Multiple testing via $FDR_L$ for large-scale imaging data

Details Multiple testing via $FDR_L$ for large-scale imaging data Multiple testing via $FDR_L$ for large-scale imaging data

2011-03-10

arxiv.org/abs/1103.1966v1

Annals of Statistics 2011, Vol. 39, No. 1, 613-642

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS848 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS848

The multiple testing procedure plays an important role in detecting the presence of spatial signals for large-scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional $\operatorname {FDR}$ procedure can lack the ability to detect statistical significance, even if the $p$-values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the $\operatorname {FDR}$ procedure. This paper first introduces a scalar quantity to characterize the extent to which the "lack of identification phenomenon" ($\operatorname {LIP}$) of the $\operatorname {FDR}$ procedure occurs. Second, we propose a new multiple comparison procedure, called $\operatorname {FDR}_L$, to accommodate the spatial information of neighboring $p$-values, via a local aggregation of $p$-values. Theoretical properties of the $\operatorname {FDR}_L$ procedure are investigated under weak dependence of $p$-values. It is shown that the $\operatorname {FDR}_L$ procedure alleviates the $\operatorname {LIP}$ of the $\operatorname {FDR}$ procedure, thus substantially facilitating the selection of more stringent control levels. Simulation evaluations indicate that the $\operatorname {FDR}_L$ procedure improves the detection sensitivity of the $\operatorname {FDR}$ procedure with little loss in detection specificity. The computational simplicity and detection effectiveness of the $\operatorname {FDR}_L$ procedure are illustrated through a real brain fMRI dataset.

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