why n’ how (i forgot the title) donald g. mclaren, ph.d. department of neurology, mgh/hms grecc,...
TRANSCRIPT
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Why N’ How (I forgot the title)
Donald G. McLaren, Ph.D.Department of Neurology, MGH/HMS
GRECC, ERNM Veteran’s Hospital
http://www.martinos.org/~mclaren
11/15/2012
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Types of Data
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Types of Data – Dependent Variable
• Task Data– Single Condition– Multiple Conditions– Multiple Predictors Per Condition
• Functional Connectivity – Correlation• Functional Connectivity -- ICA• Context-Dependent Connectivity• VBM• DTI• Other??
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Factors, Levels, Groups, ClassesContinuous Variables/Factors: Age, IQ, Volume, Behavioral measures (emotional scale, memory ability), Images, etc.Discrete Variables/Factors: Gender, Handedness, DiagnosisLevels of Discrete : Handedness: Left and Right Gender: Male and Female Diagnosis: Normal, MCI, ADGroup or Class: Specification of All Discrete Factors:• Left-handed Male MCI• Right-handed Female Normal
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Overview• From a line to the GLM and matrices
• Statistical Tests
• Contrasts
• Designs
• Power
• Caveats
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General Linear Model(GLM)
Y=aX+b
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GLM Theory
HRF AmplitudeIQ, Height, Weight
Independent Variable
Is Activity correlated with Age?
DependentVariable,Measurement
x1 x2
y2
y1
Subject 1
Subject 2
Activity
Age
Of course, you’d need more then twosubjects …
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Linear ModelIntercept: b
Slope: m
Activity
Age
x1 x2
y2
y1
System of Linear Equationsy1 = 1*b + x1*my2 = 1*b + x2*m
Y = X*
y1y2
1 x11 x2
bm= *
Matrix Formulation
X = Design Matrix = Regression Coefficients = Parameter estimates = “betas” = Intercepts and Slopes
bm
Intercept = Offset
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Hypotheses and ContrastsIs Activity correlated with Age?
Does m = 0?Null Hypothesis: H0: m=0
Intercept: b
Slope: m
Activity
Age
x1 x2
y2
y1
m= [0 1]*bm
= C*?
C=[0 1]: Contrast Matrix
bm
y1y2
1 x11 x2
bm= *
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Hypotheses and ContrastsIs Activity different from 0?
Does b = 0?Null Hypothesis: H0: b=0
Intercept: b
Slope: m
Activity
Age
x1 x2
y2
y1
b= [1 0]* bm
= C*?
C=[1 0]: Contrast Matrix
bm
y1y2
1 x11 x2
bm= *
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Hypotheses and ContrastsIs Activity different from 0?
Does b = 0?Null Hypothesis: H0: b=0
Intercept: b
Slope: mActivity
Age
x1 x2
y2
y1
b= [1 0]* bm
= C*?
C=[1 0]: Contrast Matrix
bm
y1y2
1 x11 x2
bm= *
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Hypotheses and ContrastsIs Activity different from 0?
Does b = 0?Null Hypothesis: H0: b=0
Intercept: b
Activity
Age
x1 x2
y2
y1
b= [1 0]* bm
= C*?
C=[1 0]: Contrast Matrix
bm
y1y2
1 x11 x1
bm= *
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Hypotheses and ContrastsIs Activity different from 0?
Does b = 0?Null Hypothesis: H0: b=0
Intercept: b
Activity
Age
x1 x2
y2
y1
b= [1 ]*b
= C*?
C=[1 0]: Contrast Matrix
b
y1y2
11
b= *
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More than Two Data Points
y1 = 1*b + x1*my2 = 1*b + x2*my3 = 1*b + x3*my4 = 1*b + x4*m
y1y2y3y4
1 x11 x21 x31 x4
bm= *
Y = X*+n
Intercept: b
Slope: m
Activity
Age
• Model Error• Noise• Uncertainty
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The General Linear Model
npnpnnn
pp
pp
pp
xxxY
xxxY
xxxY
xxxY
,2,21,10
3,32,321,3103
2,22,221,2102
1,12,121,1101
ppXXXY 22110
Y Y observed = predicted + random error
In Matrix Form
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Summary of the GLM
Y = X . β + ε
Observed data:
Imaging uses a mass univariate approach – that is each voxel is treated as a separate column vector of data.Y is Dependent Brain Value at various subjects/time points at a single voxel
Design matrix:
Several components which explain the observed data, i.e. the BOLD time series for the voxelTiming info: onset vectors, Om
j, and duration vectors, Dm
j
HRF, hm, describes shape of the expected BOLD response over timeOther regressors, e.g. realignment parameters
At the group level: these are covariates or grouping columns (see later slide)
Parameters:
Define the contribution of each component of the design matrix to the value of YEstimated so as to minimise the error, ε, i.e. least sums of squares
Error:
Difference between the observed data, Y, and that predicted by the model, Xβ.Not assumed to be spherical in fMRI
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Brain Imaging
• From the beginning (almost)….
[ 5 6 7 5 ]
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Spatial Normalization, Atlas Space
Subject 1
Subject 2
Subject 1
Subject 2
MNI305
Native Space MNI305 Space
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Group Analysis
Does not have to be all positive!
Contrast AmplitudesContrast Amplitudes Variances(Error Bars)
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Mass Univariate Analyses
(1) Run the GLM for each voxel.(2) Compute the statistic from the GLM for
each voxel(3) Inferences
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Statistical Parametric Map (SPM)+3%
0%
-3%
Contrast AmplitudeCON, COPE, CES
Contrast AmplitudeVariance
(Error Bars)VARCOPE, CESVAR
Significance t-Map (p,z,F)(Thresholded
p<.01)sig=-log10(p)
“Massive Univariate Analysis” -- Analyze each voxel separately
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SPM/FSL/AFNI/CUSTOM
• It is important to recognize that all programs that utilize the GLM will produce the same result. However, if your design matrices or variance correction methods are different, then you will see differences.
• Some slides show illustrations from FSL, others show illustrations from SPM, MATLAB, or other software. These can be done in all programs.
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Types Of Analysis
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GG
1
1
2
2
2
G
G
iG
G
NDOF
N
t
G
G
“Random Effects (RFx)” Analysis
RFx
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GG
“Random Effects (RFx)” Analysis
RFx
• Model Subjects as a Random Effect• Variance comes from a single source:
variance across subjects – Mean at the population mean– Variance of the population variance
• Does not take first-level noise into account (assumes 0)
• “Ordinary” Least Squares (OLS)• Usually less activation than individuals
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“Mixed Effects (MFx)” Analysis
MFx
RFx
• Down-weight each subject based on variance.• Weighted Least Squares vs (“Ordinary” LS)
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“Mixed Effects (MFx)” Analysis
MFx
• Down-weight each subject based on variance.• Weighted Least Squares vs (“Ordinary” LS)• Protects against unequal variances across
group or groups (“heteroskedasticity”)• May increase or decrease significance with
respect to simple Random Effects• More complicated to compute• “Pseudo-MFx” – simply weight by first-level
variance (easier to compute)
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“Fixed Effects (FFx)” Analysis
FFx
RFx
i
G
i
G
DOFDOF
N
t
G
G
2
22
2
2i
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“Fixed Effects (FFx)” Analysis
FFx
i
G
i
G
DOFDOF
N
t
G
G
2
22
2
• As if all subjects treated as a single subject (fixed effect)
• Small error bars (with respect to RFx)• Large DOF• Same mean as RFx• Huge areas of activation• Not generalizable beyond sample.
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Population vs Sample
Group Population(All members)Hundreds?Thousands?Billions?
Sample18 Subjects
• Do you want to draw inferences beyond your sample?
• Does sample represent entire population?
• Random Draw?
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fMRI Analysis Overview
Higher Level GLM
First Level GLM Analysis
First Level GLM Analysis
Subject 3
First Level GLM Analysis
Subject 4
First Level GLM Analysis
Subject 1
Subject 2
CX
CX
CX
CX
PreprocessingMC, STC, B0Smoothing
Normalization
PreprocessingMC, STC, B0Smoothing
Normalization
PreprocessingMC, STC, B0Smoothing
Normalization
PreprocessingMC, STC, B0Smoothing
Normalization
Raw Data
Raw Data
Raw Data
Raw Data
CX
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Second-Level Modeling
• These are all random effects (because of variance corrections and using beta’s from the first level)
• Mean across subjects divided by variance across subjects.– Low subjects with very low variance between
them can lead to a significant finding, even if no subject was significant at the single subject level
– Implications for analysis (e.g. SLBT??)
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Statistical Tests
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Implementing the T-test
Variance EstimateSqrt(Var*cT(XTX)-1c)
c = +1 0 0 0 0 0 0 0
T =
contrast ofestimated
parameters
t-test H0: cT = 0
varianceestimate
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Implementing the F-test
F = error
varianceestimate
additionalvariance
accounted forby effects of
interest
0 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 1
H0: cT = 0c =
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Contrasts and the Full Model
ate)(multivariTest -F ˆˆˆF
e)(univariatTest - tˆ)(
ˆ
ˆ
ˆt
Cin Rows J
Estimate VarianceContrast ˆ)(1ˆˆ
Contrast ˆˆ
Variance Residual ˆˆ
ˆ
EstimatesParameter )(ˆ
),0(~ , ,
1JDOF,
21DOF
212
2
1
2
T
nTT
nTT
T
n
TT
n
CXXC
C
CXXCJ
C
DOF
nn
yXXX
NnnsynXy
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T/r/F Notes• If F is a single row contrast, then F=T^2• An F-test has no direction• In many programs, T-tests are one-tailed, thus have a
p-value half of the same F-test• There are formulas to convert between T/r and other
statistics (e.g. cohen’s d)• To avoid double-dipping, when you extract an ROI to
plot the correlation and get the correlation value, DO NOT make inferences from the plots, but from the voxel-wise analysis.
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Contrasts
• Identify the Null Hypothesis– Ho: A=B
• Make the Null Hypothesis equal 0– Ho: A-B=0
• Identify the columns for A and B, apply their weights– Ho: 1*A+(-1)*B– Contrast [1 -1]
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Contrasts
• What if A and B are not individual columns as in the case of A1,A2,B1,B2…– [1 1 -1 -1] would work, but will over estimate the
magnitude of the effect– A is the average A1 A2, or Ho: (A1+A2)/2=0
• [½ ½ 0 0]
– B is the average B1 B2, or Ho: (B1+B2)/2=0• [0 0 ½ ½]
– [½ ½ -½ -½]
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GG
Higher Level GLM Analysis
=
11111
G
y = X *
Data fromone voxel
Design Matrix(Regressors)
Vector ofRegressionCoefficients(“Betas”)
Obs
erva
tions
(Low
-Lev
el C
ontr
asts
)
Contrast Matrix:C = [1]Contrast = C* = G
One-Sample Group Mean (OSGM)
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Two Groups GLM Analysis
=
11100
G1
G2
y = X *
Data fromone voxel
Obs
erva
tions
(Low
-Lev
el C
ontr
asts
) 00011
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Contrasts: Two Groups GLM Analysis
1. Does Group 1 by itself differ from 0?Ho: G1=0; Contrast = C* = G1; C = [1 0]
= 11100
G1
G2
00011
2. Does Group 2 by itself differ from 0?Ho: G2=0; Contrast = C* = G2; C = [0 1]
3. Does Group 1 differ from Group 2?Ho: G1= G2; Contrast = C* = G1- G2; C = [1 -1] 4. Does either Group 1 or Group 2 differ from 0? C has two rows: F-test (vs t-test) Concatenation of contrasts #1 and #2
1 00 1
C =
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One Group, One Covariate (Age)
=
11111
G
Age
y = X *
Data fromone voxel
Obs
erva
tions
(Low
-Lev
el C
ontr
asts
) 2133641747
Intercept: G
Slope: Age
Contrast
Age
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Contrasts: One Group, One Covariate
1. Does Group offset/intercept differ from 0?
Does Group mean differ from 0 regressing out age?
Ho: G=0; Contrast = C* = G; C = [1 0], (Treat age as nuisance)
= 11111
G
Age
2133641747
2. Does Slope differ from 0?Ho: Age=0; Contrast = C* = Age; C = [0 1]
Intercept: G
Slope: Age
Contrast
Age
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Contrasts: One Group, One Mean-Centered Covariate
= 11111
G
Age
-15-328-2011
Mean: G
Slope: Age
Contrast
Age
1. Does Group offset/intercept differ from 0?
Does Group mean differ from 0 regressing out age?
Ho: G=0; Contrast = C* = G; C = [1 0], (Treat age as nuisance)
2. Does Slope differ from 0?Ho: Age=0; Contrast = C* = Age; C = [0 1], ** Same effect as non-mean centered covariate
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Group Effects1. Does Activity vary with Disease Status?
2. Does Activity vary with Gender?
1. Is there an Interaction between DS and G?
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2x2 Group ANOVA
10
5
13
9
While this design matrix was generated in SPM, you could generate it in any of the MRI Analysis packagees or statistical programs.
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Contrasts
• Does Activity vary by Disease Status?– Ho: DS-=DS+– Ho: DS- - DS+ =0– [½ ½ -½ -½]; (group difference based on subgroups) or– [10/15 5/15 -13/22 -9/22] (pure average of subjects)
• Does Activity vary by Gender?– Ho: Male=Female– Ho: Male - Female =0– [½ -½ ½ -½]; or (group difference based on subgroups) or– [10/23 -5/14 13/23 -9/14] (pure average of subjects)
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Contrasts
• Average of Subgroups versus Average of Individuals– If you have drawn a random sample and want to talk generally about
all subjects in a group, use the contrast weighted by group size.– If you haven’t drawn a random sample or want to look at the average
effect of the group, then you want to use the contrast that is not weighted by group size.
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Contrasts• Is there an interaction?
– Ho: DS-Females-DS-Males= DS+Females-DS+Males– Ho: (DS-Females-DS-Males) – (DS+Females-DS+Males)=0– Ho: DS-Females-DS-Males – DS+Females+DS+Males=0– [1 -1 -1 1]; or
• Are the groups different?– Ho: DS-Females=DS-Males=DS+Females=DS+Males– F-test– DS-Females=DS-Males [1 -1 0 0]– DS-Males=DS+Females [0 1 -1 0]– DS+Females=DS+Males [0 0 1 -1]– [1 -1 0 0; 0 1 -1 0; 0 0 1 -1]
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Contrasts
• If there is an interaction, you can not interpret the effects of the individual factors (e.g. disease and gender)
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GLM • Important to model all known variables,
even if not experimentally interesting:– e.g. head movement,
block and subject effects – minimise residual error
variance for better stats– effects-of-interest are the
regressors you’re actually interested in
covariates
conditions:effects of interest
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64
Contrasts: Two Groups GLM Analysis
1. Does Group 1 by itself differ from 0?Ho: G1=0; Contrast = C* = G1; C = [1 0]
= 11100
G1
G2
00011
2. Does Group 2 by itself differ from 0?Ho: G2=0; Contrast = C* = G2; C = [0 1]
3. Does Group 1 differ from Group 2?Ho: G1= G2; Contrast = C* = G1- G2; C = [1 -1] 4. Does either Group 1 or Group 2 differ from 0? C has two rows: F-test (vs t-test) Concatenation of contrasts #1 and #2
1 00 1
C =
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One Group, One Covariate (Age)
=
11111
G
Age
y = X *
Data fromone voxel
Obs
erva
tions
(Low
-Lev
el C
ontr
asts
) 2133641747
Intercept: G
Slope: Age
Contrast
Age
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Contrasts: One Group, One Covariate
1. Does Group offset/intercept differ from 0?
Does Group mean differ from 0 regressing out age (mean-centered)?
Ho: G=0; Contrast = C* = G; C = [1 0], (Treat age as nuisance)
= 11111
G
Age
2133641747
2. Does Slope differ from 0?Ho: Age=0; Contrast = C* = Age; C = [0 1]
Intercept: G
Slope: Age
Contrast
Age
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One Group, One Covariate
(http://mumford.fmripower.org/mean_centering/)
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Two Groups
Do groups differ in Intercept?Do groups differ in Slope?Is average slope different than 0?…
Intercept: b1
Slope: m1
Activity
Age
Intercept: b2
Slope: m2
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Two GroupsIntercept: b1
Slope: m1
Activity
Age
Intercept: b2
Slope: m2
y11 = 1*b1 + 0*b2 + x11*m1 + 0*m2y12 = 1*b1 + 0*b2 + x12*m1 + 0*m2y21 = 0*b1 + 1*b2 + 0*m1 + x21*m2y22 = 0*b1 + 1*b2 + 0*m1 + x22*m2
y11y12y21y22
1 0 x11 01 0 x12 00 1 0 x210 1 0 x22
b1b2m1m2
=*
Y = X*
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70
Two Groups, One Covariate
• Somewhat more complicated design• Slopes may differ between the groups• What are you interested in?
• Differences between intercepts? Ie, treat covariate as a nuisance?• Differences between slopes? Ie, an interaction between group and covariate?
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Two Groups, One (Nuisance) Covariate
Is there a difference between the group means?
Synthetic Data
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Raw Data
Effect of Age Effect After Age “Regressed Out”(e.g. Age=0)
• No difference between groups• Groups are not well matched for age • No group effect after accounting for age• Age is a “nuisance” variable (but important!)• Slope with respect to Age is same across groups•If age was mean-centered, there might be a group effect!!!
•Depends on mean-centering…
Two Groups, One (Nuisance) Covariate
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=
11100
G1
G2
Age
y = X *
Data fromone voxel
Obs
erva
tions
(Low
-Lev
el C
ontr
asts
) 00011
2133641747
Two Groups, One (Nuisance) Covariate
One regressor for Age.
Different Offset Same Slope (DOSS)
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=
11100
G1
G2
Age
00011
2133641747
Two Groups, One (Nuisance) Covariate
One regressor for Age indicates that groups have same slope – makes difference between group means/intercepts independent of age.
Different Offset Same Slope (DOSS)
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Contrasts: Two Groups + Covariate
1. Does Group 1 intercept/mean differ from 0 (after regressing out effect of age)?Ho:G1=0, Contrast = C* = G1, C = [1 0 0]
2. Does Group 2 intercept/mean differ from 0(after regressing out effect of age)?Ho:G2=0, Contrast = C* = G2, C = [0 1 0]
3. Does Group 1 intercept/mean differ from Group 2 intercept/mean (after regressing out effect of age)?Ho: G1=G2, , Contrast = C* = G1- G2, C = [1 -1 0]
=
11100
G1
G2
Age
00011
2133641747
4. Does Slope differ from 0 (after regressing out the effect of group)? Does not have to be a “nuisance”!Ho: Age=0, Contrast = C* = Age, C = [0 0 1]
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Two-Groups, One Covariate, Same Slope
1,2
4
3
Model from previous slide
(http://mumford.fmripower.org/mean_centering/)
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• Slope with respect to Age differs between groups• Interaction between Group and Age• Intercept different as well
Group/Covariate InteractionTwo Groups, One Covariate, Different Slopes
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=
11100
G1
G2
Age1
Age2
y = X *
Data fromone voxel
Obs
erva
tions
(Low
-Lev
el C
ontr
asts
) 00011
213364 0 0
0 0 01747
Group-by-Age Interaction
Different Offset Different Slope (DODS)
Group/Covariate Interaction
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1. Does Slope differ between groups?Is there an interaction between group and
age? Ho: Age1=Age2, Contrast = C* = Age1-
Age2, C = [0 0 1 -1],
Group/Covariate Interaction
=
11100
G1
G2
Age1
Age2
00011
213364 0 0
0 0 01747
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Group/Covariate Interaction
=
11100
G1
G2
Age1
Age2
00011
213364 0 0
0 0 01747
Does this contrast make sense?
2. Does Group 1 intercept/mean differ from Group 2 mean (after regressing out effect of age)?Ho: G1- G2, Contrast = C* = G1- G2, C = [1 -1 0 0] Very tricky!This tests for difference at Age=0What about Age = 12?What about Age = 20?
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Group/Covariate InteractionIf you are interested in the difference between
the means but you are concerned there could be a difference (interaction) in the slopes:
1. Analyze with interaction model (DODS*)2. Test for a difference in slopes3. If there is no difference, re-analyze with
single regressor model (DOSS*)4. If there is a difference, proceed with
caution
* Freesurfer terms
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Group/Covariate Interaction
(http://mumford.fmripower.org/mean_centering/)
Model from previous slide
1
2
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Mean Centering• Across ALL subjects
– Covariate-adjusted group means
• Within each group– Each group would have the same mean as a one-sample t-
test
• Why does it matter?– The interpretation changes– Correlation between group and covariate (e.g. MMSE and
Alzheimer’s diagnosis)
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Covariates
• If you have a single group:– Demeaning covariate will not change the slope– Demeaning makes the group term the mean of
the group; whereas not demeaning makes the group term the intercept.
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Covariates
• If you have a multiple groups:– Demeaning covariate will not change the slope, no
matter how you demean it– Demeaning within each group controlling for
the covariate, but group means are uneffected– Demeaning across everyone controlling for the
covariate, but group means are effected. If you do this, you should refer to group tests as a comparison of covariate-adjusted means
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87
Longitudinal/Repeated-Measures
Did something change between visits?• Drug or Behavioral Intervention?• Training?• Disease Progression?• Aging?• Injury?• Scanner Upgrade?• Multiple tasks in the same session?
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Longitudinal
Paired DifferencesBetween Subjects
Subject 1, Visit 1
Subject 1, Visit 2
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Longitudinal Paired Analysis
=
11111
V
y = X *
Paired Diffsfrom one voxel
Design Matrix(Regressors)
Obs
erva
tions
(V1-
V2 D
iffer
ence
s in
Low
-Lev
el C
ontr
asts
)
Ho: V=0Contrast = C* = V Contrast Matrix:C = [1]
One-Sample Group Mean (OSGM): Paired t-Test
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GLM – Paired T-Test
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GLM – Repeated Measures
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Constructing Contrasts
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Constructing Contrasts
• What is the null hypothesis?
• Make the null hypothesis equal to 0
• Label the columns based on the weighting of the components of the null hypothesis– For repeated measures, form the sub-elements of
the contrast, then apply the weights
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Constructing Contrasts
• S1G1C1: [1 zeros(1,10) 1 0 1 0 0 1 0 0 0 0 0]• S1G1C2: [1 zeros(1,10) 1 0 0 1 0 0 1 0 0 0 0]• S2G1C1: [0 1 zeros(1,9) 1 0 1 0 0 1 0 0 0 0 0]• G1: [ones(1,6)/6 zeros(1,5) 1 0 1/3 1/3 1/3 1/3 1/3 1/3 0 0 0]• G1vsG2: [ones(1,6)/6 ones(1,5)/5 1 -1 0 0 0 1/3 1/3 1/3 -1/3
-1/3 -1/3] – (NOTE: This is not a valid contrast, even though it can be constructed.)
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Contrast Validity• Do you only have between-subject factors?
– All contrasts valid
• Do you only have within-subject factors?– Any contrast comparing levels of a factor/interaction is
valid– Effect of a single level is not valid
• Do you have between- and within-subject factors?– Any contrast comparing levels of a factor/interaction is
valid– Interaction contrasts are valid– Group/between-subject effects are not valid (e.g. G1vG2)– Effect of a single level is not valid
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Constructing Contrasts
• S1G1C1: [1 zeros(1,10) 1 0 1 0 0 1 0 0 0 0 0]• S1G1C2: [1 zeros(1,10) 1 0 0 1 0 0 1 0 0 0 0]• S2G1C1: [0 1 zeros(1,9) 1 0 1 0 0 1 0 0 0 0 0]• G1C1: [ones(1,6)/6 zeros(1,5) 1 0 1 0 0 1 0 0 0 0 0]• G2C1: [zeros(1,6) ones(1,5)/5 0 1 1 0 0 0 0 0 1 0 0]• *C1:[ones(1,6)/12 ones(1,5)/10 1/2 1/2 1 0 0 1/2 0 0 1/2 0
0]• *C1:[ones(1,11)/11 5/11 6/11 0 0 5/11 0 0 6/11 0 0]• C1vsC2: [zeros(1,11) 0 0 1 -1 0 1/2 -1/2 0 1/2 -1/2 0 ]• C1vsC2: [zeros(1,11) 0 0 1 -1 0 5/11 -5/11 0 6/11 -6/11 0 ]
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Power Calculations
• The probability that the test will reject the null hypothesis, when the null hypothesis is false.
• In general, you want to say that you have 80-90% power in your study.
• Estimate your effect size, specify your power, determine the sample size needed.
• CANNOT BE DONE POST-HOC!!!
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Power Calculations• Estimate your effect size
– Which brain region?• Minimum N to achieve % power in a set of regions (McLaren
et al. 2010)
– Where to find effect sizes?• Previous studies, pilot studies
• Specify your power (option A)– The higher the better, but more power means a larger N
• Specify your N (option B)– Increasing N will increase the power
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Power Calculations - $7600 study
(Mumford et al. 2008)
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Programs
• G*Power
• http://fmripower.org/
• http://fmri.wfubmc.edu/cms/talkPowerSampleSizeCalculation voxel-wise
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Caveat 1: What is analyzed…
• Missing Data– NaN– Zeros
Also AFNI/FSL
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Caveat 2: Designs
• Between-subject Designs
• Within-subject Designs
• Mixed Designs
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Pick your design Carefully
All of these designs test the same effect; however only the top 2 give you the correct RFX results and are generalizable to the population. The top right model is a variant of the GLM that creates a second error term (more on this next week).
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Pick your design Carefully
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Variance Corrections
• The issue of non-sphericity
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Repeated Measures in FSL
• Limited to designs that have no violations of sphericity.
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Misc. Considerations
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Correction for Multiple Comparisons
• Cluster-based– Monte Carlo simulation – Permutation Tests– Surface Gaussian Random Fields (GRF)
• There but not fully tested• False Discovery Rate (FDR) – built into tksurfer
and QDEC. (Genovese, et al, NI 2002)
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Clustering1. Choose a voxel/vertex-wise threshold
• Eg, 2 (p<.01), or 3 (p<.001)• Sign (pos, neg, abs)
2. A cluster is a group of connected (neighboring) voxels/vertices above a threshold
3. Cluster has a size (volume in mm3 and area in mm2)
p<.01 (-log10(p)=2)Negative
p<.0001 (-log10(p)=4)Negative
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What to report in papers
• Be explicit about the model– What are the factors– What are the covariates– What did you set as the variance and dependence for each
factor
• Be explicit about the contrast you are using• Be explicit about how to interpret the contrast
– Group means, group intercepts, covariate adjusted group means
• Be explicit about the thresholds used– Corrections for multiple comparisons– Small Volume Correction (corrected in SPM8 in late Feb. 2012)
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SPM/FSL/AFNI/CUSTOM
• It is important to recognize that all programs that utilize the GLM will produce the same result. However, if your design matrices or variance correction methods are different, then you will see differences.
• Some slides show illustrations from FSL, others show illustrations from SPM, MATLAB, or other software. These can be done in all programs.
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Useful Mailing Lists• SPM – http://www.jiscmail.ac.uk/list/spm.html
• FSL -- http://www.jiscmail.ac.uk/list/fsl.html
• Freesurfer -- http://surfer.nmr.mgh.harvard.edu/fswiki/FreeSurferSupport
• CARET -- http://brainvis.wustl.edu/wiki/index.php/Caret:Mailing_List
• I highly recommend reading the posts on these lists as they will save you time in the future.