To Block or Not to Block

1
To Block or Not to
Block?
A few notes on design optimization

• Tor D. Wager
• Columbia University

2
Five Guidelines for fMRI Design

• Scan as many subjects as possible scan as long
  as you can, considering psychological effects
  (fatigue, habituation)
• Use short blocks (lt 40 s) if you care about
  detecting differences, and event-related designs
  if you want to link activity to particular
  events.
• Limit the number of conditions pairwise
  comparisons far apart in time decrease power and
  overlap with low-frequency noise
• In event-related designs, randomize (or
  pseudo-randomize) the ordering of events that are
  close together in time
• Randomize (jitter) intervals between events
  that need to be distinguished (decorrelate their
  predicted signals after HRF convolution)

3
Design Efficiency

• To minimize standard error

Efficiency

• Efficient designs
• Maximize variance of predictors
• Minimize covariance among predictors (orthogonal
  predictors)
• In fMRI designs, formula is more complex,
  principle is the same

• What is it?
• A-optimality

4
Design efficiency in fMRI

• Formula is more complex, principle is the same
• Factor in contrasts, filtering and
  autocorrelation
• We care about the variance of a contrast

5
Design efficiency in fMRI

• Formula is more complex, principle is the same
• Factor in filtering
• Define high-pass filtering matrix K
• Filtered design matrix Z

6
Design efficiency in fMRI

• Formula is more complex, principle is the same
• Factor in autocorrelation
• Define autocorrelation matrix V

We use this. In SCNlab toolbox calcEfficiency.m

• Not equal to power, but can be converted to power
  given effect sizes

See Friston et al., 2000 Zarahn, 2001
7
Design efficiency

• Maximize variance of predictors
• Equal numbers across different trial types
• Create large manipulations Concentrate on
  extremes
• Keep designs simple (not too many event types)
• Appropriate trial ordering and spacing (more on
  this soon)
• And, always, try to create a large psychological
  effect!
• Doesnt affect predictor variance per se, whose
  scaling is arbitrary
• Does affect the magnitude of the effect relative
  to error

8
Predictor variance depends on the HRF shape and
the time on task.
Designs that are too sparse or too packed with
stimulation are non-optimal.
The maximum variance design is the one in which
stimulation perfectly matches the major frequency
of the HRF.
9
Fixed SOA 16s
Stimulus (Neural)
HRF
Predicted Data
?

Not particularly efficient
10
Fixed SOA 4s
Stimulus (Neural)
HRF
Predicted Data
Note There is little to distinguish this
predictor from the intercept, which is sensitive
to mean scanner signal
Very Inefficient
11
Randomised, SOAmin 4s
Stimulus (Neural)
HRF
Predicted Data
More Efficient
12
Maximum variance design

• For one predictor, and if the HRF shape is
  correct!

Stimulus (Neural)
HRF
Predicted Data
Sine wave, 1/33 s
13
The HRF is a low-pass (smoothing) filter
It interacts with the frequency of stimulation
The stimulation frequency and HRF shape jointly
determine predictor variance.
14
fMRI designs Block length matters
Rise and fall High predictor variance means
efficient design
15
High-pass filtering removes variance from both
the noise and the predictors
The optimal level of high-pass filtering depends
on the stimulation frequency, the noise variance
and autocorrelation, and the HRF
16
Why not use really long blocks?and effects of
high-pass filtering

• Overlap with 1/f noise
• High-pass filter reduces noise
• But removes low frequencies from design and data
• Its effects

• Reduces efficiency

17
Effects of filtering on efficiency
18 s blocks, 80 s filter
Filtering reduces efficiency But youre
removing noise, too! If the noise reduction is
great, its worth it
18
Design with multiple contrasts in mind

• There is a tradeoff between contrast dectection
  power and HRF estimation power (Liu, 2001 Wager
  Nichols, 2003, others)
• Amounts to tradeoff between creating large
  predicted variations in signal and linking
  activity precisely to specific events
• What if I care about both? Or I have multiple
  contrasts that I care about?
• Computer-aided design can help.

19

• There is a tradeoff between high detection power
  (block design is good) and high HRF estimation
  power (event-related design is good).
• Genetic algorithm and other computer-aided
  designs, or mixed block/ER designs (T. Liu), can
  do better than random ER designs on both
  detection and estimation

20
Design efficiency

• Computer-aided design
• Genetic algorithm (Wager Nichols see website
  below)
• OptSeq (Doug Greve)
• M-sequence program (Buracas).
• Genetic algorithm
• Rapid convergence on optimal designs
• Can optimize across multiple contrasts
• User can specify the relative importance of each
  contrast
• Account for high-pass filtering and
  autocorrelation
• Account for nonlinearity (simple model)
• Can optimize for combination of detection power,
  HRF estimation power, and counterbalancing

21
Comparing efficiency for different design types

• Block best for detection
• M-sequence best for shape (Buracas et al.)
• Event-related designs so-so on both
• Optimized designs good tradeoff

Block, 16 s on/off
Theoretical limit
Optimized (GA)
Contrast detection power
Event-related
m-sequences
HRF shape estimation power
22
A design scheme I like

• Event-related for psychological specificity
• Pseudorandomized trial types (using genetic
  algorithm)
• Balance detection power for A - B contrast and
  HRF shape estimation
• Minimum of 4 s between events to prevent
  nonlinear weirdness

23
Summary

• Five psychological considerations
• Stimulus predictability
• Time on task
• Participant strategy
• Temporal precision of psychological manipulations
• Unintended psychological activity

• Three analysis considerations
• Statistical efficiency Power to detect results
• Effects of filtering, autocorrelation, and
  nonlinearity
• Choice of hemodynamic response model

24
Thank you!

• Download the Genetic Algorithm toolbox at
• http//www.columbia.edu/cu/psychology/tor/

25
Design efficiency in fMRI

• Formula is more complex, principle is the same
• Factor in contrasts, filtering and
  autocorrelation
• Define filtering matrix K, autocorrelation
  matrix V
• Matrix whose rows contain a set of contrasts C
• filtered design matrix Z
• Z- pseudoinverse of Z inv(ZZ)Z

• Not equal to power, but can be converted to power
  given effect sizes

See Friston et al., 2000 Zarahn, 2001
26
Nonlinearity in BOLD signal
27
Pros and cons of blocking

• High power, if parameters chosen correctly
• Simple to implement
• Relatively robust to changes in HRF shape
• - Predictable events may change task strategy and
  activity patterns
• - Cannot infer activity related to specific
  psychological events
• - Power limited if Ss are not doing cognitive
  operation of interest throughout blocks