Once again, I find myself agreeing with Roberto's post below. In
response to Stephen's comment:
> "If we clearly state that the inference is limited by the apriori
> assumption/condition that we made, then we shouldn't have a problem."
>
> Yes, one can make the inference valid in such a manner as you suggest.
> But I don't think people do that.
I empathise with this, but can only say that there are many things
that neuroimaging researchers don't do that they should, or things
they do that they shouldn't. We need to be careful not to propose
inflexible statistical rules simply to mitigate the effects of
careless or uninformed scientific practice in either the production or
digestion of research publications, which is a mistake I think has
been made in much of traditional psychology. On this point I agree
with Roberto:
> I would argue that conditionality is the appropriate concept here, since it
> requires one to make assumptions explicit.
Even when using anatomically-defined ROIs or functional ROIs defined
on the basis of independent tasks or data, there are always
assumptions upon which the inferences rest, and which are often not
made explicit. For example, the use of an independent "localiser" task
to define a functional ROI makes an assumption of stationarity. The
term "independent" is also often mis-used in this context, in the
sense that a localiser performed by the same subject or group of
subjects is not truly independent. How "independent" then does a
localiser have to be?
The condition of orthogonality seems to me not entirely clear. Is it
the contrast vectors that need to be orthorgonal, or the contrast
estimates themselves? e.g. In my example of a face and dot
presentation task, my functional ROI might be determined using:
angry faces: 0.5
happy faces: 0.5
dots: -1
whereas my final contrast of interest is:
angry faces: 1
happy faces: -1
dots: 0
These two contrast vectors are orthogonal. But if the first contrast
is driven exclusively by angry faces producing high activation and
dots and faces producing little activation, is the ROI defined on that
basis truly orthogonal to the contrast being tested? Because in the
extreme case, it would seem to collapse to the situation in which the
mask used to restrict the search space wholly corresponds to the
contrast being tested. Would a more appropriate approach using my
example be to define a functional ROI based on a conjunction of
angry-dots and happy-dots contrasts?
-Tom
> I believe that Doug Burman raises an important point regarding orthogonality
> of contrasts. Assuming a normal distribution of the errors, then it is
> indeed the case that the two inferences are independent, since the
> underlying test statistics are independent. It is not an unusual case: the
> individual differences example I made in my original post is another example
> of such a pair of orthogonal contrasts.
>
> The distinction between dependent and independent variables (the point
> raised from Stephen in the latest post) is not so clear-cut when we are
> dealing with testing families, but this a rather involved issue. Voxel-level
> corrected significance values, the gold standard of inference in
> neuroimaging, are defined conditionally on the subset of voxels where the
> null hypothesis holds. Thus, they are conditional on a quality of the
> dependent variable (what Stephen finds objectionable). Having said this, the
> SPM strategy of using random fields to derive the rejection region always
> assumes the worst case that the null holds over the whole volume, so that
> the conditionality is no longer present. However, the whole literature on
> repeated testing and strong control (such as the relevant parts of Hochberg
> and Tamhane's book) thrives on the opportunity offered by this type of
> conditionality on the dependent variable (through multi-step testing), which
> shows that many statisticians find it ok. In the functional ROI case, we do
> the same thing: prune the testing family on the basis of properties of the
> dependent variable.
>
> It seems that Stephen needs a test which the conditionality does not include
> the selection of the subjects on which the second test is carried out.
> That's fine, it's quite possible that this may be needed for some specific
> problem. I suspect that the formal definition of the inferential differences
> that he lists in his latest post would be a challenging task. Be it as it
> may, I find the functional ROI definition for pairs of orthogonal contrasts
> logically clear and unobjectionable in the appropriate context.
>
> Stepwise regression (which isn't the same as multi-step tests) has the
> purpose of modelling the data, not generating valid p values, so is misused
> in the example of Stephen's post. (It makes a difference, though, if you are
> selecting on the nuisance covariates only). To obtain valid p values here,
> you need to include all considered models in a testing family, and derive
> the appropriate correction.
>
> Cheers,
> Roberto
>
> Quoting "Fromm, Stephen (NIH/NIMH) [C]" <[log in to unmask]>:
>
>> " 'In regions showing greater activation for angry and happy faces than
>> for dots, we found angry faces to produce greater activation than happy
>> faces'. This would be fine I think."
>>
>> I don't think this example gets at the full story, because the statement
>> could refer to inferences using two independent sets of functional data
>> to define regions; using the same set of data; or using a priori
>> anatomical regions. Of course, one could claim it's clear from context
>> in a given publication, but readers will typically unconsciously extend
>> the inference from the case at hand (dependent data) to the "stronger"
>> case (independent data). Furthermore, putting aside cases where e.g.
>> orthogonality obtains (as raised by Doug Burman), it's not at all
>> obvious what the implications of the inference from dependent data are
>> for the truly unbiased inference from independent data. And the latter
>> is really what we're after.
>>
>> Note that I'm by no means claiming that your suggestion (or more
>> generally the use of functionally defined regions) is at odds with
>> standard accepted practice in the neuroimaging community.
>>
>> Cheers
>>
>> -----Original Message-----
>> From: Tom Johnstone [mailto:[log in to unmask]]
>> Sent: Thursday, October 02, 2008 9:25 AM
>> To: Fromm, Stephen (NIH/NIMH) [C]
>> Cc: [log in to unmask]
>> Subject: Re: [SPM] Multi-masking for Multiple Comparison Correction
>>
>> I'm actually with Roberto on this one. In all these cases, we're using
>> inferential statistics. The validity of the *inference* that we make
>> based upon the statistics is the important thing in this case. If we
>> clearly state that the inference is limited by the apriori
>> assumption/condition that we made, then we shouldn't have a problem.
>>
>> Take the trivial case of a functionally defined mask based on a
>> contrast A that is used to mask the same contrast, as mentioned by
>> Stephen. Obviously the inference "in this region of the brain, A was
>> significant" would be non-valid. But if instead we made the inference
>> "in regions of the brain where A was significant we were able to show
>> that A was significant" we would be absolutely fine, statistically and
>> inferentially speaking, though a reviewer would question our sanity in
>> finding it worthwhile to report.
>>
>> A more realistic example: I perform a study in which I show people
>> angry and happy faces and black dots. I define a contrast face-dot and
>> find regions of the brain showing this effect. I use those regions as
>> a functionally-defined ROI and test the angry-happy contrast. What
>> inferences can I make? "In regions showing greater activation for
>> angry and happy faces than for dots, we found angry faces to produce
>> greater activation than happy faces". This would be fine I think. But
>> it would be wrong to drop the first part of that statement.
>>
>> -Tom
>>
>> On Thu, Oct 2, 2008 at 1:56 PM, Fromm, Stephen (NIH/NIMH) [C]
>> <[log in to unmask]> wrote:
>>>
>>> Roberto,
>>>
>>> Sorry if this isn't addressing your points; the original poster's
>>> question was a little unclear to me, because I wasn't 100% sure what
>>
>> she
>>>
>>> meant by "multi-masking."
>>>
>>> All I mean is that if you use a mask defined by the same functional
>>
>> data
>>>
>>> that you're applying the mask to, the significance will possibly be
>>> inflated.
>>>
>>> As for definitions, an example which is somewhat conceptually related
>>
>> is
>>>
>>> stepwise regression. The paper at
>>> http://publish.uwo.ca/~harshman/ssc2006a.pdf
>>> states, "When model modifications are selected using post-hoc
>>> information (e.g., in stepwise regression) standard estimates of
>>> p-values become biased." Ultimately, I think my use of "bias" here is
>>> correct, based on definitions given at Wikipedia.
>>>
>>> So, what I'm saying here is that the use of a functionally defined
>>
>> mask
>>>
>>> can lead to corrected p-values which are likely to be too small. The
>>> simplest example is using a contrast to mask itself. The uncorrected
>>> p-values are obviously unaffected by this procedure. And the
>>
>> corrected
>>>
>>> p-values are obviously decreased.
>>>
>>> My comment "the mathematics dictates that there is no bias": I mean
>>> that I assume that there are situations where there's enough
>>> independence (e.g, perhaps between the masking contrast and the
>>
>> contrast
>>>
>>> you're masking) that the bias either doesn't exist or is probably
>>> negligible, but I haven't had time to think up rigorous examples.
>>>
>>> Best regards,
>>>
>>> S
>>>
>>> -----Original Message-----
>>> From: [log in to unmask] [mailto:[log in to unmask]]
>>> Sent: Thursday, October 02, 2008 8:16 AM
>>> To: Fromm, Stephen (NIH/NIMH) [C]
>>> Cc: [log in to unmask]
>>> Subject: Re: Multi-masking for Multiple Comparison Correction
>>>
>>> Could you be more specific? I can't see what you mean by "the
>>> mathematics dictates that there is no bias". It's important to avoid
>>> misunderstandings about the terminology: bias is a technical term,
>>> defined on the power function of the test, and does not mean just
>>> wrong in some way. You should be sure that when you mention bias you
>>> do not mean "conditional on the functional data", as I mentioned in my
>>> mail.
>>>
>>> R.V.
>>>
>>> <snip>
>>>>
>>>> Except in certain circumstances, where you could show that the
>>>
>>> mathematics
>>>>
>>>> dictates that there's no bias, defining regions based on the
>>>
>>> functional data
>>>>
>>>> itself can definitely bias results, regardless of whether the
>>>> contrast is defined
>>>> a priori.
>>>>
>>>> Perhaps one can argue that the bias is slight; and it's certainly
>>>
>>> common
>>>>
>>>> practice in the neuroimaging community. But, again, procedures that
>>>
>>> look to
>>>>
>>>> the data can lead to bias.
>>>>
>>>> Of course, if one uses separately acquired data to create the
>>>
>>> contrast-
>>>>
>>>> defined ROI, that's a different matter.
>>>>
>>>>> In some specific instance, using the mask approach follows a clear
>>>>> substantive logic. For example, if you are investigating individual
>>>>> differences in cognitive capacity, you may be justified in carrying
>>>>> out a contrast first, and then look at how individual differences
>>>>> modulate the activation say, in prefrontal and parietal areas.
>>>>>
>>>>> You do have to pay for the increased power (if the procedure is
>>>
>>> really
>>>>>
>>>>> a priori), the price being that you potentially miss an effect in
>>
>> the
>>>>>
>>>>> voxels outside the mask.
>>>>>
>>>>> I do not see any simple way in which the concept of bias relates to
>>>>> this specific situation; I'd rather say that these tests are
>>>>> conditional on the a priori criterion. If the criterion is not a
>>>>> priori, they have wrong significance values (too small), with
>>>
>>> inflated
>>>>>
>>>>> type I errors.
>>>>>
>>>>> When you use a cluster approach, you also have to specify a priori a
>>>>> cluster definition threshold. Your p values are conditional on this
>>>>> threshold. If you try several thresholds, your test will have wrong
>>
>> p
>>>>>
>>>>> values.
>>>>>
>>>>> All the best,
>>>>> Roberto Viviani
>>>>> University of Ulm, Germany
>>>>>
>>>>> Quoting Amy Clements <[log in to unmask]>:
>>>>>
>>>>>> Dear Experts,
>>>>>>
>>>>>> I am pretty far away from having statistical expertise, which is
>>
>> why
>>>>>>
>>>>>> I am posing my question to the group. Recently, I have seen a
>>>>>> multitude of papers that are using a multi-masking approach to deal
>>>>>> with corrections for multiple comparisons (using main effect or
>>>>>> other effects of interest contrasts masks). While on the surface
>>>>>> this appears to seem like an optimal approach because you are
>>>>>> restricting the number of voxels included in the multiple
>>>>>> comparison, it seems like an opportunity for biasing the data and
>>>>>> obtained results--especially if you are not masking the data based
>>>>>> from a priori hypotheses (e.g., using a previously defined
>>>>>> functional ROI mask because you're interested in face processing).
>>>>>>
>>>>>> I'm not sure that I've articulated this is the best way. It seems,
>>>>>> like I mentioned previously, to have the potential to bias results,
>>>>>> but would greatly appreciate feedback. The questions typically
>>>>>> asked from the lab that I've worked in have been better suited to
>>>>>> utilizing a cluster-based approach; however, could also be served
>>
>> by
>>>>>>
>>>>>> multi-masking.
>>>>>>
>>>>>> Thanks!
>>>>>>
>>>>>>
>>>>>> Amy Stephens
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
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>>>>>>
>>>>
>>>>
>>>>
>>>
>>
>>
>>
>> --
>> School of Psychology and CLS
>> University of Reading
>> 3 Earley Gate, Whiteknights
>> Reading RG6 6AL, UK
>> Ph. +44 (0)118 378 7530
>> [log in to unmask]
>> http://www.personal.reading.ac.uk/~sxs07itj/index.html
>> http://beclab.org.uk/
>>
>
--
School of Psychology and CLS
University of Reading
3 Earley Gate, Whiteknights
Reading RG6 6AL, UK
Ph. +44 (0)118 378 7530
[log in to unmask]
http://www.personal.reading.ac.uk/~sxs07itj/index.html
http://beclab.org.uk/
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