Summary: 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 false discovery rate (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 FDR procedure.
This paper first introduces a scalar quantity to characterize the extent to which the “lack of identification phenomenon” (LIP) of the FDR procedure occurs. Second, we propose a new multiple comparison procedure, called FDR\(_L\), to accommodate the spatial information of neighboring \(p\)-values, via a local aggregation of \(p\)-values. Theoretical properties of the FDR\(_L\) procedure are investigated under weak dependence of \(p\)-values. It is shown that the FDR\(_L\) procedure alleviates the LIP of the FDR procedure, thus substantially facilitating the selection of more stringent control levels. Simulation evaluations indicate that the FDR\(_L\) procedure improves the detection sensitivity of the FDR procedure with little loss in detection specificity. The computational simplicity and detection effectiveness of the FDR\(_L\) procedure are illustrated through a real brain fMRI dataset.