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					Study Design and Efficiency

        Margarita Sarri
         Hugo Spiers
             We will talk about:
   What kinds of designs are out there?   -
    Blocked vs event-related designs
   How can I order my events?
   What is estimation efficiency?
   Which designs are more efficient?
   Spacing of events
   Sampling issues
   Filtering issues
        Event related vs Blocked designs
       Blocked / Epoch/ Box             design
          Types of trials are ‘blocked’ together e.g. AAAAA BBBBB
           AAAAA.




   Event related design
      Types of trials are interleaved and each trial is modelled separately as
       an ‘event’ e.g. AABABBAB
                          Blocked design
 typically used in experiments where the   detection of activation is the primary
goal.
 e.g localise a specific brain region showing a differential response to one type
of stimulus (e.g. faces vs houses)




   In general 2 blocks more efficient than 4.
   Ideal modulation frequency being approximately 16sec

but you may not be able to test certain things with such a design…
So you may want to go for an event related design…
                   Why should I use efMRI ?

   Flexibility and randomization
        eliminate predictability of block designs
        avoid practice effects/strategy use

   Post hoc sorting
       e.g. classification of correct vs. incorrect, subjective perception:
       aware vs. unaware, remembered vs. forgotten items, parametric
       scores: e.g. fast vs. slow RTs
                                                                               P
   Measuring novelty: Rare or unpredictable events                       L
       e.g. oddball designs.                                         H
                                                                  A
                                                              K
   Allows to look at events on a shorter time scale.
But you can also combine block and efMRI…

A block can be treated as a continuous train of event-trials

   E.g Otten, Henson & Rugg, Nature Neuroscience 2002
‘Subsequent memory’ experiment separating transient (events) and
   sustained (blocks) neural activity.

At the beginning of each trial a cue instructed subjects to make an
   phonological or semantic judgement.




           83sec   rest   83sec
Hmmm I think I like efMRI.
 But how do I order my
        trials?
                            efMRI: Sequencing of events



Deterministic                                                            Stochastic
                                  10


                                  20




designs:                          30

                                                                         designs:
                                  40


                                  50


the occurrence of events          60                                     the occurrence of
is pre-determined e.g. a          70                                     an event depends
blocked design or                                                        on a a specified
                                                                         probability e.g.
                                  80




alternating design (all the                                              random or
                                       1    2   3   4    5   6   7   8




probabilities are zero or one )                                          permuted design
                                  Blocked                                Stochastic designs
                                                                         can be stationary or
                                                                         dynamic
                                           Alternating

                                                        Random
                                                             Permuted
 How do I do I create a permuted order of
                 events?
ensure mini-runs of same stimuli…
i.e. modulate the probability of different event-types over experimental time
Permutation methods continued…
So what is
Efficiency?
                       Efficiency is…
   Efficiency is a numerical value
    which reflects the ability of your design to detect the effect of
    interest

   General Linear Model:
                          Y      =            X       .     β          +    e
                          Data        Design Matrix       Parameters       error



   Efficiency is the ability to estimate β, given the design matrix X


   Efficiency can be calculated because the variance of β is proportional
    to the variance of X
               What is variance?

   Variance = Standard Deviation        2




Standard                    Standard
Deviation                   Deviation




            High Variance
                                        Low Variance
              Testing a Hypothesis
T- Test for the difference between 2 conditions


Standard                                       Standard
Deviation                                      Deviation




                                               Higher ability to detect a difference

        Lower ability to detect a difference

 •   By reducing the variance in the design we can maximize our T values
     How do we calculate it?

   Efficiency  Inverse( Var(β) )

   Inverse( Var(β) )  Var(X)

                        T
   Var(X)  Inverse( X X )
                                    T
    X               .           X                                                                             T
                                                                                                    =     X X
A   B   C   D   A   1   1   1   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
1   0   0   0   B   0   0   0   0   0   1   1   1   1   1   0   0   0   0   0   0   0   0   0   0         A   B   C D
1   0   0   0
1   0   0   0
                C
                D
                    0
                    0
                        0
                        0
                            0
                            0
                                0
                                0
                                    0
                                    0
                                        0
                                        0
                                            0
                                            0
                                                0
                                                0
                                                    0
                                                    0
                                                        0
                                                        0
                                                            0
                                                            0
                                                                0
                                                                0
                                                                    1
                                                                    0
                                                                        1
                                                                        1
                                                                            1
                                                                            1
                                                                                1
                                                                                1
                                                                                    1
                                                                                    1
                                                                                        0
                                                                                        1
                                                                                            0
                                                                                            0
                                                                                                0
                                                                                                0
                                                                                                        A 5   0   0 0
1   0   0   0                                                                                           B 0   5   0 0
1   0   0   0
0   1   0   0                                                                                           C 0   0   5 4
0   1   0   0                                                                                           D 0   0    4 5
0   1   0   0
0   1   0   0
0   1   0   0
0   0   0   0
0   0   0   0
0   0   1   0
0   0   1   1
0   0   1   1
0   0   1   1
0
0
    0
    0
        1
        0
            1
            1              Non-
0
0
    0
    0
        0
        0
            0
            0           overlapping
                         conditions




                                                                Overlapping
                                                                 conditions
                                  T
       T          inverse (X X)
      X X
  A   B    C D        A     B   C      D
A 5   0    0 0    A   0.2    0   0      0
B 0   5    0 0    B    0    0.2  0      0
C 0   0    5 4    C    0    0   0.6   -0.4
D 0   0     4 5   D    0     0 -0.4    0.6
    The efficiency is related to the specific
         contrast you are interested in

Efficiency = inverse(σ2 cT Inverse(XTX) c)

      Where c = contrast
            σ2 = noise variance

But if we assume that noise variance σ2 is constant then:



       Efficiency = inverse (cT Inverse (XTX) c)
Efficiency = Inverse( cT Inverse(XTX) c)
    When c is Simple Effect,
    e.g. main effect of A c = [1 0 0 0]
                                 T
        CT       inverse(X X)           C
        1        A     B   C      D     1000
        0    A   0.2    0   0      0
             B    0    0.2  0      0
        0    C    0    0   0.6   -0.4
        0    D    0     0 -0.4    0.6




A, B:        Efficiency = 1 / 0.2 = 5
C, D:        Efficiency = 1 / 0.6 = 1.7
Efficiency = Inverse( cT Inverse(XTX) c)
  When c is contrast difference,
  e.g. For A – B c = [1 -1 0 0]
                                T
    CT          inverse(X X)           C
     1          A     B   C      D     1 -1 0 0
    -1      A   0.2    0   0      0
            B    0    0.2  0      0
     0      C    0    0   0.6   -0.4
     0      D    0     0 -0.4    0.6




   A-B: Efficiency = 1 / 0.4 = 2.5
   C-D: Efficiency = 1 / 2 = 0.5
                  Variable No. of Trials
                                                                                     T
                       X                                                  inv(X X)
                                                      0.5


100
                                                       1

200
                                                      1.5
300

                                                       2
400


500                                                   2.5


600
                                                       3

700
                                                      3.5
800

                                                       4
900



  0.5   1   1.5    2       2.5    3   3.5   4   4.5   4.5
                                                        0.5   1     1.5    2   2.5       3    3.5   4   4.5




Random:                          Random:                          2.1                        4.2
Events =                         Events =
   25                                                         Relative Efficiency
                                    50
How does trial order effect
      Efficiency?
Example
                         Different Designs – Boxcar Events

                                                                      T
                     X                                    inv(X X)
  A   B C   D E F
  1   0 0    0 0 0                             A         B       C      D      E        F
  1   0 1    0 0 1
  1   0 0    0 0 1                        A    0.2488     0.0377 -0.0297 -0.0396   -0.0012   -0.0873
  1   0 0    1 0 0                        B    0.0377     0.2862 -0.0941 -0.0421   -0.0873   -0.0263
  1   0 0    0 0 0                        C   -0.0297    -0.0941 0.2871 0.0495     -0.0297   -0.0941
  0   1 1    0 0 0                        D   -0.0396    -0.0421 0.0495 0.2327     -0.0396   -0.0421
  0   1 0    0 0 0
  0   1 0    1 1 0                        E   -0.0012    -0.0873 -0.0297 -0.0396    0.2488    0.0377
  0   1 0    0 1 0                        F   -0.0873    -0.0263 -0.0941 -0.0421    0.0377    0.2862
  0   1 1    0 0 1
  0   0 0    0 0 0
  0   0 0    1 0 1
  0   0 0    0 1 0                               1

  0   0 1    0 1 0
  0   0 0    0 0 0
  0   0 0    1 0 0
                                                 2


  0   0 0    0 1 0
  0   0 1    0 0 0                               3

  0   0 0    0 0 1
  0   0 0    1 0 0
                                                 4




                                                 5




Blocked
                                                 6


                                                     1      2     3       4   5    6




     Fixed
  Interleaved
            Random
          Different Designs
                                                                     T
                                                           inv(X X)
                       X
                                           1

 10

                                           2
 20

                                           3
 30


                                           4
 40


 50                                        5



 60                                        6



 70                                        7


 80
                                           8

      1    2   3   4       5   6   7   8       1       2   3     4       5     6   7     8




Blocked
                                                   5
             Fixed
          Interleaved                                      1.5
                  Random-
                   Uniform                                                   2.8
                         Random-
                         Sinusoidal                                                    3.5
      Different Designs
                                                                                                                                                                                       T
                                                                                                                                                                                 inv(X X)
                                                         X
                                                                                                                                                             1
 10

                                                                                                                                                             2
 20


                                                                                                                                                             3
 30


                                                                                                                                                             4
 40



 50                                                                                                                                                          5



 60                                                                                                                                                          6



 70                                                                                                                                                          7



 80                                                                                                                                                          8


                                                                                                                                                                 1       2   3     4   5    6    7    8




Blocked
         1


       0.8


       0.6


       0.4


       0.2
                                                                                                                                                                     5
         0


       -0.2




                                                                                                                                                                             1.5
       -0.4


       -0.6


       -0.8


        -1
              0   5   10   15   20   25   30   35   40




                                                           1


                                                         0.8


                                                         0.6


                                                         0.4




                                                                                                                                                                                           2.8
                                                         0.2


                                                           0


                                                         -0.2


                                                         -0.4


                                                         -0.6


                                                         -0.8


                                                          -1
                                                                0   5   10   15   20   25   30   35   40




                                                                                                             1


                                                                                                           0.8


                                                                                                           0.6




                                                                                                                                                                                                     3.5
                                                                                                           0.4


                                                                                                           0.2


                                                                                                             0


                                                                                                           -0.2


                                                                                                           -0.4


                                                                                                           -0.6


                                                                                                           -0.8


                                                                                                            -1
                                                                                                                  0   5   10   15   20   25   30   35   40
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 pre-
             determined.


             The variable deterministic
             design i.e. a blocked design,
             is the most efficient.
  Joel’s example of different stimulus presentations
Tasks
AB C




                    Blocked
                                       Efficiency calculation
                    design
                                 100
                                  90
                                  80
                                  70
                                  60
                                  50
                    Fully         40
                                  30
                    randomised    20
                                  10
                                   0
                                       Block    Dynamic     Randomised
                                               stochastic

                    Dynamic
                    stochastic
                    {
                        minimum SOA (inter-stimulus interval)
different designs
                        probability of occurrence
How fast can I present my
          trials?
     max.                The absolute minimum…
     oxygenation: 4-
     6s post-stimulus
                                         Early event-related fMRI studies used a long Stimulus
                                          Onset Asynchrony (SOA) to allow BOLD response to
                                          return to baseline (20-30s).
                  Peak                   However, if the BOLD response is explicitly modelled,
                                          overlap between successive responses at short SOAs can
                                          be accommodated… (assuming that successive responses
  Brief                                   add up in a linear fashion)
Stimulus
                         Undershoot      The lower limit on SOAs is dictated by nonlinear interactions
                                          among events that can be though of as saturation phenomena or
                                          ‘‘refractoriness’’ at a neuronal or hemodynamic level.

                                         But, very short SOAs (< 1s) are not advisable as the
       Initial                            predicted additive effects upon the HRF of two closely
     Undershoot                           occurring stimuli break down.




 So you can have events occurring even every 1-2 sec!
 But think of psychological validity!
And how should my events
 be spaced? optimal SOA
                Choosing the best SOA
    Optimal SOA depends on:
    Probability of occurrence (design)
    Whether one is looking for evoked responses per
     se or differences in evoked responses.
Generally SOAs that are small and randomly distributed are the most efficient.


                                                            Random SOAs ensure
  Rapid presentation rates allow for the                     that preparatory or
  maintenance of a particular cognitive or                       anticipatory
  attentional set, decrease the latitude that the          factors do not confound
  subject has for engaging alternative                     event-related responses
  strategies, or incidental processing.                     and ensure a uniform
                                                           context in which events
                                                                are presented.
Stationary Stochastic designs                                    Main effect
                                                                 Differential responses


               ONE TRIAL TYPE                       TWO TRIAL TYPES



Probability




SOA




  the most efficient SOA for differential responses is very small.
  longer SOAs of around 16 s are necessary to estimate the responses themselves.
     What should I do if I am interested in
     the main effects (‘evoked responses’)?
        to identify areas that are activated by both event types



   You can use long SOA’s (around 16 secs!).
    But behaviourally this may be inefficient
   So you can introduce ‘null’ events and
    keep your SOA short.
   These null events now provide a baseline
    against which the response to either trial
    type 1 or 2 can be estimated even using a
    very small SOA. (p=0.5 0.3)
Here is what happens when you add null events…



                     Random




   Note that although null events increase efficiency for main effects (at
   short SOA’s), they slightly decrease efficiency for differential effects
What should I do if I am interested in the differential effects?
For very short SOA’s use a randomised design
But for medium SOA’s a permuted (4-6sec) or an alternating (8sec) design is better
    To sum up: Remember that…
   Blocked designs generally more efficient
   Some random event-related designs are much
    better than others.
   Different design is appropriate depending on
    what you want to optimize.

   Critical properties to optimize
       Ordering of trials
       spacing between stimuli
    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.
Scans               TR = 4s




Stimulus (synchronous)     SOA=8s




Stimulus (asynchronous)      SOA=6s




Stimulus (random jitter)
   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
   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 low-
    frequency, 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!!
Sources
                            Summary
   Blocked designs are generally the most efficient, but blocked
    designs have restrictions.
   For event-related designs, dynamic stochastic presentation of stimuli
    is most efficient.
   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.
   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.
   Finally, there is no point scanning two tasks to look for differences
    between them if they are too different or too similar.

				
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