Testing Groups of Genes

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1 Testing Grups f Genes Part II: Scring Gene Ontlgy Terms Manuela Hummel, LMU München Adrian Alexa, MPI Saarbrücken NGFN-Curses in Practical DNA Micrarray Analysis Heidelberg, March 6, 2008

2 Bilgical questins Main idea: If yu lk fr candidate genes crrelated with a given phentype it is better t lk fr interesting gene grups first. Gruping the genes int bilgical predefined clusters can be seen as a filtering: genes frm the same grup share the same bilgy. Analysis steps: 1. Derive scre fr genes (p-value, t-statistic, even gene expressin value itself). 2. Map genes t bilgical grups and cmpute significance f these grups using a suitable test statistic. 3. Screen the significant bilgical grups fr candidate genes. Advantages: Easier t find bilgically related genes sharing the same pattern. Fewer grups t be investigated fr differential expressin than individual genes. Easier t find genes with sensible small change in expressin.

3 Gene Ontlgy The Gene Ontlgy (GO) is a cntrlled vcabulary t describe gene and gene prduct attributes ( Three Ontlgies Mlecular Functin (7825 terms) Bilgical Prcess (13860 terms) Cellular Cmpnent (1993 terms) Gene Ontlgy mlecular functin transcriptin regulatr activity binding nucleic acid binding DNA binding Relatins between GO terms are displayed in directed acyclic graphs transcriptin factr activity

4 Gene Ontlgy Genes knwn t be assciated with sme attributes are mapped t crrespnding GO terms Inheritance Each gene assciated with sme term is als mapped t all its ancestrs Overlap exists als between unrelated terms Nt every gene belngs t a leave nde {genes in the leaves} = {genes in the rt}

5 GO Analysis Mst current tls fr GO analysis use tests based n Gene Set Enrichment Khatri and Draghici (2005), Rivals et al. (2006) Testing thusands f GO terms requires sme adjustment fr multiple testing Recent appraches incrprate the special structure f the Gene Ontlgy Decrrelating the GO (elim, weight), Alexa et al. (2006) Parent-child apprach, Grssmann et al. (2007) Fcus-level apprach, Geman and Mansmann (2008)

6 Gene sets enrichment Grup enrichment: given a gene grup with sme bilgical functin, analyse the psitins f these genes in the rdered list. The gene grup is relevant, if all genes are amng the tp genes in the rdered list. Idea: Srt genes accrding t sme scre (diff. expressin) and investigate the ranks f the members f grup A (the bilgical functin) in this list. Define cutff and cunt members f grup A belw and abve cutff. Basically, ne wants t cmpare the fllwing ratis: K N x M. K N-K x x-m N (gene n the micrarray) M (genes in grup)

7 GO scring: general prblem Given: Gal: a directed acyclic graph (GO graph) and a set f items (genes) s.t.: each nde in the graph cntains sme genes the parent f a nde cntains all the genes f its child a nde can cntain genes that are nt fund in the children a subset f genes that we call significant genes (differentially expressed genes) find the ndes frm the graph (bilgical functins) that best represent the significant genes w.r.t sme scring functin (sme test statistic)

8 GO independence assumptin GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: <4.75e 06> GO: <1.89e 06> GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: <1.20e 17> GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: <1.69e 19> GO: < > GO: < > GO: < > GO: < > GO: < > GO: <7.24e 19> GO: <2.59e 05> GO: <2.17e 05> GO: < > GO: < > GO: < > GO: <1.94e 15> GO: <6.10e 14> GO: <2.28e 06> GO: <4.50e 05> GO: < > GO: <7.14e 05> GO: <9.95e 14> GO: <1.02e 12> GO: < > Nte: The clring f the ndes represent the relative significance f the GO terms: dark red is the mst significant, light yellw is the least significant frm the graph

9 The elim methd The main idea: Test hw enriched nde x is if we d nt cnsider the genes frm its significant children (x.ch[2] in ur case). Algrithm: 1. The ndes are prcessed bttm-up. This assures that all children f nde x were investigated befre nde x itself. 2. Let remved(x) be the set f genes that were remved x in a previus step by a nde in the lwer subgraph induced by nde x. Then genes(x) < genes(x) remved(x). x.ch[1] p-val = 0.89 x.ch[2] p-val = 1e-5 x.ch[3] p-val = The p-value fr nde x is cmputed using Fisher s exact test. 4. If nde x is fund significant, we remve all the genes mapped t this nde, frm all its ancestrs.

10 elim result GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: <3.01e 14> GO: < > GO: < > GO: < > GO: < > GO: < > GO: <2.29e 06> GO: < > GO: < > GO: <4.50e 05> GO: <7.14e 05> GO: <9.96e 14> GO: <1.02e 12> Tp 10 significant nde (the bxes) btained with methd elim

11 The weight methd We want t decide if nde x is better representing the list f interesting genes (is mre enriched) than any ther nde frm its neighbrhd. The main idea: Assciate single genes mapped t a nde with weights that dente their relevance. The elim algrithm uses 0-1 weights. Algrithm: x.par[1] x.par[2] x.par[3] 1. Cmpute the p-value f nde x with its current x weights. Initially all its genes have weight CASE I: Lk at the children that are mre signif- x.ch[1] p-val = 1e-15 x.ch[2] p-val = 1e-2 x.ch[3] p-val = 1e-9 x.ch[4] p-val = 1e-20 x.ch[5] p-val = 1e-6 icant than nde x (x.ch[1] and x.ch[4]). These children are lcal ptima (clred with red). x.par[1] x.par[2] x.par[3] 3. Fr each such child dwn-weight all genes mapped t it in all the ancestrs f nde x, including x. x p-val = 1e-10 Mark these children and GOTO step 1. x.ch[1] p-val = 1e-15 x.ch[2] p-val = 1e-2 x.ch[3] p-val = 1e-9 x.ch[4] p-val = 1e-20 x.ch[5] p-val = 1e-6

12 The weight methd x.par[1] x.par[2] x.par[3] x p-val = 1e-8 4. CASE II: If n child f nde x has a p-value less than the current p-value f nde x then nde x is x.ch[1] p-val = 1e-15 x.ch[2] p-val = 1e-2 x.ch[3] p-val = 1e-9 x.ch[4] p-val = 1e-20 x.ch[5] p-val = 1e-6 a lcal ptimum. x.par[1] x.par[2] x.par[3] 5. The genes in these children are dwn-weighted and the p-values fr these ndes are recmputed x p-val = 1e-7 with the new updated weights. 6. The prcessing f nde x terminates. Its p-value x.ch[1] p-val = 1e-15 x.ch[2] p-val = 1e-2 x.ch[3] p-val = 1e-9 x.ch[4] p-val = 1e-20 x.ch[5] p-val = 1e-6 can be changed later, when nde x is treated as a child f anther nde. x.par[1] x.par[2] x.par[3] x p-val = 1e-7 x.ch[1] p-val = 1e-15 x.ch[2] p-val = 1 x.ch[3] p-val = 1e-9 x.ch[4] p-val = 1e-20 x.ch[5] p-val = 1e-3

13 The weight methd The p-value f a nde is cmputed by applying Fisher s exact test n a weighted cntingency table. The quantity siggenes genes(u) is replaced with 2 6 X i {siggenes genes(u)} 3 weight[i] 7. The weights fr nde x and ne f its children are btained by sigrati(ch,x) = lg(p-value(ch)) lg(p-value(x)) r sigrati(ch, x) = p-value(x) p-value(ch) If sigrati() > 1 then nde ch is mre significant than its parent, nde x. The weights are updated using vectr peratrs: minimum n the cmpnents, the prduct f the cmpnents, etc.

14 weight result GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: <4.00e 16> GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: < > GO: <5.42e 13> GO: <2.28e 06> GO: < > GO: < > GO: < > GO: < > GO: <4.50e 05> GO: < > GO: < > GO: < > Tp 10 significant nde (the bxes) btained with methd weight

15 Algrithms review classic algrithm Calculate significance f each GO term independently. Adjust pvalues fr multiple testing (Bnferrni, FDR, etc.). Klmgrv-Smirnv test can easily be used in this case elim algrithm Ndes are prcessed bttm-up in the GO graph. It iteratively remves the genes anntated t significant GO terms frm mre general GO terms. Intuitive and simple t interpret. weight algrithm The genes btain weights that dente the gene relevance in the significant ndes. T decide if a GO term u better represents the interesting genes, the enrichment scre f nde u is cmpared with the scres f its children. Children with a better scre than u better represent the interesting genes; their significance is increased Children with a lwer scre than u have their significance reduced.

16 Influence f the p-values adjustment We had perfrmed a tw-stage analysis: classic 1. A cutff is chsen based n the distributin f the genes scres (p-values adjustment prblem). Genes abve the cutff are called DE genes. 2. The enrichment f a set f genes (GO term) is tested based n test statistics that depend n the list f DE genes. GO term rank a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c b b c b b b b b b a a a a a a a a a a a a a a a a d a a b b e e e e e e e b b b b c c b c c c c c c c d d d d c c c c c c c c c c c a c c e e b b b b b b b e e e e e e e e e e d d d d c c c c d d d d d d d d d d d c d d d d g g g g g g g g d d d d d d d d d e e e f f f f f f f f f f f f f f f f f f f g g d d d d d d d d g g g f g g g f f f f f e e e e e e e e e e e e e e e e e e e f f f f f f f f f f f f f g f f f g g g g g g g g g g g g g g g g g g g g g g g g h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j Tp k significant genes Prblem: In real-life cases the list f DE genes cntains nly a small fractin f truly DE genes. Is the result f the enrichment analysis hampered by the Results: chice f the cutff? GO term rank elim a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c e e e e e e e e e e e e e e e e e e e d d d d d d d d d d d d d d d d d d d d d d d f f d f d d d f d d f f d d d d d d e e e ef ef ef ef ef ef ef ef ef ef ef ef ef ef ef ef ef ef ef f d d f d f f f d f f d d f f f f f f f f f h h h h h h h h h h h g g h g h g h g h g h g h h h g i i i i i i i i i i i h h g h g h g h g h g h h h h h h h h h h h h h g h g g g i i i i i i i i i i i g g g g g i i i i i i i i i g h h g g i i i i i i g g g i i i i j g g j g g g g j j j j j j j Tp k significant genes weight.lg k = 515 DE genes (all genes with FDR-adjusted p-value p 0.01). Variating the cutff value des nt significantly change the rder f the mst significant GO terms (nly small swaps between the GO terms) GO term rank a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b e f d d d d d d d d d d d d c c c c c c c c d e e e e e e e e d d d d d d d d e e f e c c c c c c c c c c c e d d d d d d d d e d d d d d d d d e e e e e e e e f f c c f f f f e f f e f e f c e e e f f e e f f f f f f f f f f f f f c c c c c d d d d e e e e f e e f e f e f f f f e e f f e c c c c c c c c c c c c f f f f f c c g g g g g g g g g g g g g g i i i g g g g g g j j j j j j j i h g j j j j j j j j i i i i i i i i i i i i i j g g g i i h h i h h g h h g h h j i h i g i h h h h h j j j j j j j j j j i h j h h h i i h i g h g i h i i h g j h h h g i g g g h h h h h h h j j j h j h j j j j j i i g i g g g j i g i g i g i i i h h h h h h j j i Tp k significant genes

17 Evaluatin n simulated data We use the GO graph structure (2311 ndes), and all the genes frm HGU95aV2 Affymetrix chip (9623 mapped t the GO graph) Select nly the ndes that have the n. f mapped genes in sme range ( ) Chse randmly a number f ndes (50 in ur case) frm the selected ndes. These ndes represent the enriched ndes. Set as significant genes all the genes frm the enriched ndes. Sme nise can be intrduce: Pick 10% frm all significant genes Remve them frm the significant list Replace the genes that we remved with ther genes The gal is t recver as best as pssible the enriched ndes.

18 Simulated dataset sig all sig(wanted) all(wanted)

19 Simulated dataset

20 Quality f GO scring methds Each curve represents the average f the numbers f preselected GO terms, ver 100 simulatin runs, that are amng the tp k GO terms. The left plt represents scre 0 k and the right plt represents scre1p k. 10 t 50 genes anntated 10% nise level. N. f enriched ndes fund classic elim weight.lg weight.rati all.m N. f enriched ndes fund classic elim weight.lg weight.rati all.m (a) Tp k ndes (b) Tp k ndes 10 t 1000 genes anntated 40% nise level. N. f enriched ndes fund classic elim weight.lg weight.rati all.m N. f enriched ndes fund classic elim weight.lg weight.rati all.m (c) Tp k ndes Tp k ndes

21 Parent-Child Apprach If many differentially expressed genes are anntated t a GO term it is nt surprising that there is als fund verrepresentatin in the mre specific descendants f the term Cmpute hypergemetric p-values where the reference gene ppulatin des nt cnsist f all genes m but rather f nly all parental genes m pa(t) f a given GO term t P (X t x t X pa(t) = x pa(t) ) = min(x pa(t),m t ) k=x ( mt k ) ( mpa(t) m t x pa(t) k ( mpa(t) x pa(t) ) ) pa(t): set f parents parents f term t m t : number f genes anntated t term t m pa(t) : nr. f genes in either unin r intersectin f genes anntated t parents f t x t : number f differentially expressed genes anntated t term t Grssmann et al. (2007)

22 Parent-Child Apprach Idea is reverse t elim and weight: Children ndes might nly inherit significance frm their mre general parents Fcus lies in mre general terms

23 Simulatin Study Similar simulatin setup as in Alexa et al. (2006), but Pre-selectin f terms that actually can achieve a small p- value with the parent-child apprach Overrepresentatin f just ne term (ut f the preselected) ROC analysis Hw t design an bjective simulatin study...?

24 Fcus Level Apprach Again a different idea: Significant terms lgically must have significant ancestr terms Relevance f terms is assessed by glbal tests (e.g. glbaltest r GlbalAncva) Multiple testing prcedure n the Gene Ontlgy graph which cntrls the family-wise errr rate (FWER): Cmbines clsed testing prcedure with crrectin methd f Hlm Hlm crrectin: very fast but nt very efficient Clsed testing prcedure: very efficient in case f crrelated test statistics but cmputatinally infeasible

25 Fcus Level Apprach Chse a fcus level a set f terms H in the middle f the GO graph (as the level f detail that is f mst interest) Taking each f the terms in H as rt ndes, build subgraphs that are clsed under intersectin Iterate: 1. Test phase: Test the GO terms in H with glbal tests and crrect raw p-values by a Hlm s factr (initially H ) 2. Upward phase: Fr every hypthesis rejected in the test phase, reject all ancestrs 3. Dwnward phase: Add thse terms t H, fr which all parent hyptheses in the clsed subgraphs have been rejected 4. Hlm s phase: Recalculate Hlm s factr as the number f subgraphs which cntain unrejected hyptheses

26 Fcus Level Apprach Result is a significant subgraph starting frm the rt Leave ndes in the subgraph usually are f mst interest

27 References 1. Alexa A, Rahnenführer J, Lengauer T. Imprved scring f functinal grups frm gene expressin data by decrrelating GO graph structure. Biinfrmatics 2006; 22(13): The Gene Ontlgy Cnsrtium. Gene Ontlgy: tl fr the unificatin f bilgy. Nature Genetics 2000; 25: Geman JJ, Mansmann U. Multiple testing n the directed acyclic graph f Gene Ontlgy. Biinfrmatics 2008; 24(4): Grssmann S, Bauer S, Rbinsn PN, Vingrn M. Imprved detectin f verrepresentatin f Gene-Ontlgy anntatins with parent-child analysis. Biinfrmatics 2007; 23(22): Khatri P, Draghici S. Ontlgical analysis f gene expressin data: current tls, limitatins, and pen prblems. Biinfrmatics 2005; 21(18): Rivals I, Persnnaz L, Taing L, Ptier MC. Enrichment r depletin f a GO categry within a class f genes: which test? Biinfrmatics 2007; 23(4):