Marot, Guillemette

Ternynck, Camille

Vandewalle, V

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HAL Id: hal-02400525https://hal.archives-ouvertes.fr/hal-02400525Submitted on 9 Dec 2019HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Linking different kinds of Omics data through amodel-based clustering approachV Vandewalle, Camille Ternynck, Guillemette MarotTo cite this version:V Vandewalle, Camille Ternynck, Guillemette Marot. Linking different kinds of Omics data througha model-based clustering approach. IFCS 2019, Aug 2019, Thessalonique, Greece. ￿hal-02400525￿Introduction Presentation of the model Application on a real datasetLinking different kinds of Omics data througha model-based clustering approachV. Vandewalle1,2, Camille Ternynck1, Guillemette Marot1,21 Université de Lille, EA 26942 Inria Lille, Modal teamIFCS MeetingThessalonikiAugust 28th, 20191/23Introduction Presentation of the model Application on a real datasetHeterogeneous Omics data applicationCentral dogma of molecular biologyDNA→ RNA→ ProteinsGene expression measurements• microarray measurements: continuous variables• RNAseq measurements: count variablesFor gene gPatient 1 Patient 2 · · · Patient nGene g microarray 1 xg11 xg12 · · · xg1n...microarray ng xgng 1 xgng 2 · · · xgng nRNAseq 1 yg11 yg12 · · · yg1n...RNAseq mg ygmg 1 xgmg 2 · · · xgmg n2/23Introduction Presentation of the model Application on a real datasetUsual related questions• High dimensional framework with many genes• Low number of subjects• Differential expression analysis: find gene with expressionrelated to some disease• Normalization of the data: remove some undesirable bias• Often RNA transformations performed (log-transformation,normalized log-transformation, variance stabilizingtransformation, . . . ) to treat this count variable as acontinuous one3/23Introduction Presentation of the model Application on a real datasetConsidered frameworkInitial questions• Data normalisation framework: make RNAseq and microarray on thesame "scale".• How can we detect that some RNAseq and microarray measurementsbelong to the same genes (group of genes)?Clustering of genes1. Use the genes memberships information of the measurements,2. Not use the genes membership information (in many settings geneinformation not available)⇒ how to cluster variables from the samegene?Similarity criterionCluster together genes which have the same distribution with respect to bothmicroarray and RNAseq measurements.4/23Introduction Presentation of the model Application on a real datasetConsidered frameworkInitial questions• Data normalisation framework: make RNAseq and microarray on thesame "scale".• How can we detect that some RNAseq and microarray measurementsbelong to the same genes (group of genes)?Clustering of genes1. Use the genes memberships information of the measurements,2. Not use the genes membership information (in many settings geneinformation not available)⇒ how to cluster variables from the samegene? Semi-supervised setting, partial gene membershipinformation!Similarity criterionCluster together genes which have the same distribution with respect to bothmicroarray and RNAseq measurements.4/23Introduction Presentation of the model Application on a real datasetIllustration• Information on thedistribution⇒ forget the individuallevel' symbolic data insome sense5/23Introduction Presentation of the model Application on a real datasetData• n patients, described by G genes• for each patient i , each gene g is described by:• ng continuous microarray measurements xg1i , . . . , xgng i• mg count RNAseq measurements yg1i , . . . , ygmg i• assume that the genes come from K different clusters• zg ∈ {0, 1}K denoting the cluster for gene g in binary coding.Model• For each gene g, zg is a realization of the random variableZg ∼M(1;π1, . . . , πK )• Z1, . . . , ZG are assumed independent and identically distributed• xgji the microarray measurement for the measure number j(j ∈ {1, . . . , ng}) of the patient number i for the gene g is a realization ofthe random variable Xgji .• yg`i the RNAseq measurment for the measure number `(` ∈ {1, . . . ,mg}) of the patient number i for the gene g is a realizationof the random variable Ygji .6/23Introduction Presentation of the model Application on a real datasetDetail of the model assumptionsParametric model• measures on each patient are assumed independent• given the gene cluster each measure are independent• Xgji |Zg = k ∼ N (µk ;σk )• Yg`i |Zg = k ∼ P(λk )Remarks1. λk should be an increasing function of µk , but this contraint is notimposed to simplify the estimation process (no need of a link functionbetween λk and µk )2. gene membership of each probe assumed to be known: often the casefor human expression data, however not for bacterial data ...3. model able to cope with partial gene information, however foridentifiability reasons it is needed that each cluster contains at least onegene for which we have observed both RNAseq and microarraymeasurements.7/23Introduction Presentation of the model Application on a real datasetParameters estimation (1/2)Parameters estimated by maximum likelihood through the EM algorithmE-stept (r)gk = P(Zgk = 1|xg , yg ; θ(r))withP(Zgk = 1|xg , yg) ∝ πk∏ni[(∏ngj=1 f (xgji ;αk ))×(∏mg`=1 h(yg`i ;βk ))]where f is the pdf for microarray data and h the pdf for RNAseq data.M-stepπ(r+1)k =∑Gg=1 t(r)gkGα(r+1)k = arg maxαk∑Gg=1 t(r)gk∑ni=1∑ngj=1 ln f (xgji ;αk )β(r+1)k = arg maxβk∑Gg=1 t(r)gk∑ni=1∑mg`=1 ln h(yg`i ;βk ),Remarks• the model collapses all the data of a same gene g• clustering of genes ' clustering of distributions8/23Introduction Presentation of the model Application on a real datasetParameters estimation (2/2)Computations considerably speed up by the use of sufficient statistics:µ(r+1)k =1n(r+1)kG∑g=1t (r)gk1n × ngn∑i=1ng∑j=1xgji =1n(r+1)kG∑g=1t (r)gk x̄gσ2k(r+1)=1n(r+1)kG∑g=1t (r)gk1n × ngn∑i=1ng∑j=1(xgji − µ(r+1)k )2=1n(r+1)kG∑g=1t (r)gk σ2xg +1n(r+1)kG∑g=1t (r)gk (µ(r+1)k − x̄g)2λ(r+1)k =1n(r+1)kG∑g=1t (r)gk1n ×mgn∑i=1mg∑`=1yg`i =1n(r+1)kG∑g=1t (r)gk ȳggene g can be summarized by:• M-step: (x̄g , σ2xg , ȳg).• E-step: ng and mg additionally needed.• log-likelihood: ∑mg`=1∑ni=1 log(yg`i !) additionally needed.9/23Introduction Presentation of the model Application on a real datasetPresentation of the dataThe Cancer Genome Atlas (TCGA) dataset• Data about the Acute Myeloid Leukemia 1• 169 patients• Keep genes with:• Only one RNAseq measure• Non null RNAseq values for at least 9 patients• At least one microArray measure• Keep probes related to only one gene• At the end: 16,741 genes with an RNAseq measure andone or more microarray measures1https://portal.gdc.cancer.gov/projects/TCGA-LAML10/23Introduction Presentation of the model Application on a real datasetLink RNAseq / microarray11/23Introduction Presentation of the model Application on a real datasetLink between standard deviation and average forRNAseq data12/23Introduction Presentation of the model Application on a real datasetResults of a clustering in 10 clusters (1/2)Remarks• It is essentially theRNAseq whichdetermines thecluster membership!• How to explain thisparticularly biginfluence?13/23Introduction Presentation of the model Application on a real datasetResults of a clustering in 10 clusters (1/2)Model parameters:cluster prop mean_array var_array mean_seq1 0.26 3.46 1.14 19.532 0.15 5.27 2.64 736.303 0.15 5.92 2.98 1577.264 0.15 4.13 1.74 220.135 0.12 6.32 3.57 2938.476 0.09 6.60 3.88 5207.637 0.05 7.15 4.96 9332.418 0.02 7.80 6.45 18148.489 0.01 8.79 8.98 41936.7610 0.00 9.61 12.76 179799.30• Small clusters have an higher mean• The mean array value is monotetic according to the mean seqvalue• Huge differences according to the cluster for mean seq value14/23Introduction Presentation of the model Application on a real datasetExplanation of the influence of RNAseq• Count for RNAseq overdispersed⇒ Poisson not accurate, the mixture model prioritizes toimprove this bad fit,⇒ better fit using negative binomial distribution.15/23Introduction Presentation of the model Application on a real datasetNegative binomial distribution fitp(y |r , p) = Γ(r + y)pr (1− p)yΓ(r)Γ(y + 1)r : size, p: probability, µ = r(1− p)/p: expectationMaximum likelihood estimationExpression of p according to r and the datap =NrNr +∑Ni=1 yiPartial derivate according to rd`(r |y1, . . . , yN)dr= N ln(NrNr +∑Ni=1 yi)− NΨ(r) +N∑i=1Ψ(r + yi ) = 0,Ψ: digamma function, i.e. derivate of the Gamma function.• Non-closed form, found by numerical optimisation• Algorithm implemented in fitdistrplus• No sufficient statistic available due to the digamma function16/23Introduction Presentation of the model Application on a real datasetNew preliminary analysis based on a negativebinomial fit on each geneOutlier removed (log-value) :gene mean_array var_array size_seq mu_seqTBC1D21 1.26 -2.26 12.55 -2.2417/23Introduction Presentation of the model Application on a real datasetResults with the model based clustering approachClustering in 10 clusters• Now it seems thatmicroarray datadominates theclustering process• It should be mainly dueto bad fit of Gaussiandistribution18/23Introduction Presentation of the model Application on a real datasetExplication of the influence of microarray data• Unimodaldistribution notaccurate for a lotof variables.• Consider mixtureof Gaussian⇒ Increase the costof the algorithm,work in progress. . .19/23Introduction Presentation of the model Application on a real datasetClustering of genes based on summary of each gene• Rationale: as the number of patients n increases, the summary ofeach gene becomes consistent.• Use clustering of genes based on summaries provided by Gaussianand negative binomial fit for each gene.• Model based clustering with mixture of gaussian of these summaries• Easier to balance the influence of each kind of data.BIC indicates approximately 14 clus-ters20/23Introduction Presentation of the model Application on a real datasetAnalysis of the results of the Gaussian mixture• More accurateresults, howevercluster poorlyseparated• ICL selects 3clusters21/23Introduction Presentation of the model Application on a real datasetResulting empirical distribution in each cluster on theinitial data• Can be used tocluster new databased only onRNAseq• Then deduce thedistribution ofmicroarray datagiven theobservedRNAseq data22/23Introduction Presentation of the model Application on a real datasetConclusion and perspectiveConclustion• Approach very sensitive to model assumptions• Difficulty to balance the influence of each kind of variables• Empirical solution through clustering of summariesPerspectives• Work in progress to stabilize the approach• Take into account dependency of the measurements for apatient• Simultaneous clustering of patients and genes23/23

Linking different kinds of Omics data through a model-based clustering approach

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Linking different kinds of Omics data through a model-based clustering approach

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