Brain networks construction using Bayes FDR and average power function

2019 ◽  
Vol 29 (3) ◽  
pp. 866-878
Author(s):  
Piero Quatto ◽  
Nicolò Margaritella ◽  
Isa Costantini ◽  
Francesca Baglio ◽  
Massimo Garegnani ◽  
...  
Keyword(s):  
Time Series ◽  
False Discovery Rate ◽  
Correlation Coefficient ◽  
Power Function ◽  
Multiple Testing ◽  
Statistical Power ◽  
Brain Connectivity ◽  
Average Power ◽  
Statistical Error ◽  
False Discovery

Brain functional connectivity is a widely investigated topic in neuroscience. In recent years, the study of brain connectivity has been largely aided by graph theory. The link between time series recorded at multiple locations in the brain and the construction of a graph is usually an adjacency matrix. The latter converts a measure of the connectivity between two time series, typically a correlation coefficient, into a binary choice on whether the two brain locations are functionally connected or not. As a result, the choice of a threshold τ over the correlation coefficient is key. In the present work, we propose a multiple testing approach to the choice of τ that uses the Bayes false discovery rate and a new estimator of the statistical power called average power function to balance the two types of statistical error. We show that the proposed average power function estimator behaves well both in case of independence and weak dependence of the tests and it is reliable under several simulated dependence conditions. Moreover, we propose a robust method for the choice of τ using the 5% and 95% percentiles of the average power function and False Discovery Rate bootstrap distributions, respectively, to improve stability. We applied our approach to functional magnetic resonance imaging and high density electroencephalogram data.

scholarly journals Wavelet analysis for non-stationary, nonlinear time series

2016 ◽  
Vol 23 (4) ◽  
pp. 257-267 ◽  
Author(s):  
Justin A. Schulte
Keyword(s):  
Time Series ◽  
Phase Transitions ◽  
Wavelet Analysis ◽  
False Discovery Rate ◽  
Multiple Testing ◽  
Nonstationary Time Series ◽  
Nonlinear Interactions ◽  
Quasi Biennial Oscillation ◽  
False Discovery ◽  
Biennial Oscillation

Abstract. Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16 and 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.

scholarly journals 2dFDR: a new approach to confounder adjustment substantially increases detection power in omics association studies

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Sangyoon Yi ◽  
Xianyang Zhang ◽  
Lu Yang ◽  
Jinyan Huang ◽  
Yuanhang Liu ◽  
...  
Keyword(s):  
Multiple Testing ◽  
Statistical Power ◽  
Association Studies ◽  
Control Procedure ◽  
Multiple Testing Correction ◽  
New Approach ◽  
False Discovery ◽  
Traditional Procedure ◽  
Extensive Evaluation ◽  
Confounder Adjustment

AbstractOne challenge facing omics association studies is the loss of statistical power when adjusting for confounders and multiple testing. The traditional statistical procedure involves fitting a confounder-adjusted regression model for each omics feature, followed by multiple testing correction. Here we show that the traditional procedure is not optimal and present a new approach, 2dFDR, a two-dimensional false discovery rate control procedure, for powerful confounder adjustment in multiple testing. Through extensive evaluation, we demonstrate that 2dFDR is more powerful than the traditional procedure, and in the presence of strong confounding and weak signals, the power improvement could be more than 100%.

On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics

2000 ◽  
Vol 25 (1) ◽  
pp. 60-83 ◽  
Author(s):  
Yoav Benjamini ◽  
Yosef Hochberg
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
Meta Analysis ◽  
Test Statistics ◽  
Adaptive Procedure ◽  
New Approach ◽  
False Discovery ◽  
Behavioral Studies ◽  
Simultaneous Testing ◽  
Independent Test

A new approach to problems of multiple significance testing was presented in Benjamini and Hochberg (1995), which calls for controlling the expected ratio of the number of erroneous rejections to the number of rejections–the False Discovery Rate (FDR). The procedure given there was shown to control the FDR for independent test statistics. When some of the hypotheses are in fact false, that procedure is too conservative. We present here an adaptive procedure, where the number of true null hypotheses is estimated first as in Hochberg and Benjamini (1990), and this estimate is used in the procedure of Benjamini and Hochberg (1995). The result is still a simple stepwise procedure, to which we also give a graphical companion. The new procedure is used in several examples drawn from educational and behavioral studies, addressing problems in multi-center studies, subset analysis and meta-analysis. The examples vary in the number of hypotheses tested, and the implication of the new procedure on the conclusions. In a large simulation study of independent test statistics the adaptive procedure is shown to control the FDR and have substantially better power than the previously suggested FDR controlling method, which by itself is more powerful than the traditional family wise error-rate controlling methods. In cases where most of the tested hypotheses are far from being true there is hardly any penalty due to the simultaneous testing of many hypotheses.

On “Field Significance” and the False Discovery Rate

2006 ◽  
Vol 45 (9) ◽  
pp. 1181-1189 ◽  
Author(s):  
D. S. Wilks
Keyword(s):  
False Discovery Rate ◽  
Statistical Power ◽  
Statistical Significance ◽  
Significance Test ◽  
P Value ◽  
Test Statistic ◽  
Global Test ◽  
Additional Advantage ◽  
Counting Procedure ◽  
False Discovery

Abstract The conventional approach to evaluating the joint statistical significance of multiple hypothesis tests (i.e., “field,” or “global,” significance) in meteorology and climatology is to count the number of individual (or “local”) tests yielding nominally significant results and then to judge the unusualness of this integer value in the context of the distribution of such counts that would occur if all local null hypotheses were true. The sensitivity (i.e., statistical power) of this approach is potentially compromised both by the discrete nature of the test statistic and by the fact that the approach ignores the confidence with which locally significant tests reject their null hypotheses. An alternative global test statistic that has neither of these problems is the minimum p value among all of the local tests. Evaluation of field significance using the minimum local p value as the global test statistic, which is also known as the Walker test, has strong connections to the joint evaluation of multiple tests in a way that controls the “false discovery rate” (FDR, or the expected fraction of local null hypothesis rejections that are incorrect). In particular, using the minimum local p value to evaluate field significance at a level αglobal is nearly equivalent to the slightly more powerful global test based on the FDR criterion. An additional advantage shared by Walker’s test and the FDR approach is that both are robust to spatial dependence within the field of tests. The FDR method not only provides a more broadly applicable and generally more powerful field significance test than the conventional counting procedure but also allows better identification of locations with significant differences, because fewer than αglobal × 100% (on average) of apparently significant local tests will have resulted from local null hypotheses that are true.

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