Conjunction revisited. NeuroImage

The Wellcome Department of Imaging Neuroscience and Institute of Cognitive Neuroscience, University College London, 17 Queen Square, London, WC1N 3AR, UK.
NeuroImage (Impact Factor: 6.36). 04/2005; 25(3):661-7. DOI: 10.1016/j.neuroimage.2005.01.013
Source: PubMed


The aim of this note is to revisit the analysis of conjunctions in imaging data. We review some conceptual issues that have emerged from recent discussion (Nichols, T., Brett, M., Andersson, J., Wager, T., Poline, J.-B., 2004. Valid Conjunction Inference with the Minimum Statistic.) and reformulate the conjunction of null hypotheses as a conjunction of k or more effects. Analyses based on minimum statistics have typically used the null hypothesis that k = 0. This enables inferences about one or more effects (k > 0). However, this does not provide control over false-positive rates (FPR) for inferences about a conjunction of k = n effects, over n tests. This is the key point made by Nichols et al., who suggest a procedure based on supremum P values that provides an upper bound on FPR for k = n. Although valid, this is a very conservative procedure, particularly in the context of multiple comparisons. We suggest that an inference on a conjunction of k = n effects is generally unnecessary and distinguish between congruent contrasts that test for the same treatment and incongruent contrasts of the sort used in cognitive conjunctions. For congruent contrasts, the usual inference, k > 0, is sufficient. With incongruent contrasts it is sufficient to infer a conjunction of k >u effects, where u is the number of contrasts that share some uninteresting effect. The issues highlighted by Nichols et al., have important implications for the design and analysis of cognitive conjunction studies and have motivated a change to the SPM software, that affords a test for the more general hypothesis k >u. This more general conjunction test is described.

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Available from: Daniel E Glaser, Oct 02, 2015
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    • "reas specifically involved in coding peripersonal and extrapersonal space , using the following contrasts : ( WN - WO ) ∩ ( ON - OO ) and ( WO - WN ) ∩ ( OO - ON ) , respectively ( Friston et al . , 1999 ) . To this aim , we performed an SPM ' conjunction null ' analysis ( Nichols et al . , 2005 ) . Given the conservative nature of this analysis ( Friston et al . , 2005 ) , we report data with a p - value < 0 . 001 uncorrected . A threshold of 10 was applied on cluster dimension . For all analyses , location of the activation foci was determined in the stereotaxic space of the MNI coordinates system . Those cerebral regions for which maps are provided were also localized with reference to cytoarchitect"
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    Behavioural neurology 09/2015; · 1.45 Impact Factor
    • "Therefore , we performed a conjunction analysis using statistical parametric maps (SPMs) of the minimum T-statistic over the previous contrasts (im-TOM vs. im-NONTOM and ex- TOM vs. ex-NONTOM). Inference was based on P-values adjusted for the search volume using random field theory [for details on the exact procedure see Friston et al., 2005]. The SPM8 algorithm for conjunction (testing the conjunction null hypothesis as recommended in Nichols et al. [2005]) assumes that the P-value of the conjunction is the square root of the P-value of the involved contrasts. "
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    Human Brain Mapping 09/2015; DOI:10.1002/hbm.22907 · 5.97 Impact Factor
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    • "A compromise is to require evidence that at least r out of n null hypotheses are false, for some user specified r. Such tests of the 'partial conjunction null hypothesis' were used in Friston et al. (2005) and then studied by Benjamini and Heller (2008). The extremes r = 1 and r = n correspond to the usual metaanalysis tests and conjunction testing respectively. "
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    ABSTRACT: Admissibility of meta-analysis has been well understood since Allan Birnbaum's work in the 1950s. Any valid combined p-value obeying a monotonicity constraint is optimal at some alternative and hence admissible. In an exponential family context, the admissible tests reduce to those with a convex acceptance region. The partial conjunction null hypothesis is that at most r - 1 of n independent component hypotheses are non-null with r = 1 corresponding to a usual meta-analysis. Benjamini and Heller (2008) provide a valid test for this null by ignoring the r - 1 smallest p-values and applying a valid meta-analysis p-value to the remaining n - r + 1 p-values. We provide sufficient conditions for the admissibility of their test among monotone tests. A generalization of their test also provides admissible monotone tests and we show that admissible monotone tests are necessarily of that generalized form. If one does not require monotonicity then their test is no longer admissible, but the dominating tests are too unreasonable to be used in practice.
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