Network-based statistic: Identifying differences in brain networks
Research Highlights
►Large-scale functional or structural brain connectivity can be modeled as a network, or graph. ►This paper presents a statistical approach to identify connections in such a graph that may be associated with a diagnostic status in case-control studies, changing psychological contexts in task-based studies, or correlations with various cognitive and behavioral measures. ►The new approach, called the network-based statistic (NBS), is a method to control the family-wise error rate (in the weak sense) when mass-univariate testing is performed at every connection comprising the graph. ►To potentially offer a substantial gain in power, the NBS exploits the extent to which the connections comprising the contrast or effect of interest are interconnected. ►The NBS is based on the principles underpinning traditional cluster-based thresholding of statistical parametric maps. ►The purpose of this paper is to: (i) introduce the NBS for the first time; (ii) evaluate its power with the use of receiver operating characteristic (ROC) curves; and, (iii) demonstrate its utility with application to a real case-control study involving a group of people with schizophrenia for which resting-state functional MRI data was acquired. ►The NBS identified a expansive dysconnected subnetwork in the group with schizophrenia, primarily comprising fronto-temporal and occipito-temporal dysconnections, whereas a mass-univariate analysis controlled with the false discovery rate failed to identify a subnetwork.
Introduction
It has become fashionable in the field of neuroimaging to model and analyze the brain in terms of a network. With the popularization of complex systems theory and the emergence of network science, graph models have become especially popular for they open up the door to a systems-theoretic description of the brain. That is, a description where brain complexity can be reduced to an account of the interactions between basic neuronal elements.
The graph model of the brain is an abstract structure used to represent pairwise relations between interregional ensembles of neuronal elements, referred to as nodes. These pairwise relations, or links, can either be of a functional origin and represent coherent physiological activity between neural ensembles, or they can be of a structural origin and represent anatomical connections formed by white-matter axonal fiber tracts.
The graph model has been used in neuroimaging research as a framework to test the structure-function hypothesis (Honey et al., 2009, Honey et al., 2010, Ramani et al., 2004, Skudlarski et al., 2008, Sporns et al., 2000) and as a methodological tool to examine brain network organization, topology and complex dynamics (Bullmore et al., 2009, Hagmann et al., 2008, Sporns et al., 2004). It has been found that the human brain exhibits various nontrivial organizational and topological properties, such as: assortativity, centrality, clustering, efficiency, hierarchy, hubs, modularity, robustness, small-worldness, synchronizability, etc. (see Bullmore & Sporns, 2009, for a review). Differences in one or more of these properties have been found in people with Alzheimer's disease (He et al., 2008, Stam et al., 2007), attention-deficit disorder (Wang et al., 2009), multiple sclerosis (He et al., 2009) and schizophrenia (Bassett et al., 2008, Liu et al., 2008, Rubinov et al., 2009) as well as associations with age and gender (Gong et al., 2009, Wang et al., 2010), and intelligence (van den Heuvel et al., 2009, Li et al., 2009).
The graph model also provides an ideal framework to identify functional or structural connections associated with a particular effect or contrast of interest; for example, a group difference in a case-control comparison, a difference due to changing task conditions in a functional paradigm, or a correlation with some clinical measure. To this end, mass-univariate testing of the hypothesis is undertaken, after which the family-wise error rate (FWE) is controlled with a generic procedure, such as the false discovery rate (FDR) (Genovese et al., 2002). Specifically, a test statistic and corresponding p-value is independently computed for each link based on the strength of the pairwise association the link represents. The strength of a pairwise association between nodes is usually measured as the value of temporal correlation (functional) or the total number of interconnecting streamlines (structural).
The advantage of this approach is that it does not require interpretation of any abstract organizational or topological properties. Its main disadvantage though is the inherent massive number of multiple comparisons that must be performed. To appreciate the massiveness of the multiple comparisons problem, consider the following: performing a mass-univariate analysis on a statistical parametric map involves in the order of thousands of multiple comparisons, say 1000 voxels for concreteness; however, if each of these 1000 voxels delineates a unique node, the number of multiple comparisons increases to a staggering connections. With such a large number of multiple comparisons, together with a potentially low contrast-to-noise ratio, mass-univariate testing may not offer sufficient power.
Note that when the hypothesis of interest is associated with a global network measure, the issue of multiple comparisons does not arise. This paper exclusively focuses on multiple hypothesis testing, where one instead tests the hypothesis of interest at each network connection, thereby introducing more localizing power at the cost of a massive number of multiple comparisons.
The main contribution of this paper is to present a potentially more powerful method to control the FWE when performing this kind of analysis. The new method is called the network-based statistic (NBS) and can be thought of as a translation of conventional cluster statistics (Bullmore et al., 1999, Nichols and Holmes, 2001) to a graph. In brief, the NBS operates as follows: foremost, the test statistic computed for each link is thresholded to construct a set of suprathreshold links. Any connected structures, or components in graph parlance, that may be present in the set of suprathreshold links are then identified. A p-value is assigned to each identified component by indexing its size with the null distribution of maximal component size.
In this way, the NBS attempts to utilize the presence of any structure exhibited by the connections comprising the effect or contrast of interest to yield greater power than what is possible by independently correcting the p-values computed for each link using a generic procedure to control the FWE. In this paper, any procedure for controlling the FWE that treats each link independently will be referred to as a link-based controlling procedure, or simply link-based FWE control.
The NBS is not intended as a replacement for link-based FWE control. In particular, the NBS offers no power if the links associated with the contrast or effect of interest are in isolation of each other and do not form any connected structures. Therefore, in addition to introducing and demonstrating the utility of the NBS, one of the main purposes of this paper is to undertake a quantitative evaluation of the gain (and potential loss) in statistical power offered by our new approach. To this end, the paper comprises three parts: Section 2: introduction of the NBS by way of an illustrative example; Section 3: evaluation of the power of the NBS with use of receiver operating characteristic (ROC) curves; and, Section 4: demonstration of the NBS in the context of a real case-control study involving resting-state functional MRI data acquired in 12 people with schizophrenia and 15 controls.
Section snippets
Methods
To use the NBS, one must first generate a connectivity matrix for each subject. The connectivity matrix is intrinsic to the graph model and its computation has been described in (Bullmore & Sporns, 2009) and many references therein. As such, the main focus of this section is the implementation of the NBS after the connectivity matrix stage has been reached, though a brief overview of getting to this stage is provided for completeness.
Performance evaluation
Receiver operating characteristic (ROC) curves are presented in this section to evaluate the specificity and sensitivity of the NBS as well as link-based FWE control under a range of different network topologies, contrast extents and contrast-to-noise ratios. The FDR served as the link-based controlling procedure, and thus any reference to FDR in this section is synonymous with link-based FWE control.
An ROC curve is a plot of the true positive rate (TPR) against the false positive rate (FPR),
Application
The purpose of this section is to present new results derived from application of the NBS to a real case-control study involving a group of people with schizophrenia. In this section, a pair of nodes showing a weaker association in the group with schizophrenia is referred to as a dysconnection and the set of all such dysconnections is referred to as the dysconnected subnetwork.
Discussion
With continuing popularization of the graph model in all kinds of neuroimaging research, we believe there is a need for statistical approaches to identify connections in this model that may be associated with an effect or contrast of interest; for example, diagnostic status in a case-control comparison, a difference due to changing task conditions in a functional paradigm, pharmacological modulation, or correlation with some external behavioral measure. While mass-univariate testing is an
Conclusion
This paper presented a new approach, called the network-based statistic (NBS), to identify functional or structural connectivity differences in neuroimaging data that is modeled as a network. With the use of receiver operating characteristic (ROC) curves, the NBS was shown to yield substantially greater statistical power than generic procedures for controlling the FWE, as long as any connectivity differences were structured in such a way that they formed connected components. The fact that the
Acknowledgments
We are grateful for the assistance provided by Dr Manfred Kitzbichler and Dr Ulrich Müller in acquiring and preprocessing the MRI data used to validate our algorithm in Section 4. AZ is supported by the Australian Research Council (DP0986320). AF is supported by a National Health and Medical Research Council CJ Martin Fellowship (ID: 454797).
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