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Subject:

Re: which interval to jitter in a rapid event-related design?

From:

G Elliott Wimmer <[log in to unmask]>

Reply-To:

G Elliott Wimmer <[log in to unmask]>

Date:

Wed, 15 Jul 2009 02:05:37 +0100

Content-Type:

text/plain

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text/plain (114 lines)

Hi Richard,

One important thing to keep in mind when finding optimal designs for HRF analysis of 
reward studies is that jittering events within a series of predicted reward events *itself 
induces prediction errors*.  Basically, the statistical gain of jittering the duration between 
a reward-predicting cue and the outcome seem to be overshadowed by the cost.  For 
example, consider a task where subjects learn that a cue signals a 50% probability that a 
reward will appear 4s later; if on a later trial, the reward appears after 10s instead, a 
negative reward prediction will occur at 4s because this is when the reward was actually 
expected.  If cue-reward latencies are jittered a lot of the time, these kind of temporal 
reward prediction errors will occur, even though blind deconvolution may be more 
optimal.

It might seem OK to jitter only by a few seconds between cue-reward events, avoiding 
bigger prediction error problems with large jitters as above.  However, various estimates 
put the jitter range necessary to temporally decompose the HRF - the range necessary to 
get any statistical benefit - at around 10s+.  While the timing accuracy of dopamine 
neurons in signaling reward prediction errors is not extremely precise (c.f. Fiorillo et al. 
2008), random unexpected delays of 0-10s might nevertheless be expected to have 
effects.

As a prominent example, McClure et al. 2003, a member of the first pair of fMRI papers 
on reward prediction errors, induced prediction errors solely by jittering the time between 
the cue and the reward, and only by 4s (this is also why so-called 'catch' trials, where 
parts of trials are skipped in order to get better deconvolution, are rarely if ever 
employed in fMRI studies of reward).

These points may not be totally conclusive, however, as in your case few if any fMRI 
studies of reward prediction errors have systematically made reward timing unpredictable 
from task onset.  (Although some studies have jittered price revelation in decision tasks.)

But if cue and reward prediction errors are orthogonal anyway there remains no benefit 
to jittering the cue-reward duration.  This also gets at your point about possible 
correlations between card onset (cue) and outcome (reward) prediction errors.  In fact, 
prediction errors at cue onset and reward outcome will on average equal zero.  This is 
just a result of the reinforcement learning algorithm learning to make accurate 
predictions about the environment (for a bare bones example, imagine a game where 
predictions are made about reward points deterministically associated with particular 
stimuli: for the 100-point stim, stim onset gives a prediction error of +100 and reward 
outcome (of 100) gives an error of 0; for a 50-point stim, onset error is +50, outcome 
error is 0, etc; this generalizes to the probabilistic case).  Thus, deconvolving the BOLD 
signal between card onset and outcome onset should not be corrupted by correlations 
between these signals (though a constant 2s+ between trial events seems necessary just 
from a psychological point of view.

Finally, on the SOA (or ITI, between-trials) jitter, I would suggest using a jitter.  From a 
purely statistical point of view, as noted earlier, jitter doesn't help deconvolution if trials 
are uncorrelated.  However, neurally, a regular (e.g. 2s) interval between every trial will 
nevertheless also induce temporal predictions about the upcoming trial as the brain learns 
the periodicity.  These prediction effects could pollute measurements of signals of interest 
(e.g. a regular "carrier" periodicity may exist in the BOLD signal related to this 
expectancy, a signal I've observed in studies myself).  Also c.f. Sirotin and Das, Nature 
2009 on anticipatory BOLD signals.


On Thu, 9 Jul 2009 16:30:09 +1000, Richard Morris <[log in to unmask]> wrote:

>Dear fMRI gurus,
>
>I'm interested in designing an experiment examining reward-related
>positive and negative prediction errors in the striatum. But as a
>relative newbie I need some help with a rapid event-related design.
>The basic problem is I don't know which intervals in my task I need to
>vary or jitter and which intervals can remain fixed.
>
>The task consists of a series of trials in which participants are
>presented with a hand of cards and must learn to predict whether it is
>a winning hand or not. Thus, they are presented with cards and they
>make a prediction (win or lose) and then they are told whether the
>cards won or lost that hand (the outcome). So there are at least two
>intervals which can be varied: an interval between trials (SOA?) and
>an interval between card presentation and outcome (ISI).
>
>I'm primarily interested in activity during the outcome. My hypothesis
>is that when a win is unexpected, the outcome should evoke more
>activity (in the striatum) relative to when the win is expected
>(correctly predicted). Conversely, when a loss is unexpected, the
>outcome should evoke less activity than an expected loss.
>
>As I understand it, if the interval between trials or the cards and
>the outcome is too short (e.g., < 14 seconds), then the BOLD signal
>from the outcome must be deconvolved from any BOLD signal which still
>persists from earlier stimulus presentations (e.g., the cards
>presentation). To assist with this, experimenters typically jitter the
>SOA and this is the point I need some guidance on.
>
>Which interval do I need to jitter? Is it the interval between cards
>and outcome (the ISI) or the interval between trials (the ITI)?
>
>Furthermore, I'm not sure that it will be easy to deconvolve the BOLD
>signal during the outcome from any BOLD that is still persisting from
>the immediately preceding card presentation. I think the BOLD signal
>to the card presentation will be opposite to the BOLD evoked by the
>outcome, and so any differences between expected and unexpected
>outcomes will be masked or obscured. In particular, the cards which
>precede an unexpected win are likely to evoke a small BOLD signal
>(while the outcome will evoke a large BOLD signal) and conversely, the
>cards which precede an expected win are likely to evoke a large BOLD
>signal (while the outcome evokes a small BOLD signal). Thus, the
>hypothesized difference in BOLD evoked by expected and unexpected wins
>(expected < unexpected) will be reduced by the persisting (and
>opposite) differences produced by the card presentation (expected >
>unexpected).
>
>I believe the same problem exists for unexpected and expected losses
>for similar reasons, but I'll spare you the details right now.
>
>Thanks so much for reading this far and I really appreciate any help
>or guidance you can provide.
>
>All the best,
>
>Rich.

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