Design Efficiency Tom Jenkins Cat Mulvenna MfD March 2006

What is efficiency?  How well you experimental design answers the question you are interested in  A numerical value which reflects the ability of your design to detect the effect of interest

What is efficiency?  GLM: Y=Xβ + ε  Aim is to minimise variance in β, which will be reflected in more significant t and F test results  2 ways to minimise variance in β - data or design  As design efficiency increases variance in β decreases  Efficiency can be calculated because the variance in β is proportional to the variance in X  1/var(β) = Var(X) = X T X

What is efficiency?  A measure of how reliable the PEs are, defined as the inverse of the variance of a contrast of PEs  E(c,X) α 1/c T (X T X) -1 c  E=efficiency, c=contrast, X=design matrix  Equation tells us that efficiency varies even within a model depending on contrast of interest

What is efficiency?  Signal processing perspective  Maximise “energy” of predicted fMRI time series- i.e. the sum of squared signal values at each scan. This is proportional to the variance of the signal  To best detect signal in presence of noise, maximise variability of signal

How can we maximise efficiency?  Blocks or events?  Sequencing (order of stimuli)  Spacing (timing of stimuli, SOA)  Stimulus presentation in relation to scan acquisition  Filtering in SPM  Psychological validity

Sequencing: Efficiency calculations

hrf Brief Stimulus Undershoot Initial Undershoot Peak

Convolution with hrf

Inefficient design

Stochastic Design

Block design

Fourier Transform

Spacing- effect of SOA for events

Effect of null events on contrast efficiency

Permuted, Random and Alternating designs

Stimulus timing in relation to scan acquisition SOA as a multiple of TR SOA not a multiple of TR or jitter introduced

Filtering

Long block length-effect of high pass filter

Summary  Blocked designs most efficient but limitations  Event related designs: dynamic stochastic most efficient  Think about SOA- often smaller the better within reason.  For blocked designs optimal block length is 16s.  Don’t pick an SOA which is a multiple of your TR  Try not to contrast events that are further apart in time than your high pass filter  Compare tasks that are neither too different or too similar

References and Acknowledgemnets  Rik Henson cbu.cam.ac.uk/Imaging/Common/fMRIefficie ncy cbu.cam.ac.uk/Imaging/Common/fMRIefficie ncyhttp:// cbu.cam.ac.uk/Imaging/Common/fMRIefficie ncy  Catherine Jones MfD 2004  Human Brain Function  Liu et al Efficiency, power and entropy in event related fMRI with multiple trial types Neuroimage 2004;

Thankyou MfD 2006