Proportional thresholding in resting-state fMRI functional connectivity networks and consequences for patient-control connectome studies: Issues and recommendations

Abstract

Graph theoretical analysis has become an important tool in the examination of brain dysconnectivity in neurological and psychiatric brain disorders. A common analysis step in the construction of the functional graph or network involves "thresholding" of the connectivity matrix, selecting the set of edges that together form the graph on which network organization is evaluated. To avoid systematic differences in absolute number of edges, studies have argued against the use of an "absolute threshold" in case-control studies and have proposed the use of "proportional thresholding" instead, in which a pre-defined number of strongest connections are selected as network edges, ensuring equal network density across datasets. Here, we systematically studied the effect of proportional thresholding on the construction of functional matrices and subsequent graph analysis in patient-control functional connectome studies. In a few simple experiments we show that differences in overall strength of functional connectivity (FC) - as often observed between patients and controls - can have predictable consequences for between-group differences in network organization. In individual networks with lower overall FC the proportional thresholding algorithm has to select more edges based on lower correlations, which have (on average) a higher probability of being spurious, and thus introduces a higher degree of randomness in the resulting network. We show across both empirical and artificial patient-control datasets that lower levels of overall FC in either the patient or control group will most often lead to differences in network efficiency and clustering, suggesting that differences in FC across subjects will be artificially inflated or translated into differences in network organization. Based on the presented case-control findings we inform about the caveats of proportional thresholding in patient-control studies in which groups show a between-group difference in overall FC. We make recommendations on how to examine, report and to take into account overall FC effects in future patient-control functional connectome studies.

Stage-dependent remodeling of projections to motor cortex in ALS mouse model revealed by a new variant retrograde-AAV9

“…Each of the a priori defined seed regions allowed for the identification of well-known functional brain networks in healthy humans (Smith et al, 2009) (Figure 9A), which indicated robust seed locations for the functional connectome analysis. Overall functional connectivity analysis demonstrated no statistically significant differences between groups ( t  = −0.51, p=0.613), which rules out a potential bias in the overall level of connectivity (van den Heuvel et al, 2017). However, network-based statistics of functional connectome data revealed significantly increased functional connectivity (hyper-connectivity) between regions frontal to the pMO, namely the dorsolateral prefrontal association cortex and the pMO itself, both homolaterally and contralaterally ( t  ≥ 2.81, p≤0.0065, corrected; Figure 9B).…”

“…Overall functional connectivity was computed and used as a regressor (van den Heuvel et al, 2017) prior to subjecting the data to a two-sided parametric Student's t- test in order to test for pairwise differences between ALS patients and controls using the network-based statistics approach (Zalesky et al, 2010). …”

Adolescent Tuning of Association Cortex in Human Structural Brain Networks

“…These results align with our own, through the strong dependence of the properties of graphs thresholded to fixed edge densities (as in Khundrakpam et al (2013)) on the mean of the correlation distributions from which they were derived. Networks with lower correlations lead to more random topology, exhibiting higher efficiency and lower clustering (Fornito et al 2013; van den Heuvel et al 2017). Therefore, our finding of decreases in structural correlation within association cortical areas aligns with reports by Khundrakpam et al (2013) of increased regional efficiency in these regions.…”

“…Nodal topological organization was assessed using (analogous) measures of degree, defined as the number of edges connected to a node, and average Euclidean distance spanned by a node’s retained edges. We have focused on simple graph-theoretical measures, such as edge density and node degree, for two reasons: (1) our bootstrap-thresholded networks display variable edge density, which many “higher-order” graph-theoretical measures show a strong dependence on (van Wijk et al 2010), and (2) even in correlation-based networks thresholded to fixed edge density, graph theoretical properties display a dependence on more elementary statistics such as properties of the correlation distribution (van den Heuvel et al 2017). …”

Minimum spanning tree analysis of the human connectome

“…Proportional thresholding is frequently applied to weighted connectivity matrices to overcome this problem and yield networks that are matched in terms of total number of connections; network characteristics are then based on this thresholded network containing a subset of strong connections. However, this approach affects the graph properties in an unpredictable manner, because the impact of setting a threshold varies, depending on the underlying network topology (Stam et al, 2014; van den Heuvel et al, 2017; van Wijk et al, 2010). Handling of the thresholding problem is likely to be one of the reasons that empirical studies have reported contradictory findings, for example of both increased and decreased characteristic shortest path length in patients with Alzheimer's Disease (Fornito et al, 2013; Tijms et al, 2013).…”