Transcript final3

Efficiency in Experimental
Design
Catherine Jones
MfD2004
Overview
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What is efficiency?
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How can we maximise it?
What is efficiency?
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SPM uses the General Linear Model: Y = Xβ + ε
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The significance of the t & F statistics reflect the variance of β and the size of the
error. As the variance of β decreases the statistical significance increases.
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There are two ways to reduce the variance of β: (1) data (2) design matrix.
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Efficiency is the ability to estimate β, given the design matrix (X) you have
specified i.e. it reflects how well your experimental design can answer the
question you are interested in.
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As the efficiency of the model increases, the variance of β decreases (and vice
versa).
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Efficiency can be calculated because the variance of β is proportional to the
variance of X
1
Var(β)
=
Var(X)
=
XTX
Therefore…
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Efficiency is the process of maximising your chance of
finding the experimental effect
It is defined by:
e(c,X)
1
cT (XTX)-1c
where e = efficiency, c = contrast, X = design matrix
And is thus specific to a particular contrast
Ways to maximise efficiency…
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Event related vs Blocked designs
Sequencing of events (i.e. the ordering)
Spacing of events (i.e. the timing)
Spacing of events in relation to fMRI data collection
Temporal filtering
Psychological validity
First… a bit of background info…
Creating a model of the neural response
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The stimulus model predicts the pattern of neural activity, but the BOLD
response does not resemble this neat on/off pattern.
Thus, the stimulus model is convolved with the Haemodynamic Response
Function (HRF), a stereotyped model of the BOLD signal following an event, to
give a regressor that is entered into the Design Matrix.
The HRF reflects that following neural activity,
there is a peak in the BOLD signal after approx.
5s, which persists for approx. 30s.
Peak
Brief
Stimulus
Undershoot
Initial
Undershoot
Convolved design and HRF
Event related vs Blocked designs
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Blocked designs // PET
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Types of trials are ‘blocked’ together e.g. AAAAA BBBBB
AAAAA. Also described as an Epoch design.
Event related designs // ERPs
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Types of trials are interleaved and each trial is modelled
separately as an ‘event’ e.g. AABABBAB
Advantages of efMRI
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Can randomise or counterbalance trial order to reduce contextual
bias and minimise differences related to cognitive ‘set’ or strategy
use.
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Some experimental designs cannot be blocked e.g. oddball designs.
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Can use post-hoc classification of trials e.g. separately model trials
with correct or incorrect responses, following post-scanning testing
or depending on subjective perception.
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Improves temporal resolution such that you can look at events on a
shorter time scale.
Disadvantage of efMRI
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There is typically less efficiency in event related designs
Efficiency related to the sequencing of events
Stochastic designs: at each
point at which an event could
occur there is a specified
probability of that event
occurring. The timing of when
the events occur is specified.
Non-occurrence = null event.
Deterministic designs: the
occurrence of events is predetermined.
The variable deterministic
design i.e. a blocked design,
is the most efficient.
But what if I want to use efMRI?
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When using an efMRI design, mini runs of the same stimuli may be
the most efficient.
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You can modulate the probability of the events using a sine wave
i.e. a dynamic stochastic presentation.
Joel’s example of different stimulus presentations
Tasks
ABC
Blocked
design
Fully
randomised
Efficiency calculation
100
90
80
70
60
50
40
30
20
10
0
Block
Dynamic
stochastic
Dynamic
stochastic
Randomised
Efficiency related to the spacing of events
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Stimulus Onset Asynchronies (SOAs) are the units of time between
subsequent events i.e. they corresponds to the inter-stimulus interval.
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Generally speaking, SOAs that are small (SOAmin) and randomly distributed
are the most efficient.
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The SOAs are generally shorter than the BOLD response, but this overlap is
modelled by the HRF - successive responses are assumed to add in a linear
fashion.
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But, very short SOAs (< 1s, Friston et al, 1999) are not advisable as the
predicted additive effects upon the HRF of two closely occurring stimuli
break down.
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For random designs (i.e. ABBBAABAB) efficiency in detecting differential effects
between event types (e.g. A-B) increases with shorter SOAs. SOAmin is best!
Note that it is more efficient to have relatively longer SOAs with main effect contrasts
(i.e. A+B).
If you include null events (a third, unmodelled event type) then efficiency is slightly
compromised for A-B but increases for contrast A+B, in which the contrast is
measured relative to baseline. Now, SOAmin is the most efficient for A-B and A+B.
This is shift in efficiency is related to the fact that null events allow the baseline value
to be lower and therefore the difference between A+B and the baseline is bigger.
Some designs require alternating presentation of stimuli (i.e. ABABABAB), in
this case the most efficient SOA is approx. 8s.
Some designs require a longer SOA, if the SOA needs to be >8s then it may be
best to go for a permuted design (i.e. pseudorandom ABBABABAAB).
Timing of the SOAs in relation to the TR
If the TR (Repetition Time of slice collection) is divisible by the SOA then data
collected for each event will be from the same slices, at the same points along the
HRF.
TR = 4s
Scans
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Stimulus (synchronous)
Stimulus (asynchronous)
SOA=8s
SOA=6s
Stimulus (random jitter)
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Therefore, either choose a TR and SOA that are not divisible or introduce a ‘jitter’
such that the SOA is randomly shifted.
Temporal Filtering: The High Pass Filter
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A temporal filter is used in fMRI to get rid of
noise, thus increasing the efficiency of the
data.
Non-neuronal noise tends to be of lowfrequency, including ‘scanner drift’ and
physiological phenomenon.
Applying a high pass filter means that
parameters that occur at a slow rate are
removed from the analysis.
The default high pass filter in SPM is 128s,
thus if you have experimental events
occurring less frequently than once every
128s then the associated signal will be
removed by the filter!!
Don’t forget… the tasks!
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A studies efficiency is only as good as the tasks that
have been chosen.
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Typically, control tasks should control for all processes in
the experimental task, bar the component of interest.
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i.e. There should be as few explanations for your
resulting data as possible.
Summary
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Blocked designs are generally the most efficient, but blocked
designs have restrictions.
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For event-related designs, dynamic stochastic presentation of stimuli
is most efficient.
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However, the most optimal design for your data depends on the
SOA that you use. The general rule is the smaller your SOA the
better, but sometimes a small SOA may not be possible.
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Also, the most optimal design for one contrast may not be optimal
for another e.g. the inclusion of null events improves the efficiency of
main effects at short SOAs, at the cost of efficiency for differential
effects.
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Finally, there is no point scanning two tasks to look for differences
between them if they are too different or too similar.
A big thank you to…
Joel and Lucy