Design EfficiencyDesign Efficiency

Tom JenkinsTom Jenkins

Cat MulvennaCat Mulvenna

MfD March 2006MfD March 2006

What is efficiency?What is efficiency?

How well you experimental design answers How well you experimental design answers the question you are interested inthe question you are interested in

A numerical value which reflects the ability A numerical value which reflects the ability of your design to detect the effect of interestof your design to detect the effect of interest

What is efficiency?What is efficiency?

GLM: Y=Xβ + εGLM: Y=Xβ + ε Aim is to minimise variance in β, which will be Aim is to minimise variance in β, which will be

reflected in more significant t and F test resultsreflected in more significant t and F test results 2 ways to minimise variance in β - data or design2 ways to minimise variance in β - data or design As design efficiency increases variance in β As design efficiency increases variance in β

decreasesdecreases Efficiency can be calculated because the variance Efficiency can be calculated because the variance

in β is proportional to the variance in Xin β is proportional to the variance in X 1/var(β) = Var(X) = X1/var(β) = Var(X) = XTTXX

What is efficiency?What is efficiency?

A measure ofA measure of how reliable the PEs are, defined as how reliable the PEs are, defined as the inverse of the variance of a contrast of PEsthe inverse of the variance of a contrast of PEs

E(c,X) α 1/cE(c,X) α 1/cTT (X (XTTX) X) -1-1cc

E=efficiency, c=contrast, X=design matrixE=efficiency, c=contrast, X=design matrix

Equation tells us that efficiency varies even within Equation tells us that efficiency varies even within a model depending on contrast of interesta model depending on contrast of interest

What is efficiency?What is efficiency?

Signal processing perspectiveSignal processing perspective Maximise “energy” of predicted fMRI time Maximise “energy” of predicted fMRI time

series- i.e. the sum of squared signal values series- i.e. the sum of squared signal values at each scan. This is proportional to the at each scan. This is proportional to the variance of the signalvariance of the signal

To best detect signal in presence of noise, To best detect signal in presence of noise, maximise variability of signalmaximise variability of signal

How can we maximise efficiency?How can we maximise efficiency?

Blocks or events?Blocks or events? Sequencing (order of stimuli)Sequencing (order of stimuli) Spacing (timing of stimuli, SOA)Spacing (timing of stimuli, SOA) Stimulus presentation in relation to scan Stimulus presentation in relation to scan

acquisitionacquisition Filtering in SPMFiltering in SPM Psychological validityPsychological validity

Sequencing: Efficiency calculationsSequencing: Efficiency calculations

hrfhrf

BriefStimulus

Undershoot

InitialUndershoot

Peak

Convolution with hrfConvolution with hrf

Inefficient designInefficient design

Stochastic DesignStochastic Design

Block designBlock design

Fourier TransformFourier Transform

Spacing- effect of SOA for eventsSpacing- effect of SOA for events

Effect of null events on contrast Effect of null events on contrast efficiencyefficiency

Permuted, Random and Alternating Permuted, Random and Alternating designsdesigns

Stimulus timing in relation to scan Stimulus timing in relation to scan acquisitionacquisition

SOA as a multiple of TR

SOA not a multiple of TRor jitter introduced

FilteringFiltering

Long block length-effect of high pass Long block length-effect of high pass filterfilter

SummarySummary

Blocked designs most efficient but limitationsBlocked designs most efficient but limitations Event related designs: dynamic stochastic most Event related designs: dynamic stochastic most

efficientefficient Think about SOA- often smaller the better within Think about SOA- often smaller the better within

reason. reason. For blocked designs optimal block length is 16s.For blocked designs optimal block length is 16s. Don’t pick an SOA which is a multiple of your TRDon’t pick an SOA which is a multiple of your TR Try not to contrast events that are further apart in Try not to contrast events that are further apart in

time than your high pass filtertime than your high pass filter Compare tasks that are neither too different or too Compare tasks that are neither too different or too

similarsimilar

References and AcknowledgemnetsReferences and Acknowledgemnets

Rik Henson Rik Henson http://www.mrc-cbu.cam.ac.uk/Imaging/Comhttp://www.mrc-cbu.cam.ac.uk/Imaging/Common/fMRIefficiencymon/fMRIefficiency

Catherine Jones MfD 2004Catherine Jones MfD 2004 Human Brain FunctionHuman Brain Function Liu et al Efficiency, power and entropy in Liu et al Efficiency, power and entropy in

event related fMRI with multiple trial types event related fMRI with multiple trial types Neuroimage 2004; 401-413.Neuroimage 2004; 401-413.

ThankyouThankyou

MfD 2006MfD 2006