Neuroimaging for Machine Learners Validation and inference
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1 GIGA in silico medicine, ULg, Belgium Neuroimaging for Machine Learners Validation and inference Christophe Phillips, Ir. PhD. PRoNTo course June 2017
2 Univariate analysis: Introduction: within & between subjects analysis GLM, contrasts & Statistical inference Multiple comparison problem & other inference levels Conclusion 2
3 Univariate analysis: Introduction: within & between subjects analysis GLM, contrasts & Statistical inference Multiple comparison problem & other inference levels Conclusion 3
4 4
5 BOLD signal Standard univariate approach Input Time... Standard Statistical Analysis (encoding) Voxel-wise GLM model estimation Independent statistical test at each voxel Correction for multiple comparisons Output Univariate statistical Parametric map Find the mapping g from explanatory variable X to observed data Y g: X Y 5
6 Within subject analysis : «first level» analysis data = series of measurements from 1 subject, typically «functional MRI» (fmri) modelling BOLD response time series activation task or resting connectivity sometimes with parametric modulation and/or confounding regressor output = contrast images, statistical maps, connectivity maps, and «cleaned» signal 6
7 Between subjects analysis : «second level» analysis data = 1 (or few) image(s)/subject from group(s) of subjects, e.g. contrast image, tissue density, deformation map, FDG-PET scan, modelling group effect/differences or regressing subjects score (confound/interest) output = «raw» signal, contrast images and statistical maps 7
8 FDG-PET scan Quantitative MRI 8
9 Univariate analysis: Introduction: within & between subjects analysis GLM, contrasts & Statistical inference Multiple comparison problem & other inference levels Conclusion 9
10 General Linear Model 1 p 1 1 N: # images p: # regressors N Y = N X p + N GLM defined by: design matrix X error term ε distribution ~ N 0, V Y X 10
11 Design matrix example Single subject fmri time series Aim: model BOLD signal variation over time/scans, with 4 conditions + movement parameters + mean each condition event modelled by HRF with 2 derivatives ( Taylor expansion) 11
12 Design matrix example Aim: model group effect with: Separate group averages Group comparison with two-sample t-test 12
13 Design matrix example 13
14 Design matrix example Single subject fmri time series Group comparison with two-sample t-test 14
15 General Linear Model 1 p 1 1 N Y = N Y X p X + N ~ N 0, V NOTE: GLM applied to each and every voxel individually! Estimation of the β s in a (weighted) least-square sense. 15
16 T-test & contrast A contrast selects a specific effect of interest: contrast c = vector of length p. c T β = linear combination of regression coefficients β. c T = [ ] c T β = 1x 1 + 0x 2 + 0x 3 + 0x 4 + 0x c T = [ ] c T β = 0x x 2 + 1x 3 + 0x 4 + 0x Under i.i.d assumptions ~ N 0, I c T ˆ T T T 1 ~ N( c 2, c ( X X ) c) 16
17 1 t-test example: Passive word listening versus rest c T = [ 1 0 ] Q: activation during listening? X Design matrix Null hypothesis: 1 0 t c T ˆ Std( c T ˆ) SPMresults: Height threshold T = {p<0.001} voxel-level T ( Z ) Statistics: p-values adjusted for search volume set-level p c p corrected p uncorrected mm mm mm Inf cluster-level voxel-level Inf k E p uncorrected p FWE-corr p FDR-corr T ( Z ) p Inf uncorrected Inf Inf mm mm mm Inf Inf Inf Inf Inf
18 Classical inference The Null Hypothesis H 0 = what we want to disprove (no effect). The Alternative Hypothesis H A = outcome of interest. Significance level α: Acceptable false positive rate α. Observation of test statistic t = a realisation of T p( T u H0) threshold u α Null Distribution of T t u Reject H 0 in favour of H A if t > u α p-value = evidence against H 0. p( T t H0) P-val 18 Null Distribution of T
19 F-test & contrast Null Hypothesis H 0 : True model is X 0 (reduced model) X 0 X 1 X 0 Test statistic: ratio of explained variability and unexplained variability (error) RSS ˆ 2 full RSS 0 ˆreduced 2 Full model? or Reduced model? 1 = rank(x) rank(x 0 ) 2 = N rank(x) 19
20 F-test example: movement related effects 20
21 Univariate analysis: Introduction: within & between subjects analysis GLM, contrasts & Statistical inference Multiple comparison problem & other inference levels Conclusion 21
22 Multiple comparison problem High Threshold t > 5.5 Med. Threshold t > 3.5 Low Threshold t > 0.5 Good Specificity Poor Power (risk of false negatives) Poor Specificity (risk of false positives) Good Power 22
23 Multiple comparison problem Noise Signal Signal+Noise 23
24 Multiple comparison problem Use of uncorrected p-value, = % 11.3% 12.5% 10.8% 11.5% 10.0% 10.7% 11.2% 10.2% 9.5% Percentage of Null Pixels that are False Positives Use of corrected p-value, =0.1 FWE 24
25 Multiple comparison problem Inference with multiple comparison in neuroimaging depends on: search volume = # tests performed smoothness of the data size & shape of volume of interest statistics employed (t- or F-) + degrees of freedom usually derived from data and test performed 25
26 More inference levels 26
27 More inference levels 27
28 Univariate analysis: Introduction: within & between subjects analysis GLM, contrasts & Statistical inference Multiple comparison problem & other inference levels Conclusion 28
29 Conclusion From a neuroimager perspectives, GLM is useful for: Localising an effect of interest, while accounting for effects of no interest confounding effects HRF shape (for fmri) Clean signal & functional connectivity 29
30 Conclusion From a machine learner perspectives, GLM is useful for: Check for «is there any effect?» Data filtering (e.g. confound removal) HRF deconvolution for fmri (single event modeling) or subject s response extraction (contrast building) Feature selection/masking 30
31 Thank you for your attention! Any question? 31
32 32
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