Multiple testing via FDRL for large-scale imaging data

Abstract

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 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 FDRL, to accommodate the spatial information of neighboring p-values, via a local aggregation of p-values. Theoretical properties of the FDRL procedure are investigated under weak dependence of p-values. It is shown that the FDRL procedure alleviates the LIP of the FDR procedure, thus substantially facilitating the selection of more stringent control levels. Simulation evaluations indicate that the FDRL procedure improves the detection sensitivity of the FDR procedure with little loss in detection specificity. The computational simplicity and detection effectiveness of the FDRL procedure are illustrated through a real brain fMRI dataset.

Multiple testing under dependence via graphical models

“…Despite FDR-control challanges, dependence also brings opportunities for decreasing FNR. This efficiency issue has been investigated (Yekutieli & Benjamini, 1999; Genovese et al, 2006; Benjamini & Heller, 2007; Zhang et al, 2011), indicating FNR could be decreased by leveraging the dependence among hypotheses. Several approaches have been proposed, such as dependence kernels (Leek & Storey, 2008), factor models (Friguet et al, 2009) and principal factor approximation (Fan et al, 2012).…”

Local tests for identifying anisotropic diffusion areas in human brain with DTI

“…Since in a real DTI data set, the number of voxels, each of which corresponds to a hypothesis test, is typically large, false discovery rate (FDR) techniques [Benjamini and Hochberg (1995), Storey (2002), Storey, Taylor and Siegmund (2004), Zhang, Fan and Yu (2011)] are incorporated in our numerical works to control the error rates. Two FDR procedures are employed in our study, namely, the conventional FDR procedure by Storey (2002) and the FDR L procedure by Zhang, Fan and Yu (2011), which is capable of capturing the spatial information in imaging data.…”

“…Let { T 1 , …, T N } be the set of statistics for all voxels over the entire brain, where T v for any voxel v ∈ {1, …, N } is the FA or Smooth-FA value, if the FA-threshold or Smooth-FA-threshold approach is used; is the p -value based on , if the -FDR approach is used; is the p̃ -value if the -FDR L approach is used, where p̃ stands for the median smoothed p-value of [Zhang, Fan and Yu (2011)]. For any given threshold t , if we classify a voxel v as anisotropic based on T v ∈ R ( t ), where R ( t ) = { T v : T v ≥ t , v = 1, …, N } when T v is the FA or Smooth-FA value; R ( t ) = { T v : T v ≤ t , v = 1, …, N } when T v is the p - or p̃ -value, then,…”

Towards Better FDR Procedures for Discrete Test Statistics

“…(See Storey et al (2004) for a variant of S ( ) and of \ F DR (t), whose potential erroneous behavior is discussed in Chen and Doerge (2012).) However, it should be noted that \ F DR (t) may display the so-called "lack of identi…ability phenomenon" (LIP) found by Zhang et al (2011), in the sense that for m given p-values, the minimal achievable level of the estimated FDR, \ F DR (t), in t for a …xed S ( ) is greater than , i.e.,…”