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An empirical Bayes normalization method for connectivity metrics in resting state fMRI.

Chen S, Kang J, Wang G - Front Neurosci (2015)

Bottom Line: Moreover, the normalization function maps the original connectivity metrics to values between zero and one, which is well-suited for the graph theory based network analysis and avoids the information loss due to the (negative value) hard thresholding step.We apply the normalization method to a simulation study and the simulation results show that our normalization method effectively improves the robustness and reliability of the quantification of brain functional connectivity and provides more powerful group difference (biomarkers) detection.We illustrate our method on an analysis of a rs-fMRI dataset from the Autism Brain Imaging Data Exchange (ABIDE) study.

View Article: PubMed Central - PubMed

Affiliation: Department of Epidemiology and Biostatistics, University of Maryland College Park, MD, USA.

ABSTRACT
Functional connectivity analysis using resting-state functional magnetic resonance imaging (rs-fMRI) has emerged as a powerful technique for investigating functional brain networks. The functional connectivity is often quantified by statistical metrics (e.g., Pearson correlation coefficient), which may be affected by many image acquisition and preprocessing steps such as the head motion correction and the global signal regression. The appropriate quantification of the connectivity metrics is essential for meaningful and reproducible scientific findings. We propose a novel empirical Bayes method to normalize the functional brain connectivity metrics on a posterior probability scale. Moreover, the normalization function maps the original connectivity metrics to values between zero and one, which is well-suited for the graph theory based network analysis and avoids the information loss due to the (negative value) hard thresholding step. We apply the normalization method to a simulation study and the simulation results show that our normalization method effectively improves the robustness and reliability of the quantification of brain functional connectivity and provides more powerful group difference (biomarkers) detection. We illustrate our method on an analysis of a rs-fMRI dataset from the Autism Brain Imaging Data Exchange (ABIDE) study.

No MeSH data available.


Related in: MedlinePlus

(A) Heatmaps of truth the connectivity between the first 30 nodes are differentially expressed between the two groups; (B–D) Heatmaps of the test results using Wilcoxon signed-rank test and FDR control with q = 0.1 (red = reject and blue = fail to reject) of the original correlations z, the probit (variance stablizing) transformed correlation, and the normalized correlations gs(z), respectively, under the scenario of no systematic sifts; (E,F) Heatmaps of the test results of the original correlations z and the normalized correlations gs(z) under the scenario of with systematic shifts.
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Figure 5: (A) Heatmaps of truth the connectivity between the first 30 nodes are differentially expressed between the two groups; (B–D) Heatmaps of the test results using Wilcoxon signed-rank test and FDR control with q = 0.1 (red = reject and blue = fail to reject) of the original correlations z, the probit (variance stablizing) transformed correlation, and the normalized correlations gs(z), respectively, under the scenario of no systematic sifts; (E,F) Heatmaps of the test results of the original correlations z and the normalized correlations gs(z) under the scenario of with systematic shifts.

Mentions: Ideally, the test results reveal the 435 “true positives” with 0 “false positives.” Figure 5 shows the testing results by different methods and scenarios. Figure 5A reflects the true differentially expressed connectivity expressions between the two groups for the first 30 nodes (red) and the rest are at the level (blue). Figure 5B shows the testing results between the two groups based on the non-normalized correlations. Figure 5C are the testing results based on the probit (variance stablizing) transformed correlations (the logit transformation performance is very similar). Figure 5D are the testing results based on the empirical Bayes normalized correlations. Figures 5E,F are the test results of non-normalized and normalized correlations under the scenario with systematic shifts. Based on all the differentially expressed connectivity/biomarker discovery results, the normalized connectivity metrics have much lower type I and II errors. Table 1 summarizes the detailed results with comparison to the truth over 100 times of simulations. The number of false positive testing results of non-normalized correlations is about 17 times of the normalized correlations, and the number of false negative testing results is more than about 20 times; the difference is even larger in the shifted scenario. The performance of probit variance stablizing transformed correlations are similar to the original correlations. The levels of random shift (σ2) affect the performance of the differential detection, however after the empirical Bayes normalization the shift almost has no impact on the result findings. Therefore, the simulation study results indicate that our normalization method can effectively scale the connectivity to appropriate level and improves the power to identify the true differentially expressed connectivity with low false positive rate. When the is more dispersed and connected component is right skewed, the two mixture components are more mixed and thus the false positives and false negatives increase. Yet, our method outperforms the non-normalized correlations for differentially expressed feature detection. Overall, the empirical Bayes normalization model provides a more robust pathway for connectivity expression quantification and enables biomarker discovery with both high sensitivity and specificity.


An empirical Bayes normalization method for connectivity metrics in resting state fMRI.

Chen S, Kang J, Wang G - Front Neurosci (2015)

(A) Heatmaps of truth the connectivity between the first 30 nodes are differentially expressed between the two groups; (B–D) Heatmaps of the test results using Wilcoxon signed-rank test and FDR control with q = 0.1 (red = reject and blue = fail to reject) of the original correlations z, the probit (variance stablizing) transformed correlation, and the normalized correlations gs(z), respectively, under the scenario of no systematic sifts; (E,F) Heatmaps of the test results of the original correlations z and the normalized correlations gs(z) under the scenario of with systematic shifts.
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Show All Figures
getmorefigures.php?uid=PMC4584951&req=5

Figure 5: (A) Heatmaps of truth the connectivity between the first 30 nodes are differentially expressed between the two groups; (B–D) Heatmaps of the test results using Wilcoxon signed-rank test and FDR control with q = 0.1 (red = reject and blue = fail to reject) of the original correlations z, the probit (variance stablizing) transformed correlation, and the normalized correlations gs(z), respectively, under the scenario of no systematic sifts; (E,F) Heatmaps of the test results of the original correlations z and the normalized correlations gs(z) under the scenario of with systematic shifts.
Mentions: Ideally, the test results reveal the 435 “true positives” with 0 “false positives.” Figure 5 shows the testing results by different methods and scenarios. Figure 5A reflects the true differentially expressed connectivity expressions between the two groups for the first 30 nodes (red) and the rest are at the level (blue). Figure 5B shows the testing results between the two groups based on the non-normalized correlations. Figure 5C are the testing results based on the probit (variance stablizing) transformed correlations (the logit transformation performance is very similar). Figure 5D are the testing results based on the empirical Bayes normalized correlations. Figures 5E,F are the test results of non-normalized and normalized correlations under the scenario with systematic shifts. Based on all the differentially expressed connectivity/biomarker discovery results, the normalized connectivity metrics have much lower type I and II errors. Table 1 summarizes the detailed results with comparison to the truth over 100 times of simulations. The number of false positive testing results of non-normalized correlations is about 17 times of the normalized correlations, and the number of false negative testing results is more than about 20 times; the difference is even larger in the shifted scenario. The performance of probit variance stablizing transformed correlations are similar to the original correlations. The levels of random shift (σ2) affect the performance of the differential detection, however after the empirical Bayes normalization the shift almost has no impact on the result findings. Therefore, the simulation study results indicate that our normalization method can effectively scale the connectivity to appropriate level and improves the power to identify the true differentially expressed connectivity with low false positive rate. When the is more dispersed and connected component is right skewed, the two mixture components are more mixed and thus the false positives and false negatives increase. Yet, our method outperforms the non-normalized correlations for differentially expressed feature detection. Overall, the empirical Bayes normalization model provides a more robust pathway for connectivity expression quantification and enables biomarker discovery with both high sensitivity and specificity.

Bottom Line: Moreover, the normalization function maps the original connectivity metrics to values between zero and one, which is well-suited for the graph theory based network analysis and avoids the information loss due to the (negative value) hard thresholding step.We apply the normalization method to a simulation study and the simulation results show that our normalization method effectively improves the robustness and reliability of the quantification of brain functional connectivity and provides more powerful group difference (biomarkers) detection.We illustrate our method on an analysis of a rs-fMRI dataset from the Autism Brain Imaging Data Exchange (ABIDE) study.

View Article: PubMed Central - PubMed

Affiliation: Department of Epidemiology and Biostatistics, University of Maryland College Park, MD, USA.

ABSTRACT
Functional connectivity analysis using resting-state functional magnetic resonance imaging (rs-fMRI) has emerged as a powerful technique for investigating functional brain networks. The functional connectivity is often quantified by statistical metrics (e.g., Pearson correlation coefficient), which may be affected by many image acquisition and preprocessing steps such as the head motion correction and the global signal regression. The appropriate quantification of the connectivity metrics is essential for meaningful and reproducible scientific findings. We propose a novel empirical Bayes method to normalize the functional brain connectivity metrics on a posterior probability scale. Moreover, the normalization function maps the original connectivity metrics to values between zero and one, which is well-suited for the graph theory based network analysis and avoids the information loss due to the (negative value) hard thresholding step. We apply the normalization method to a simulation study and the simulation results show that our normalization method effectively improves the robustness and reliability of the quantification of brain functional connectivity and provides more powerful group difference (biomarkers) detection. We illustrate our method on an analysis of a rs-fMRI dataset from the Autism Brain Imaging Data Exchange (ABIDE) study.

No MeSH data available.


Related in: MedlinePlus