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My first 100 Tb of data

My first 100 Tb of data. STATISTICAL METHODS FOR NEW TECHNOLOGY WORKING GROUP. Ciprian M. Crainiceanu Johns Hopkins University http://www.biostat.jhsph.edu/smnt. Members of the group. Key personnel C.M. Crainiceanu, B.S. Caffo, A.-M. Staicu, S. Greven, D. Ruppert, C.-Z. Di Senior Students

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My first 100 Tb of data

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  1. My first 100 Tb of data STATISTICAL METHODS FOR NEW TECHNOLOGY WORKING GROUP Ciprian M. Crainiceanu Johns Hopkins University http://www.biostat.jhsph.edu/smnt

  2. Members of the group • Key personnel • C.M. Crainiceanu, B.S. Caffo, A.-M. Staicu, S. Greven, D. Ruppert, C.-Z. Di • Senior Students • V. Zipunnikov, J.-A. Goldsmith • Other statisticians (>20) • Scientific collaborators • Direct collaboration • Solving important scientific problems • Diverse scientific applications

  3. Scientific Collaborators • Susan Bassett – fMRI, Alzheimer’s • Danny Reich – DTI, DCE-MRI, MS • Brian Schwartz – lead exposure, VBM, DTI, white matter imaging • Stewart Mostofsky – fMRI, rsfcMRI, Autism, ADHD, Turrets • Naresh Punjabi – EEG, sleep, sleep diseases • Dzung Pham / PilouBazin – Cortical shape, thickness, lesion detection, MS • Dean Wong – PET, fMRI substance abuse • Susan Resnick –BLSA • Jerry Prince – BLSA, ADNI • Jim Pekar, Peter Van Zijl – 7T MRI, fMRI, rsfcMRI preprocessing, scanner physics • Christos Davatzikos- RAVENS • Susumu Mori – DTI, tractography • Dana Boatman – ECOG, EEG, epilepsy • Graham Redgrave – fMRI, DTI, Huntington’s, anorexia/bulimia • Tudor Badea, Bruno Jednyak – Neuron classification, morphometry, 3D structure and shape • Tom Glass – Gizmos • Merck – EEG, neuroimaging • Pfizer – imaging biomarkers?

  4. Observational Studies 2.0

  5. Longitudinal Functional Principal Component Analysis (LFPCA) • I=1000, J=4, D=100: 15’ • I=1000, J=8, D=200: 70’ Greven, Crainiceanu, Caffo, Reich, 2010. LFPCA, EJS, to appear

  6. A simple regression formula • Data compression via longitudinal PCA • MoM estimators of covariance matrices, smoothing • Need: all covariance operators • Solution: regress Yij(d)Yik(d’) on 1, Tik, Tij, TikTij, djk

  7. Variance explained (FA, 3 yrs of long. data)

  8. Longitudinal Penalized Functional Regression

  9. LPFR: recipe and ingredients

  10. PASAT/MD (Corp. Call.), PD (Cortic. spinal)

  11. Functional regression • No paper on longitudinal functional regression • No paper published with this data structure • Longitudinal extensions are not “simple” • Technical details are hard without the correct “recipe” for known and published “ingredients” • No available method that scales up Goldsmith, Feder, Crainiceanu, Caffo, Reich, 2010. PFR, JCGS, to appear Goldsmith, Crainiceanu, Caffo, Reich, 2010. LPFR, to appear?

  12. Population Value Decomposition (PVD)

  13. PVD Yi = P ViD + Ei • P is T*A • D is B*F • Vi is A*B • A << T, B << F

  14. Singular Value Decomposition (SVD) summarizes variance One subject Time Subject-specific Data Frequency. Frequency Diagonal Matrix Eigenvariates Eigenfrequencies

  15. Default PVD (Start here) Eigenvariates SVD Subject-specific Data Eigenfrequencies Low rank approximation SVD Population decomposition Stacked across subjects Projecting original data onto population bases ... … Subject-specific Data Caffo BS, Crainiceanu CM, Verduzco G, Joel SE, Mostofsky SH, Bassett SS, Pekar JJ. Two-Stage decompositions for the analysis of functional connectivity for fMRI with application to Alzheimer’s disease risk. NeuroImage (In Press).

  16. Population eigenimages

  17. Currently: • Deploying PVD to the 1000 Functional Connectomes Project • http://www.nitrc.org/projects/fcon_1000/ • Comparing rsfcMRI in stroke versus normal subjects

  18. HD-MFPCA/RAVENS Images

  19. Multilevel Functional Principal Component Analysis (MFPCA)

  20. MFPCA

  21. HD-MFPCA

  22. HD-MFPCA, Step 1

  23. HD-MFPCA, Step 2

  24. Main message, backed by 100Tb of data • Eventually, good tech makes into observational and clinical trials • Longitudinal/Multilevel FDA is the natural next step in FDA • Data is changing the way we do business: availability, size, complexity • Likely: funding will be based much more on relevance than on technical ability

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