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Group analyses

Group analyses. Will Penny. Wellcome Trust Ce ntre for Neuroimaging University College London. GROUP ANALYSIS Fixed Effects Analysis (FFX) Random Effects Analysis (RFX) Multiple Conditions Factorial Designs. GROUP ANALYSIS Fixed Effects Analysis (FFX) Random Effects Analysis (RFX)

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Group analyses

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  1. Group analyses Will Penny Wellcome Trust Centre for Neuroimaging University College London

  2. GROUP ANALYSIS • Fixed Effects Analysis (FFX) • Random Effects Analysis (RFX) • Multiple Conditions • Factorial Designs

  3. GROUP ANALYSIS • Fixed Effects Analysis (FFX) • Random Effects Analysis (RFX) • Multiple Conditions • Factorial Designs

  4. Subject 1 For voxel v in the brain Effect size, c ~ 4Within subject variability, sw~0.9

  5. Subject 3 For voxel v in the brain Effect size, c ~ 2Within subject variability, sw~1.5

  6. Subject 12 For voxel v in the brain Effect size, c ~ 4Within subject variability, sw~1.1

  7. Fixed Effects Analysis Time series are effectively concatenated – as though we had one subject with N=50x12=600 scans. sw = [0.9, 1.2, 1.5, 0.5, 0.4, 0.7, 0.8, 2.1, 1.8, 0.8, 0.7, 1.1]Mean effect, m=2.67Average within subject variability (stand dev), sw =1.04Standard Error Mean (SEMW) = sw /sqrt(N)=0.04Is effect significant at voxel v?t=m/SEMW=62.7p=10-51

  8. Fixed Effects Analysis Modelling all subjects at once • Simple model • Lots of degrees of freedom • Large amount of data • Assumes common varia Subject 1 Subject 2 Subject 3 … Subject N

  9. GROUP ANALYSIS • Fixed Effects Analysis (FFX) • Random Effects Analysis (RFX) • Multiple Conditions • Factorial Designs

  10. Subject 1 For voxel v in the brain Effect size, c ~ 4

  11. Subject 3 For voxel v in the brain Effect size, c ~ 2

  12. Subject 12 For voxel v in the brain Effect size, c ~ 4

  13. Whole Group For group of N=12 subjects effect sizes are c = [4, 3, 2, 1, 1, 2, 3, 3, 3, 2, 4, 4]Group effect (mean), m=2.67Between subject variability (stand dev), sb =1.07Standard Error Mean (SEM) = sb /sqrt(N)=0.31Is effect significant at voxel v?t=m/SEM=8.61p=10-6

  14. Random Effects Analysis (RFX) For group of N=12 subjects effect sizes are c= [3, 4, 2, 1, 1, 2, 3, 3, 3, 2, 4, 4]Group effect (mean), m=2.67Between subject variability (stand dev), sb =1.07This is called a Random Effects Analysis because we are comparing the group effect to the between-subject variability.

  15. Summary Statistic Approach For group of N=12 subjects effect sizes are c = [3, 4, 2, 1, 1, 2, 3, 3, 3, 2, 4, 4]Group effect (mean), m=2.67Between subject variability (stand dev), sb =1.07This is also known as a summary statistic approach because we are summarising the response of each subject by a single summary statistic – their effect size.

  16. RFX versus FFX With Fixed Effects Analysis (FFX) we compare the group effect to the (average) within-subject variability. It is not an inference about the sample from which the subjects were drawn. With Random Effects Analysis (RFX) we compare the group effect to the between-subject variability. It is an inference about the sample from which the subjects were drawn. If you had a new subject from that population, you could be confident they would also show the effect.

  17. RFX: Summary Statistic First level DataDesign MatrixContrast Images

  18. RFX: Summary Statistic First level Second level DataDesign MatrixContrast Images SPM(t) One-sample t-test @ 2nd level

  19. Face data

  20. Face data Go to a voxel and press “PLOT” -> “Plot against scan or time”

  21. GROUP ANALYSIS • Fixed Effects Analysis (FFX) • Random Effects Analysis (RFX) • Multiple Conditions • Factorial Designs

  22. ANOVA Condition 1 Condition 2 Condition3Sub1 Sub13 Sub25Sub2 Sub14 Sub26... ... ...Sub12 Sub24 Sub36ANOVA at second level (eg clinical populations). If you have two conditions this is a two-sample t-test.

  23. Condition 1 Condition 2 Condition 3 Response Each dot is a different subject

  24. ANOVA within subject Condition 1 Condition 2 Condition3Sub1 Sub1 Sub1Sub2 Sub2 Sub2... ... ...Sub12 Sub12 Sub12ANOVA within subjects at second level (eg same subjects on placebo, drug1, drug2).This is an ANOVA but with subject effects removed. If you have two conditions this is a paired t-test.

  25. Condition 1 Condition 2 Condition 3 Response Each colour is a different subject

  26. Condition 1 Condition 2 Condition 3 Response With subject effects (means) subtracted, the difference in conditions is more apparent

  27. GROUP ANALYSIS • Fixed Effects Analysis (FFX) • Random Effects Analysis (RFX) • Multiple Conditions • Factorial Designs

  28. https://en.wikibooks.org/wiki/SPM/Group_Analysis

  29. Partitioned Error Approach It is recommended that group analysis be implemented in SPM using a “partitioned error” approach. This requires setting up a second-level design matrix to test for each effect of interest. If you have more than one experimental factor the analysis involves many steps as there are many effects to test for (due to the combinatorial nature of factorial designs).

  30. Two groups (between-subject factor) • Two conditions per subject (pre and post treatment)

  31. Summary Group Inference usually proceeds with RFX analysis, not FFX. Group effects are compared to between rather than within subject variability. Can also use ANOVA at second level for inference about multiple experimental conditions.. W. Penny and A. Holmes. Random effects analysis. In Statistical Parametric Mapping: The analysis of functional brain images. Elsevier, London, 2006 J Mumford and T Nichols. Simple Group fMRI Modelling and Inference. Neuroimage, 47(4):1469-75, 2009.

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