Faster Family-wise Error Control for Neuroimaging with a Parametric Bootstrap

In neuroimaging, hundreds to hundreds of thousands of tests are performed across a set of brain regions or all locations in an image. Recent studies have shown that the most common family-wise error (FWE) controlling procedures in imaging, which rely on classical mathematical inequalities or Gaussian random field theory, yield FWE rates that are far from the nominal level. Depending on the approach used, the FWER can be exceedingly small or grossly inflated. Given the widespread use of neuroimaging as a tool for understanding neurological and psychiatric disorders, it is imperative that reliable multiple testing procedures are available. To our knowledge, only permutation joint testing procedures have been shown to reliably control the FWER at the nominal level. However, these procedures are computationally intensive due to the increasingly available large sample sizes and dimensionality of the images, and analyses can take days to complete. Here, we develop a parametric bootstrap joint testing procedure. The parametric bootstrap procedure works directly with the test statistics, which leads to much faster estimation of adjusted \emph{p}-values than resampling-based procedures while reliably controlling the FWER in sample sizes available in many neuroimaging studies. We demonstrate that the procedure controls the FWER in finite samples using simulations, and present region- and voxel-wise analyses to test for sex differences in developmental trajectories of cerebral blood flow

A statistical framework for testing functional categories in microarray data

Ready access to emerging databases of gene annotation and functional pathways has shifted assessments of differential expression in DNA microarray studies from single genes to groups of genes with shared biological function. This paper takes a critical look at existing methods for assessing the differential expression of a group of genes (functional category), and provides some suggestions for improved performance. We begin by presenting a general framework, in which the set of genes in a functional category is compared to the complementary set of genes on the array. The framework includes tests for overrepresentation of a category within a list of significant genes, and methods that consider continuous measures of differential expression. Existing tests are divided into two classes. Class 1 tests assume gene-specific measures of differential expression are independent, despite overwhelming evidence of positive correlation. Analytic and simulated results are presented that demonstrate Class 1 tests are strongly anti-conservative in practice. Class 2 tests account for gene correlation, typically through array permutation that by construction has proper Type I error control for the induced null. However, both Class 1 and Class 2 tests use a null hypothesis that all genes have the same degree of differential expression. We introduce a more sensible and general (Class 3) null under which the profile of differential expression is the same within the category and complement. Under this broader null, Class 2 tests are shown to be conservative. We propose standard bootstrap methods for testing against the Class 3 null and demonstrate they provide valid Type I error control and more power than array permutation in simulated datasets and real microarray experiments.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS146 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Accelerating Permutation Testing in Voxel-wise Analysis through Subspace Tracking: A new plugin for SnPM

Permutation testing is a non-parametric method for obtaining the max null distribution used to compute corrected $p$-values that provide strong control of false positives. In neuroimaging, however, the computational burden of running such an algorithm can be significant. We find that by viewing the permutation testing procedure as the construction of a very large permutation testing matrix, $T$, one can exploit structural properties derived from the data and the test statistics to reduce the runtime under certain conditions. In particular, we see that $T$ is low-rank plus a low-variance residual. This makes $T$ a good candidate for low-rank matrix completion, where only a very small number of entries of $T$ ($\sim0.35\%$ of all entries in our experiments) have to be computed to obtain a good estimate. Based on this observation, we present RapidPT, an algorithm that efficiently recovers the max null distribution commonly obtained through regular permutation testing in voxel-wise analysis. We present an extensive validation on a synthetic dataset and four varying sized datasets against two baselines: Statistical NonParametric Mapping (SnPM13) and a standard permutation testing implementation (referred as NaivePT). We find that RapidPT achieves its best runtime performance on medium sized datasets ($50 \leq n \leq 200$), with speedups of 1.5x - 38x (vs. SnPM13) and 20x-1000x (vs. NaivePT). For larger datasets ($n \geq 200$) RapidPT outperforms NaivePT (6x - 200x) on all datasets, and provides large speedups over SnPM13 when more than 10000 permutations (2x - 15x) are needed. The implementation is a standalone toolbox and also integrated within SnPM13, able to leverage multi-core architectures when available.Comment: 36 pages, 16 figure

Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package

For right-censored data perhaps the most commonly used tests are weighted logrank tests, such as the logrank and Wilcoxon-type tests. In this paper we review several generalizations of those weighted logrank tests to interval-censored data and present an R package, interval, to implement many of them. The interval package depends on the perm package, also presented here, which performs exact and asymptotic linear permutation tests. The perm package performs many of the tests included in the already available coin package, and provides an independent validation of coin. We review analysis methods for interval-censored data, and we describe and show how to use the interval and perm packages.