slide1 l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
False Discovery Rate for Functional Neuroimaging Thomas Nichols Department of Biostatistics University of Michigan PowerPoint Presentation
Download Presentation
False Discovery Rate for Functional Neuroimaging Thomas Nichols Department of Biostatistics University of Michigan

Loading in 2 Seconds...

play fullscreen
1 / 23

False Discovery Rate for Functional Neuroimaging Thomas Nichols Department of Biostatistics University of Michigan - PowerPoint PPT Presentation


  • 949 Views
  • Uploaded on

False Discovery Rate for Functional Neuroimaging Thomas Nichols Department of Biostatistics University of Michigan With thanks to... Christopher Genovese & Nicole Lazar Carnegie Mellon University Keith Worlsey McGill University Outline Introduction to Functional Neuroimaging

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'False Discovery Rate for Functional Neuroimaging Thomas Nichols Department of Biostatistics University of Michigan' - bernad


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1
False Discovery RateforFunctional NeuroimagingThomas NicholsDepartment of BiostatisticsUniversity of Michigan

With thanks to...

Christopher Genovese &

Nicole Lazar

Carnegie Mellon University

Keith Worlsey

McGill University

outline
Outline
  • Introduction to Functional Neuroimaging
  • Multiple Comparison Problem
  • A Multiple Comparison Solution: False Discovery Rate (FDR)
  • FDR Properties
  • FDR Example
introduction functional neuroimaging

Tap fingers

Rest

Introduction:Functional Neuroimaging
  •  Neuronal Activity  Blood Flow
    • Many functional neuroimaging methods measurecorrelates of blood flow
  • Functional Magnetic Resonance Imaging (fMRI)
    • Based on intrinsic properties of tissue
    • Blood Oxygenation Level Dependent effect (BOLD)
    •  Blood flow  fMRI Signal
fmri multiple comparisons problem
fMRI Multiple Comparisons Problem

1,000

  • 4-Dimensional Data
    • 1,000 multivariate observations,each with 100,000 elements
    • 100,000 time series, each with 1,000 observations
  • Massively UnivariateApproach
    • 100,000 hypothesistests
  • Massive MCP!

. . .

3

2

1

solutions for multiple comparison problem
Solutions forMultiple Comparison Problem
  • A MCP Solution Must Control False Positives
    • How to measure multiple false positives?
  • Familywise Error Rate (FWER)
    • Chance of any false positives
    • Controlled by Bonferroni & Random Field Methods
  • False Discovery Rate (FDR)
    • Proportion of false positives among rejected tests
slide7

11.3%

11.3%

12.5%

10.8%

11.5%

10.0%

10.7%

11.2%

10.2%

9.5%

6.7%

10.5%

12.2%

8.7%

10.4%

14.9%

9.3%

16.2%

13.8%

14.0%

Control of Per Comparison Rate at 10%

Percentage of Null Pixels that are False Positives

Control of Familywise Error Rate at 10%

FWE

Occurrence of Familywise Error

Control of False Discovery Rate at 10%

Percentage of Activated Pixels that are False Positives

benjamini hochberg procedure

p(i) i/V q/c(V)

Benjamini & Hochberg Procedure
  • Select desired limit q on E(FDR)
  • Order p-values, p(1)p(2) ...  p(V)
  • Let r be largest i such that
  • Reject all hypotheses corresponding top(1), ... , p(r).

1

p(i)

p-value

i/V q/c(V)

0

0

1

i/V

JRSS-B (1995) 57:289-300

benjamini hochberg procedure9
Benjamini & Hochberg Procedure
  • c(V) = 1
    • Positive Regression Dependency on Subsets
      • Technical condition, special cases include
        • Independent data
        • Multivariate Normal with all positive correlations
      • Result by Benjamini & Yekutieli, Annals of Statistics, in press.
  • c(V) = i=1,...,V 1/i log(V)+0.5772
    • Arbitrary covariance structure
benjamini hochberg varying signal extent

Signal Intensity 3.0

Signal Extent 1.0

Noise Smoothness 3.0

Benjamini & Hochberg:Varying Signal Extent

p = z =

1

benjamini hochberg varying signal extent11

Signal Intensity 3.0

Signal Extent 2.0

Noise Smoothness 3.0

Benjamini & Hochberg:Varying Signal Extent

p = z =

2

benjamini hochberg varying signal extent12

Signal Intensity 3.0

Signal Extent 3.0

Noise Smoothness 3.0

Benjamini & Hochberg:Varying Signal Extent

p = z =

3

benjamini hochberg varying signal extent13

Signal Intensity 3.0

Signal Extent 5.0

Noise Smoothness 3.0

Benjamini & Hochberg:Varying Signal Extent

p = 0.000252 z = 3.48

4

benjamini hochberg varying signal extent14

Signal Intensity 3.0

Signal Extent 9.5

Noise Smoothness 3.0

Benjamini & Hochberg:Varying Signal Extent

p = 0.001628 z = 2.94

5

benjamini hochberg varying signal extent15

Signal Intensity 3.0

Signal Extent 16.5

Noise Smoothness 3.0

Benjamini & Hochberg:Varying Signal Extent

p = 0.007157 z = 2.45

6

benjamini hochberg varying signal extent16

Signal Intensity 3.0

Signal Extent 25.0

Noise Smoothness 3.0

Benjamini & Hochberg:Varying Signal Extent

p = 0.019274 z = 2.07

7

benjamini hochberg properties
Benjamini & Hochberg: Properties
  • Adaptive
    • Larger the signal, the lower the threshold
    • Larger the signal, the more false positives
      • False positives constant as fraction of rejected tests
      • Not a problem with imaging’s sparse signals
  • Smoothness OK
    • Smoothing introduces positive correlations
fdr example
FDR: Example
  • Verbal fluency data
  • 14 42-second blocks
      • ABABAB...
      • A: Two syllable words presented aurally
      • B: Silence
  • Imaging parameters
    • 2Tesla scanner, TR = 7 sec
    • 84 64x64x64 images of 3 x 3 x 3 mm voxels
fdr example plot of fdr inequality
FDR Example:Plot of FDR Inequality

p(i) ( i/V ) ( q/c(V) )

fdr example20
FDR: Example

FDR  0.05Indep/PRDSt0 = 3.8119

FDR  0.05Arbitrary Cov.t0 = 5.0747

FWER  0.05Bonferronit0 = 5.485

fdr software for spm
FDR Software for SPM

http://www.sph.umich.edu/~nichols/FDR

fdr conclusions
FDR: Conclusions
  • False Discovery Rate
    • A new false positive metric
  • Benjamini & Hochberg FDR Method
    • Straightforward solution to fNI MCP
    • Just one way of controlling FDR
      • New methods under developmente.g. C. Genovese or J. Storey
  • Limitations
    • Arbitrary dependence result less sensitive

Start

Ill

http://www.sph.umich.edu/~nichols/FDR

Prop

positive regression dependency
Positive Regression Dependency
  • Does fMRI data exhibit total positive correlation?
  • Example
    • 160 scan experiment
    • Spatialautocorrelationof residuals
    • Single voxelwith all others
  • Negative correlationexists!