Big Data Integration in Biomedical Studies: A Few Personal Views and Experiences

Transcription

1 Big Data Integration in Biomedical Studies: A Few Personal Views and Experiences Hongtu Zhu, Ph.D Department of Biostatistics and Biomedical Research Imaging Center The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA

2 Big Data Outline BIAS and Big Data Integration Image-on-Scalar Models Image-on-Genetic Association Models Prediction Models

3 Big Data

4 What is Big Data? 5V=Volume, Velocity, Variety, Value, and Veracity The size of big data is beyond the ability of commonly used software tools to capture, manage, and process within a tolerable elapsed time. Alzheimer s Disease Neuroimaging Initiative (US$134 millions) Philadelphia Neurodevelopmental Cohort (PNC) Human Connectome Project (HCP) Big Data in Boxes

5 How to promote statistics in Big Data industry? Closely collaborate with people who are collecting Big Data Work as a team to develop new methods, packages, and textbooks with nice case studies Organize more workshops and short courses Train next-generation statisticians: training grants and new courses a data scientist; an excellent programmer; an applied mathematician

6 How to make important contributions to Big Data? Start with a few big data bases Start with a few methodological and clinical projects Develop a package with a set of good computational and statistical tools to efficiently extract important information from large Big data

7 BIAS: Biostatistics and Imaging AnalysiS and Big Data Integration

8 BIAS: Biostatistics and Imaging Analysis Lab Man Power Computer Power Programming Power Statistics Mathematics

9 aims to simulate the complete human brain on Supercomputers to better understand how it functions. The Brain Research through Advancing Innovative Neurotechnologies or BRAIN, aims to reconstruct the activity of every single neuron as they fire simultaneously in different brain circuits, or perhaps even whole brains.

10 Big Neuroimaging Data NIH normal brain development 1000 Functional Connectome Project Alzheimer s Disease Neuroimaging Initiative National Database for Autism Research (NDAR) Human Connectome Project Philadelphia Neurodevelopmental Cohort Genome superstruct Project

11 Complex Study Design cross-sectional studies; clustered studies including longitudinal and twin/familial studies; ρ 1 5 ρ 5 9 ρ 1 9

12 Neuroimaging research example neuroscience Neuroimaging Applications Structural MRI Structural MRI Diffusion MRI Functional MRI Overview Complementary techniques Diffusion MRI - Variety of acquisitions - Measurement basics - Limitations & artefacts - Analysis principles - Acquisition tips Functional MRI (task) Functional MRI (resting)

13 Complex Data Structure Multivariate Imaging Measures Smooth Functional Imaging Measures Whole-brain Imaging Measures 4D-Time Series Imaging Measures

14 Medical Informatics & Management Big Data Integration Disease Etiology Prevention Treatment Medical Industry Care Policy System Science Insurance Economics Pharmaceutical

15 Big Data Integration E B E: environmental factors G D G: genetic markers D: disease Selection

16 Image-on-Scalar Models

17 Big Data Integration E B E: environmental factors G D G: genetic markers D: disease Selection

18 The NIMH Strategic Plan Strategic Objective 1: Promote Discovery in the Brain and Behavioral Sciences to Fuel Research on the Causes of Mental Disorders Identifying and validating high sensitivity and specificity biomarkers that define valid subtypes of the major mental illnesses. Strategic Objective 2: Chart Mental Illness Trajectories to Determine When, Where, and How to Intervene Conducting longitudinal studies that track changes in behavior with brain structure, connectivity, and function, in order to characterize the progression from primary changes to subsequent clinical presentation, and to identify predictors of divergence from the typical trajectory.

19 Smoothed Functional Data Covariates (e.g., age, gender, diagnostic)

20 Case 1: DTI Fiber Tract Data Data (e) Diffusion properties (e.g., FA, RA) Grids Y i (s j ) = (y i,1 (s j ),, y i,m (s j )) T {s 1,,s ng } Covariates (e.g., age, gender, diagnostic) x 1,, x n FA MD

21 Longitudinal Data Longitudinal Tract Data Spatial-temporal Process t y i (s,t 3 ) y i (s,t 2 ) y i (s,t 1 ) Functional Mixed Effect Models s y i (s,t) = x i (t) T B (s)+ z i (t) T ξ i (s)+η i (s,t)+ε i (s,t) Objectives: Dynamic functional effects of covariates of interest on functional response.

22 Ex 1: Longitudinal Tract Data genu DTImaging parameters: TR/TE = 5200/73 ms Slice thickness = 2mm In-plane resolution = 2x2 mm^2 b = 1000 s/mm^2 One reference scan b = 0 s/mm^2 Repeated 5 times when 6 gradient directions applied.

23 Ex 1: Longitudinal Tract Data

24 Ex 1: Longitudinal Tract Data

25 Neuroimaging Data with Discontinuity Noisy Piecewise Smooth Function with Unknown Jumps and Edges Subject1 Subject2 Covariates (e.g., age, gender, diagnostic, stimulus)

26 Case 2: Piecewise Smooth Data Mathematics. Noisy Piecewise Smooth Functions with Unknown Jumps and Edges Image is the point or set of points in the range corresponding to a designated point in the domain of a given function. Ω is a compact set. f ( x ) M R m x Ω R k f : Ω M R m f ( x) k d x < for some k>0 Ω

27 M2: Spatial Varying Coefficient Model Decomposition: y i (d) = f (x i,b(d) +η i (d)) +ε i (d),d D Piecewise Smooth Short-range Correlation Varying Coefficients Long-range Correlation B(d) L K η ij ()~ SP(0, Ση ) ε ij ( ) ~ SP(0,Σ ε ), 3D volume/ 2D surface Covariance operator: Σ y (d,d ') = Σ η (d,d ') + Σ ε (d,d) Li, Zhu, Shen, Lin, Gilmore, and Ibrahim (2011). JRSSB. Zhu, Fan, and Kong (2014) JASA

28 Spatial Varying Coefficient Model Cartoon Model B k (d) Disjoint Partition D L = l= 1 Dl and Dl Dl ' = φ Piecewise Smoothness: Lipschitz condition Smoothed Boundary Local Patch Degree of Jumps

29 Kernel-based Smoothing Methods Arias-Casto, Salmon, Willett (2011) Local constant/linear Yaroslavsky/Bilateral Filter Nonlocal Means PS

30 Kernel-based Smoothing Methods Propogation-Seperation Method J. Polzehl and V. Spokoiny, (2000,2005) Features Increasing Bandwidth 0 < h < h <! < h = S r 0 1 Adaptive Weights 0 Adaptive Estimates

31 Simulation

32 Simulation

33 ADNI PET data ADNI PET data EX2: ADNI PET Data Data were obtained from the Alzheimer s Disease Neuroimaging Initiative (ADNI) database. We consider PET scans obtained at baseline, 6 months, and 12Data months. were obtained from the Alzheimer s Disease Subjects Neuroimaging are classified Initiative as having (ADNI) mild database. cognitive impairment (MCI), We consider as AD patients, PET scans or as obtained Normal at Controls baseline, (NC). 6 months, and 12 months. Subjects are classified At as screening: Cont d having mild cognitive impairment (MCI), as AD patients, or as Normal Controls (NC). Diagnostic status age (years) N male N female AD 75.9± At screening: MCI 76.3± NC 77.0± Diagnostic status age (years) N male N female We randomly chose 80 subjects for the training set to develop AD 75.9± the prediction model. MCI 76.3± We predicted NC the PET scans 77.0± at 4.2 month 12, 30 based on 20 the baseline and 6-month scans for 79 subjects in the test set. We used gender, diagnostic status (MCI, AD, NC), and age (55-90 years) as covariates for the semi-parametric model. Hyun,J.W., Li, Y. M., J. H. Gilmore, Z. Lu, M. Styner, H. Zhu (2014) SGPP. NeuroImage

34 Prediction results-cont d EX2: ADNI PET Data (a) (b) (c) Figure : Observed (upper panel) and predicted (bottom panel) PET images at month 12 for (a) an AD patient, (b) an MCI subject, and (c) a NC subject. One selected slice is shown.

35 EX2: Prediction ADNI results-cont d PET Data (a) (b) (c) Prediction results-cont d Figure : rtmspe maps for prediction of ADNI PET images at month 12 for 79 test subjects. Selected slices are shown for (a) Semi-parametric model; (b) Semi-parametric Table : rtmspe model+fpca; for ADNI PET(c) images Semi-parametric model+fpca+spatial-temporal model. Semi-parametric model Semi-parametric mode+fpca Semi-parametric model+fpca+spatial-temporal model

36 Image-on-Genetic Association Models

37 The NIMH Strategic Plan Strategic Objective 1: Promote Discovery in the Brain and Behavioral Sciences to Fuel Research on the Causes of Mental Disorders Identify the genetic and environmental factors associated with mental disorders. Strategic Objective 2: Chart Mental Illness Trajectories to Determine When, Where, and How to Intervene When identifying behavioral, neural, and/or genetic markers along the trajectory of illness, design the studies to consider variation in relation to age, sex, gender, race, ethnicity, and other important socio-demographic factors.

38 Big Data Integration E B E: environmental factors G D G: genetic markers D: disease Selection

39 Statistical Methods Hibar, et al. HBM 2012

40 Data Structure Person No.1. Person No.1000 Imaging: 3D Matrix. 3D Matrix Genetic : Person No Person No. 100 SNP1 SNP2. SNP

41 M3: High Dimensional Regression Model Data {(Y i, X i ) :i = 1,,n} Y i = {y i (v) :v V} {X i (g) : g G 0 } Phenotype Genotype Error Y X B E n p y n p x p x p y n p y (p x,n, p y )

42 Sparse Projection Regression Model Sun, Zhu, Liu, and Ibrahim (2014) JASA

43 Sparse Projection Regression Model

44 Sparse and Low-rank Representation Sparsity and Structure on B. Low Rank B b X Sparsity E B p x p y Regularization Methods Lasso 1, 2, 3,. SCAD, MCP,.. b Y p λ (B) p λ (b X ) p λ (b Y ) p λ (E B ) Shen, Shen, and Zhu (201?)

45 E n p y Factor Model Long-range Correlation Short-range Correlation E i Λ ξ i η i p y 1 p y q p y 1 q 1 Σ E Λ Σ η Zhu, Zakaria, Lu, and Ibrahim (2014) JASA Λ T

46 M4: Voxel-wise GWAS Hibar, et al. HBM 2012

47 M4: Voxel-wise GWAS Fast Sure-Independence Screening Procedure WC2S SNP Each SNP Huang,. and Zhu (2014)

48 EX3: 93 ROI-GWAS

49 EX4: Whole Brain-GWAS

50 Prediction Models

51 Alzheimers Disease Big Data DREAM Challenge 1 Its goal is to apply an open science approach to rapidly identify accurate predictive AD biomarkers that can be used by the scientific, industrial and regulatory communities to improve AD diagnosis and treatment. Sub 1: Predict the change in cognitive scores 24 months after initial assessment. Sub 2: Predict the set of cognitively normal individuals whose biomarkers are suggestive of amyloid perturbation. Sub 3: Classify individuals into diagnostic groups using MR imaging.

52 Big Data Integration E B E: environmental factors G D G: genetic markers D: disease Selection

53 HRM versus FRM Data {(y i, X i ) :i =1,, n} X i = {X i (d) : d D} y i =< X i,θ > +ε i Strategy 1: Discrete Approach (High-dimension Regression Model (HRM)) Strategy 2: Functional Regression Model (FRM) y i =θ 0 + D θ(d) X i (d)m(d)+ε i

54 High-dimension Regression Model Approach 1: Regularization Methods Key Conditions: Sparsity of S Restricted null-space property for design matrix X

55 High-dimension Regression Model Tensor Structure: Ultra-high dimensionality (256^3) Spatial structure Zhou, Li, and Zhu (2013) Li, Zhou, and Li (2013) CP decomposition Tucker decomposition θ

56 Scalar-on-Image Models Simulations Key Conditions: Tensor Approximation B Restricted space property for X and B

57 Scalar-on-Image Models Strategy 2: Functional Approach y i =θ 0 + y i =θ 0 + D θ k k=1 θ(d) X i (d)m(d)+ε i D θ(d) = θ k ψ k (d) k=1 ψ k (d) X i (d)m(d)+ε i Basis Methods: fixed and data-driven basis functions K θ = {θ(d) = θ k ψ k (d) : (θ 1, ) 2 } C(d, d ') = Cov(X(d), X(d ')) = λ k ζ k (d)ζ k (d ') k=1 k=1

58 Key Conditions Key Conditions: an excellent set of basis functions Sparsity of basis representation Decay rate of spectral of C or {θ k : k =1, } K 1/2 CK 1/2 θ(d) K θ k ψ k (d) k=1 K << n

59 Extensions M5: Functional linear Cox regression models M6: Generalized scalar-to-image regression models M7: Multiscale Functional Linear models

60 M5: Functional Linear Cox Regression Model Data {(y i, X i ) :i =1,, n} X i = {X i (d) : d D} Model y i = min(t i,c i ) h(t) = f (t) / S(t) = h 0 (t)exp(z i T γ + X i (s) = µ(s) + Consistency j=1 T i : failure time; C i :censored time ξ ij φ j (s) + ε i (s) Asymptotic distribution of score test X i (s)β(s)ds) S

61 M5: Functional Linear Cox Regression Model Mild Cognitive Impairment subjects Interested in predicting the timing of an MCI patient that converts to AD by integrating the imaging data, the clinical variables, and genetic covariates. Full Model: AUC=0.96 Partial Model: AUC=0.82

62 jects (Rudin et al. 1992). Most current research on functional regression has focused on ensional functional predictors. Exceptions for two-dimensional predictors using splines uillas and Lai (2010) and Reiss and Ogden (2010). Some recent work (Zhou et al. 2013; M6: Generalized scalar-to-image regression models Data {(y i, X i ) :i =1,, n} X i = {X i (d) : d D} th et al. 2013; Huang et al. 2013; Reiss et al. 2013) has considered neuroimaging appliith two-dimensional and three-dimensional predictors. We propose a new TV framework ssion with 2-d image predictors. This approach can be easily extended to k-d image preith k 2. Further, most of theoretical work on functional regression has focused on asymptotic Model convergence y ~ exponential rate for the excess family(µ,φ) risk. In this paper, we derive nonasymptotic nds on the risk by exploiting various techniques from compressive sensing, as well as oximation theory. g(µ) These techniques = θ T 0 Z+ allows < X,βus to 0 > obtain finite-sample bounds that hold h probability, and are specified explicitly in terms of the sample size n Total n, the Variation image size and the image smoothness. Estimation: we have a new observation (y X (n+1) i ;µ(x, we i ;γ would,β( ))) like to + use λ X β (n+1) TV to predict Y n+1. Let ˆ imate of the coefficient i=1image from the training data which are n i.i.d. copies of (Y,X), ) ),...,(Y n,x (n) ). The accuracy of the prediction can be measured by its excess risk: Non-asymptotic Error Bound: R 2n = n E D X (n+1), ˆ 0E 2 o 1/2, represents taking expectation over (Y n+1,x (n+1) ) only. In this paper, we are interested

63 M6: Generalized scalar-to-image regression models TV Lasso Lasso on WL

64 M7: Multiscale Functional Linear models Data {(y i, X i ) :i =1,, n} X i = {X i (d) : d D} Models (A1) D = ( K D k ) D 0 k=1 Informative sets + Irrelevant set (A2) (A3) y {X(d) :d D 0 } y p({x(d) :d D 1 },,{X(d) :d D K })

65 Simulation I: Classification Class 0 Class 1 0 White 1 Green 2 Red Figure 1: Simulation Study I: the left and right panels are respectively true images for classes 0 and 1. X i (d) = β 0 (d) + β 1 (d)y i + ε i (d) Type I Type II Type III The white and green color in the left panel respectively corresponds to 0(g) = 0 and 1 for g = (g 1,g 2,g 3 ) The white, green and red N(0,4) Short-range correlation Long-range correlation color in the right panel respectively corresponds to 0(g) + 1 (g) = 0, 1, and 2 for g =(g 1,g 2,g 3 ) The di erence between Classes 0 and 1 images lies in the red cuboid region.

66 red cuboid region. For each type of noise, we simulate 100 images by linear model (1), where 60 images Simulation I: Classification are from Class 0 and the rest 40 images are from Class 1. Then we use SWPCA to get Table 1: Misclassification rates for PCA and SWPCA under the di erent number of PCs. Noise Number of PCs PCA SWPCA1 SWPCA2 SWPCA3 Type I Type II Type III

67 ension reduction and then do classification analysis on the low dimensional space. ults for PCA is shown on the third column of Table 1. The performance of SWPC rall much better than PCA. Simulation I: Classification ble 2: Classification performance comparison for SWPCA and other classification m Noise slda spls SLR SVM ROAD PCA SWPCA Type I Type II Type III slda: sparse discriminant analysis spls: sparse partial least squares analysis SLR: sparse logistic regression SVM: support vector machine ROAD: Here we also compare classification performance of SWPCA with other classifica thods. The first compared classification method is sparse discriminant analysis (Cl nsen et al., 2011) with the corresponding software slda. The classification errors A in the second column of Table 2 are more than or equal to 0.27 for three di e

68 PET mance of SWPCA with other classification methods. The real data is Alzheimer s Disease Neuroimaging Initiative (ADNI) pet data (Jagust et al., 2010). Alzheimer s disease (AD) EX5: ADNI-PET is the most common form of dementia and results in the loss of memory, thinking and language skills. ADNI is a worldwide project, launched in 2003, and is to develop biological AD NC

69 of the biological markers to the understanding of the progression of Alz n the human brain. Here we consider the real data, which contains es. ADNI e one out test: *95*69 3D-images are split into a training set with images and a test set of one image. Simulation is repeated 196times, erro 94 AD subjects and 104 NC subjects age error on predicting testing image. Table 3: Results of Real Data: average misclassification rates. slda spls slogistic SVM ROAD PCA SWPCA

70 ASA: Statistics in Imaging Section SAMSI 2013 Neuroimaging Data Analysis Challenges in Computational Neuroscience July Summer School August Opening Workshop Shape Analysis Spike Train Analysis Big Data Integration Compressed Sensing Functional Data Analysis Thank You!!