~ Outline ~ 1. Normalization Quality filtering Rank-Invariant selection for non-differentially expressed genes Fit normalization curve

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Augustine Curtis
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1 Statstcal Issus n cdna Mcroarray Analyss Issus n cdna mcroarray analyss: qualty fltrn, channl normalzaton, modls of varatons and assssmnt of n ffcts G.C. Tsn, M. Oh, L. Rohln, J.C. Lao and W.H. Won Ima Analyss Idntfy spot ara and xtract ntnsts for ach spot Normalzaton Normalzn dy ffcts, sld ffcts, tc. Nuclc Acds Rsarch Jun/15/001 Downstram Analyss Clustrn and classfcaton Assss Exprsson Lvl Rplcats and hrarchcal modls Outln 1. Normalzaton Qualty fltrn Rank-Invarant slcton for non-dffrntally xprssd ns Ft normalzaton curv Data structur: Calbraton Ornal mrna pool : sampl A : sampl B Rvrsd transcrpton & labln Comparatv Ornal mrna pool. Assssmnt of n xprsson lvl Hrarchcal modl 3. Proram wth ntrfac on th IE browsr Alorthms and mthods dvlopd n th papr C1S1 C1 C1S CS1 C Hybrdz onto dffrnt slds CS R1S1 R1 R1S RS1 R RS

Dnhardt s soluton Qualty fltrn (15) Qualty Indx: m = Cy5 Cy3 CV = std m ) man( m ) ( Calb CS1CS4 C3S1C3S Non C3S1 15 Comp C4S1C4S3 R1S1R1S RS1RS

2 Sampls: E. col rown n actat or lucos 15-n projct: ach n s spottd four tms 419-n projct: ach n s snly spottd slds n th xprmnt C1S1C1S sampls n Cy3 sampls n Cy5 Dnhardt s soluton Qualty fltrn (15) Qualty Indx: m = Cy5 Cy3 CV = std m ) man( m ) ( Calb CS1CS4 C3S1C3S Non C3S1 15 Comp C4S1C4S3 R1S1R1S RS1RS C4S1C4S 419 Calb Comp C1S1C1S CS1CS R1S1R1S RS1RS Intnsty plot Normalzaton: (why normalzaton ndd?) Calbraton: apply th sam sampls on both dys (E. Col rown n lucos). Purpl and oran rprsnt two rplcat slds. ( lo( Cy5) lo( Cy3) )/ A = + M = lo( Cy5 Cy3) ( lo( Cy5) lo( Cy3) )/ A = + M = lo( Cy5 Cy3)

Normalzaton n calbraton xprmnt: Ft M ˆ = fˆ( A) by Lowss functon n S-Plus Normalzaton n comparatv xprmnt: Currnt popular mthods: Hous-kpn ns : Slct a st of non-dffrntally xprssd ns accordn to xprncs.

3 Normalzaton n calbraton xprmnt: Ft M ˆ = fˆ( A) by Lowss functon n S-Plus Normalzaton n comparatv xprmnt: Currnt popular mthods: Hous-kpn ns : Slct a st of non-dffrntally xprssd ns accordn to xprncs. Thn us ths ns to normalz. M = M Mˆ Normalzd Lo rato: M = M Mˆ Constant normalzaton factor : Us man or mdan of ach dy to normalz. ANOVA modl (Churchll s roup) Avra-ntnsty-dpndnt normalzaton: Robust nonlnar rrsson(lowss) appld on whol nom. (Spd s roup) Slct nvarant ns computatonally (rank-nvarant mthod). Thn apply Lowss. (Won s roup) Normalzaton: Normalzaton: (Won roup) Data: E. Col. Chp, 4000 ns, from Lao lab. Rank-nvarant mthod (Schadt t al. 001, Tsn t al. 001): G = 0 { : abs( rank( Cy3 ) rank( Cy5 ) < 5} Itratv slcton : S S = = { : Rank( Cy5 ) Rank( Cy3 ) < p* G & l < Rank( Cy5 + Cy3 )/ ) < G l} { : S & Rank ( Cy5 ) Rank ( Cy3 ) p * S } 1 S 1 < S 1 1 Ida: If a partcular n s up- or down- rulatd, thn ts Cy5 rank amon whol nom wll snfcantly dffrnt from Cy3 rank. Itratv slcton hlps to slct a mor consrvd nvarant st whn numbr of ns s lar. Blu ponts ar nvarant ns slctd by rank-nvarant mthod. Rd curvs ar stmatd by Lowss and xtrapolaton.

4 x s N(, k k χ :sld varaton. Hrarchcal Modl A vrson of mprcal Bays ) N( θ, h h χ x : normalzd loratos, lo( Cy5 Cy3). :xprmnt, s :sld, :n. θ : undrlyn tru xprsson lvl. : xprmntal(cultural) varaton. Not only xs ar obsrvd...((0.75, 0.67), (0.45, 0.51)) h and k ar adjustabl paramtrs. ) p( θ ) 1 C1S1 Ornal mrna pool C1 C1S CS1 C CS Assss Exprsson Lvl (contnud): How to spcfy th pror? Emprcal Bays: Us mprcal data to hlp spcfy hyprparamtrs (, A common vrson of EB s usually achvd by ntratn out ntrmdat paramtrs and maxmz th rsultn marnal lklhood. p( (, ), max X = p,, θ,, X ) d dθd d, It s hard to mplmnt n ths thr - layr hrarchcal modl. ). Assss Exprsson Lvl (contnud): Anothr vrson of EB: Estmat paramtrs n pror from mprcal data. = ( y ) ( 1), s, s y G S E = Not: ( y, y ) G( E 1) (btwn slds varaton) (btwn xprmnt varaton) Snc thr ar thousands of ns, th common problm of data and ttn ovr - confdnt pror n EBs allvatd. Th stmaton of s mor consrvatv. C1S1 Ornal mrna pool C1 C1S CS1 rusn C CS MCMC for hrarchcal modl: 1. Comput ( ) θ,, x x s, = (0) x ( ) + χ E+ h 1 N, s, θ, E h E s ( xs ) + j= 1 s= 1 χ s1 + K+ se + k k s + x θ N, s + s +

Spd: mplmnt 4000 ns n around 0 mnuts n C but up to hours n R. Rsult: Th 95% probablty ntrvals n th 15-n and 419-n projcts corrspond to 0.73 to 1.4 and 0.61 to 1.6 fold chan rspctvly.

5 Assumptons n th modl: 1. Unform pror on thta.. Common sld varaton n dffrnt xprmnts. 3. Normal dstrbuton. Computaton concrn whn rlaxn th modl: Now th smulaton convrs n 4000 tms n contrast to 100,000 tms n common hrarchcal modl. Th fast convrnc s du to th smpl normal modl and th conjuat pror. Spd: mplmnt 4000 ns n around 0 mnuts n C but up to hours n R. Rsult: Th 95% probablty ntrvals n th 15-n and 419-n projcts corrspond to 0.73 to 1.4 and 0.61 to 1.6 fold chan rspctvly. Download pa In th fw stron dsarmnt ns of two projcts, w found that most of thm ar roupd n som pathways, such as mte, mtb, arol, arog, and arof. Ths susts that ths stron dsarmnts may rflct ral bolocal varaton btwn th culturs usd n th two dffrnt projcts. Multpl comparson: W hav not dscussd how to account for multpl comparsons,.. slctn apparntly dffrntally xprssd ns from th lar numbr of ns n th nom.

6 Othr ssus n cdna mcroarray: 1. Dffrnt chocs of rfrnc sampl: a) Normal patnt or tm 0 sampl n tm cours study b) Poold sampls c) Embryonc clls d) Commrcal kt. Exprmntal dsn ssus () Calbraton: Us th sam sampl on both dys for hybrdzaton. Calbraton xprmnts hlp to valdat xprmnt qualty and n-spcfc varablty.

7 () Rplcats: (rplcat spots, slds) Multpl-spottn hlps to dntfy local contamnatd spots but wll rduc numbr of ns n th study. Mult-sta straty: Us snl-spottn to nclud as many ns as possbl for plot study. Idntfy a subst of ntrstn ns and thn us multpl-spottn. Rplcat slds hlp to vrfy rproducblty on th sld lvl. () Rvrs lablln: Sampl A Sampl B Advanta: Cancl out lnar normalzaton scaln and smplfs th analyss. Howvr, th lnar assumpton s oftn not tru. Hlp to cancl out n-labl ntractons f t xsts. (v) Dsn ssus: (a) Rfrnc dsn (b) Loop dsn (c) Balanc dsn (c) v sampls wth v+ xprmnts v sampls wth v xprmnts

ST 524 NCSU - Fall 2008 One way Analysis of variance Variances not homogeneous

ST 524 NCSU - Fall 2008 One way Analysis of variance Variances not homogeneous ST 54 NCSU - Fall 008 On way Analyss of varanc Varancs not homognous On way Analyss of varanc Exampl (Yandll, 997) A plant scntst masurd th concntraton of a partcular vrus n plant sap usng ELISA (nzym-lnkd