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Design Efficiency

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

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Design Efficiency

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  1. Design Efficiency Tom Jenkins Cat Mulvenna MfD March 2006

  2. 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

  3. 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) = XTX

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

  5. 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

  6. 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

  7. Sequencing: Efficiency calculations

  8. Peak Brief Stimulus Undershoot Initial Undershoot hrf

  9. Convolution with hrf

  10. Inefficient design

  11. Stochastic Design

  12. Block design

  13. Fourier Transform

  14. Spacing- effect of SOA for events

  15. Effect of null events on contrast efficiency

  16. Permuted, Random and Alternating designs

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

  18. Filtering

  19. Long block length-effect of high pass filter

  20. 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

  21. References and Acknowledgemnets • Rik Henson http://www.mrc-cbu.cam.ac.uk/Imaging/Common/fMRIefficiency • Catherine Jones MfD 2004 • Human Brain Function • Liu et al Efficiency, power and entropy in event related fMRI with multiple trial types Neuroimage 2004; 401-413.

  22. Thankyou MfD 2006

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