe o ming ela i ely well compa ed o o he
me hods. Howe e , spa ialDENe ou pe o med DESeq2, a aining a powe o o e 0.82 a an
FDR o 0.01 and exceeding 0.90 a an FDR o 0.02. In con as , DESeq2 eached only 0.81 powe
a he same FDR le el o 0.02. These indings highligh he impo ance o accoun ing o spa ial
con ounding e ec s when iden i ying di e en ially exp essed genes.
We u he conduc ed 30 independen simula ion uns o compa e spa ialDENe wi h o he
compe ing models using FDR and powe as p ima y e alua ion me ics. Fo each simula ion scena io,
we calcula ed he FDR, powe , and he co esponding composi e me ics, F1 sco e, and Youden’s J
s a is ic, o assess he o e all pe o mance o he models comp ehensi ely. The F1 sco e and Youden’s
J s a is ic a e de ined as
F1 =2(1−FDR)Powe
(1−FDR) +Powe ,Youden’s J =Powe −FDR.(13)
Bo h he F1 sco e and Youden’s J s a is ic in eg a e powe and FDR o p o ide a uni ied measu e o
a me hod’s ue pe o mance. Me hods ha achie e highe alues o hese me ics a e conside ed o
pe o m be e o e all, as hey e ec i ely balance sensi i i y and alse disco e y con ol.
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YoudenJ
F1
FDR Powe
(a) (b)
(d)
(c)
Figu e 2: Benchma king analysis in syn he ic da a: (a) False disco e y a e, (b) Powe , (c) uni ied F1
sco e, (d) Youden’s J s a is ic.
Figu e 2a & b show he box plo o he FDR and powe o DESeq2, EdgeR, Limma, MAST,
Monocle, and Spa ialDENe . Findings showed ha DESeq2 and Spa ialDENe had simila le els
o FDR, which is be e han o he compe ing models. Howe e , judging by he powe , Spa ialDENe
ou pe o med DESeq2 and o he compe ing models (Figu e 2b). Mo eo e , Monocle had he highes
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