Multiple Contrast Test (MCT) for Dose-response Microarray studies: A Resampling-based Approach

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1 Multiple Cotrast Test (MCT) for Dose-respose Microarray studies: A Resamplig-based Approach Setia Pramaa Iteruiversity Istitute for Biostatistics ad Statistical Bioiformatics, Uiversiteit Hasselt, Diepebeek, Belgium Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

2 Research Team I-Biostat Setia Pramaa Da Li Ziv Shkedy J&J Pharmaceutical Research ad Developmet A De Bodt Hirich Göhlma Willem Talloe Luc Bijes Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

3 Outlie Itroductio to Dose-respose Microarray Studies Testig for Mootoic Tred Multiple Cotrast Test Resamplig-based MCT (Permutatios ad SAM) Applicatio Simulatio Studies Cocludig Remarks Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

4 Dose-respose studies The fudametal study i drug discovery Mai Goal: Discover good drugs, strog effects o specific biological pathways, miimal effects o all other pathways First questio: ivestigate the depedece of the pheotypic respose o doses Target-based drug discovery: to see the drug effects o the (disease associated) gees Dose-respose microarray studies: Moitorig of gee expressio with respect to icreasig doses To idetify a subset of gees with a mootoic tred Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

5 Dose-respose i Microarray The study Compoud Dose 0/Cotrol Dose 1 Dose 2 Dose K Oe gee profile Y Gee 1 Gee 2 Gee m Data Structure Y Y Y m Y Y Y m Y Y Y Y m Y Y m Y Y Y K11 K12 K1m Y Y Y d0 d1 dk Dose levels KK KK KK 1 2 m Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

6 Testig for Mootoic Treds Gee specific test: H 0 : µ(d 0 ) = µ(d 1 ) = = µ(d K ) H Up 1 : µ(d 0 ) µ(d 1 ) µ(d K ) or H Dow 1 : µ(d 0 ) µ(d 1 ) µ(d K ) with at least oe iequality The Likelihood Ratio Test (Ē 2 01 ) The t-type test statistics: Williams Marcus The M test The Modified M (M ) (Li et al, 2007) Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

7 Testig for Mootoic Treds The Likelihood Ratio Test Ē 2 01 : (+) Provides the highest power (-) Less robust agaist departure from ormality A alterative: multiple cotrast test (MCT, Mukerjee, 1986) Bretz (1999) applied MCT o Williams ad Marcus tests to icrease power The distributio of MCT is the multivariate t distributio I microarray, sample size is usually small: problematic for the asymptotic distributio Solutio: A resamplig-based approach Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

8 Multiple Cotrast Test (MCT) The alterative hypotheses are decomposed ito several elemetary alteratives, eg, H Up H Up Sigle Cotrast Test: 1 : µ(d 0 ) µ(d 1 ) µ(d 2 ) = µ(d 3 ) 1 : µ(d 0 ) = µ(d 1 ) µ(d 2 ) = µ(d 3 ) T SC = cȳ/s c 2 /, c are cotrast coefficiets c = 1, & S 2 is pooled variace MCT statistics: The maximum over the T SC : T MC = max{t SC 1, T SC 2,, T SC r }, Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

9 Williams ad Marcus type MCT Williams-type cotrast matrix: C Wil 1 0 K 1 = K 1 + K K K K K K 1 + K K 1 ++ K Marcus-type cotrast matrix for K=3 ad equal sample size: C Marc K=3 = /2 1/2 1 1/3 1/3 1/3 1/2 1/ /3 1/3 1/ Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

10 The M ad Modified M (M ) MCT Pooled variace for Williams ad Marcus: S = K i=0 i j=1 (Y ij ˆµ i ) 2 /(N K) The MCT for the M ad M tests are the same as Marcus MCT with adjusted for the variace: For the M: S = K i=0 i j=1 (Y ij ˆµ i )2 /(N K) For the M : S = K i=0 i j=1 (Y ij ˆµ i )2 /(N I), ad I is the uique umber of isotoic meas Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

11 MCT Permutatio: Adjustmet for Multiplicity I each gee ad i each sigle cotrast test (SCT) the p-value is obtaied by permutatios The obtaied p-values matrix: p11 SC p SC 12 p1r SC p21 SC p22 SC p2r SC p SC m1 pm2 SC pmr SC pmr SC : p-values of SCT r: umber of cotrast m: umber of gees Two dimesios multiplicity adjustmet: Withi gees: FWER adjustmet: MaxT, ad Holm Across gees: BH-FDR Adjustmet Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

12 Sigificace Aalysis of Microarray MCT (SAM-MCT) The SAM (Tusher et al, 2001) is implemeted to overcome the problem of small variace gees SAM regularized MCT: A fudge factor s 0 is added to the maximum cotrast test T MC, eg, T MC SAM = c max Ȳ s 0 + S( c max ) 2 /) s 0 is obtaied from the percetile of the gee-wise se distributio that miimizes the CV of MAD of T MC SAM Permutatio proposed by Tusher et al (2001) is implemeted Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

13 Applicatio to Huma Epidermal Study Huma Epidermal Study: Ivestigate a compoud for ski cacer 4 dose levels with 3 samples at each dose level Each array cosists of 16,998 gees Results: Number of rejected ull hypotheses Method Williams Marcus M M Multivariate t/bh-fdr Holm/BH-FDR MaxT/BH-FDR SAM - s SAM + s Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

14 Simulatios Study: Settigs Ivestigate the performace i terms of power ad the FDR cotrol 100 datasets were geerated ad each cosists of 1000 gees Four dose levels with differet sample size (= 3, 4, 5 & 6) Differet % of differetially expressed gees (10%, 15%, 20%, 25% ) Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

15 Simulatios Study: Permutatios Williams, Max T Marcus, Max T Power % DE gees Power % DE gees M, Max T ModM, Max T Power % DE gees Power % DE gees Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

16 Simulatios Study: SAM-MCT Williams Marcus Power Power M ModM Power Power Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

17 Cocludig Remarks The resamplig-based iferece MCT advatages: Relaxes the assumptio of the tests such as the ormality Ca be implemeted i ay statistic (ie, the M ad M tests) From the simulatio studies: Williams & Marcus MCT permutatio-based performed as good as the asymptotic distributio I permutatio-based MCT, the M & Modified M provide higher power The MCT-SAM especially the M & Modified M SAM-MCT outperformed other tests As sample size icrease, the power of the methods are similar Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

18 Thak you for your attetio All thigs are poiso ad othig is without poiso; oly the dose makes that a thig is o poiso (Paracelsus) Setia Pramaa () MCT Microarray Experimets Miami, FL, August 3rd, / 18

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