help > Graph Theory Interpretation of Repeated Meas?
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Jan 22, 2015 12:01 AM | Jeff Browndyke
Graph Theory Interpretation of Repeated Meas?
Hello all,
I'm trying to understand how to interpret some positive graph theory results I've obtained with CONN (14p).
I have modeled an analysis that examines differences pre/post intervention between groups with the assumption that one group (X) would perform worse post-intervention than the other group (Y).
Between Subjects Contrast
Group X (1), Group Y (-1)
Between Conditions Contrast (Pre/Post intervention scans)
Baseline (1), Followup (-1)
Using AAL and the graph theory viewer with cost function set to 0.20 (one-sided), I obtained the following for the contrast above:
Global Efficiency (p-FDR 0.05, one-sided):
network 0.01 1.28 10 0.114778
(10) 0.17 6.98 10 0.000019 0.002043 (left inferior frontal gyrus, pars triangularis)
(2) 0.13 4.41 10 0.000653 0.034935 (left frontal pole)
Local Efficiency
-nothing survives p-FDR correction
Betweenness Centrality
-nothing survives p-FDR correction
Cost (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 0.18 6.08 10 0.000059 0.006320
(2) 0.11 5.11 10 0.000228 0.012220
Average Path Length
-nothing survives p-FDR correction
Clustering Coefficient
-nothing survives p-FDR correction
Degree (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 19.50 6.08 10 0.000059 0.006320
(2) 11.67 5.11 10 0.000228 0.012220
So, essentially, I have statistically significant results for these two closely located nodes for global efficiency, cost and degree. How should I interpret this? And, any recommendations on how to follow-up on these observations? I have no prior research support to suggest a direction of examination, which is why I opted for voxel-to-voxel and graph theory analyses. BTW - the voxel-to-voxel analyses found differences in intrinsic connectivity and integrated local correlation in very proximal areas as those popping as significant in the Graph theory nodes (e.g., left PFC).
Thanks for any pointers or assistance.
Jeff
I'm trying to understand how to interpret some positive graph theory results I've obtained with CONN (14p).
I have modeled an analysis that examines differences pre/post intervention between groups with the assumption that one group (X) would perform worse post-intervention than the other group (Y).
Between Subjects Contrast
Group X (1), Group Y (-1)
Between Conditions Contrast (Pre/Post intervention scans)
Baseline (1), Followup (-1)
Using AAL and the graph theory viewer with cost function set to 0.20 (one-sided), I obtained the following for the contrast above:
Global Efficiency (p-FDR 0.05, one-sided):
network 0.01 1.28 10 0.114778
(10) 0.17 6.98 10 0.000019 0.002043 (left inferior frontal gyrus, pars triangularis)
(2) 0.13 4.41 10 0.000653 0.034935 (left frontal pole)
Local Efficiency
-nothing survives p-FDR correction
Betweenness Centrality
-nothing survives p-FDR correction
Cost (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 0.18 6.08 10 0.000059 0.006320
(2) 0.11 5.11 10 0.000228 0.012220
Average Path Length
-nothing survives p-FDR correction
Clustering Coefficient
-nothing survives p-FDR correction
Degree (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 19.50 6.08 10 0.000059 0.006320
(2) 11.67 5.11 10 0.000228 0.012220
So, essentially, I have statistically significant results for these two closely located nodes for global efficiency, cost and degree. How should I interpret this? And, any recommendations on how to follow-up on these observations? I have no prior research support to suggest a direction of examination, which is why I opted for voxel-to-voxel and graph theory analyses. BTW - the voxel-to-voxel analyses found differences in intrinsic connectivity and integrated local correlation in very proximal areas as those popping as significant in the Graph theory nodes (e.g., left PFC).
Thanks for any pointers or assistance.
Jeff
Jan 22, 2015 02:01 AM | Alfonso Nieto-Castanon - Boston University
RE: Graph Theory Interpretation of Repeated Meas?
Hi Jeff,
If I am interpreting correctly you are looking at the group x intervention interaction, and the positive-side directionality that you are focusing on looks at differences between followup and baseline that are higher in group Y compared to groupX (e.g. a larger decrease in the followup condition -after treatment- for group X).
Global efficiency is a measure of node "centrality" (a measure of this node relative importance within the network). Degree and cost both measure the number of edges/connections from each node (you can simply report "cost" since in these analyses the statistics of these two measures will always be the same). The results that you find (significant global efficiency and cost interaction effects in two nodes) are consistent with a larger decrease in centrality for these two nodes during followup in group X. That decrease is also likely mediated by a decreased in the number of connections (degree/cost) of these nodes. In order to make sure that this interpretation is accurate I would recommend that you run post-hoc analyses looking at the global efficiency and cost of each individual group (X and Y) and each individual condition (pre- and post- intervention). In this way you can ascertain whether global efficiency and cost is really decreasing when comparing followup vs. baseline conditions and that decrease is larger in group X (it could also be due, for example, to increases in global efficiency and cost when comparing followup vs. baseline, which are larger in group Y).
Other additional analyses that may be of interest would be:
a) looking at two-sided results to make sure you a a priori directionality hypothesis is not missing other potentially interesting interaction effects;
b) looking, as you mention, to voxel-to-voxel analyses (e.g. intrinsic connectivity looks at the total strength of connections between a voxel and the rest of the brain, so it is somewhat related to the graph-theory "degree/cost" measures; local connectivity instead looks only at the strength of connections between a voxel and its neighbors so it is again somewhat similar to "degree/cost" measures but restricted to only to connectivity with nearby areas; looking at these results can help you better interpret your original results and/or finding other effects which may be not apparent in the original analyses);
and/or c) performing post-hoc seed-to-voxel and ROI-to-ROI connectivity analyses (same interaction tests) that look in more detail at the connectivity between these two nodes/seeds and the rest of the brain (is it a somewhat widespread reduction in connectivity in group X after treatment, or is it focused to only a subgroup of target ROIs/areas?)
Hope this helps
Alfonso
Originally posted by Jeff Browndyke:
If I am interpreting correctly you are looking at the group x intervention interaction, and the positive-side directionality that you are focusing on looks at differences between followup and baseline that are higher in group Y compared to groupX (e.g. a larger decrease in the followup condition -after treatment- for group X).
Global efficiency is a measure of node "centrality" (a measure of this node relative importance within the network). Degree and cost both measure the number of edges/connections from each node (you can simply report "cost" since in these analyses the statistics of these two measures will always be the same). The results that you find (significant global efficiency and cost interaction effects in two nodes) are consistent with a larger decrease in centrality for these two nodes during followup in group X. That decrease is also likely mediated by a decreased in the number of connections (degree/cost) of these nodes. In order to make sure that this interpretation is accurate I would recommend that you run post-hoc analyses looking at the global efficiency and cost of each individual group (X and Y) and each individual condition (pre- and post- intervention). In this way you can ascertain whether global efficiency and cost is really decreasing when comparing followup vs. baseline conditions and that decrease is larger in group X (it could also be due, for example, to increases in global efficiency and cost when comparing followup vs. baseline, which are larger in group Y).
Other additional analyses that may be of interest would be:
a) looking at two-sided results to make sure you a a priori directionality hypothesis is not missing other potentially interesting interaction effects;
b) looking, as you mention, to voxel-to-voxel analyses (e.g. intrinsic connectivity looks at the total strength of connections between a voxel and the rest of the brain, so it is somewhat related to the graph-theory "degree/cost" measures; local connectivity instead looks only at the strength of connections between a voxel and its neighbors so it is again somewhat similar to "degree/cost" measures but restricted to only to connectivity with nearby areas; looking at these results can help you better interpret your original results and/or finding other effects which may be not apparent in the original analyses);
and/or c) performing post-hoc seed-to-voxel and ROI-to-ROI connectivity analyses (same interaction tests) that look in more detail at the connectivity between these two nodes/seeds and the rest of the brain (is it a somewhat widespread reduction in connectivity in group X after treatment, or is it focused to only a subgroup of target ROIs/areas?)
Hope this helps
Alfonso
Originally posted by Jeff Browndyke:
Hello all,
I'm trying to understand how to interpret some positive graph theory results I've obtained with CONN (14p).
I have modeled an analysis that examines differences pre/post intervention between groups with the assumption that one group (X) would perform worse post-intervention than the other group (Y).
Between Subjects Contrast
Group X (1), Group Y (-1)
Between Conditions Contrast (Pre/Post intervention scans)
Baseline (1), Followup (-1)
Using AAL and the graph theory viewer with cost function set to 0.20 (one-sided), I obtained the following for the contrast above:
Global Efficiency (p-FDR 0.05, one-sided):
network 0.01 1.28 10 0.114778
(10) 0.17 6.98 10 0.000019 0.002043 (left inferior frontal gyrus, pars triangularis)
(2) 0.13 4.41 10 0.000653 0.034935 (left frontal pole)
Local Efficiency
-nothing survives p-FDR correction
Betweenness Centrality
-nothing survives p-FDR correction
Cost (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 0.18 6.08 10 0.000059 0.006320
(2) 0.11 5.11 10 0.000228 0.012220
Average Path Length
-nothing survives p-FDR correction
Clustering Coefficient
-nothing survives p-FDR correction
Degree (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 19.50 6.08 10 0.000059 0.006320
(2) 11.67 5.11 10 0.000228 0.012220
So, essentially, I have statistically significant results for these two closely located nodes for global efficiency, cost and degree. How should I interpret this? And, any recommendations on how to follow-up on these observations? I have no prior research support to suggest a direction of examination, which is why I opted for voxel-to-voxel and graph theory analyses. BTW - the voxel-to-voxel analyses found differences in intrinsic connectivity and integrated local correlation in very proximal areas as those popping as significant in the Graph theory nodes (e.g., left PFC).
Thanks for any pointers or assistance.
Jeff
I'm trying to understand how to interpret some positive graph theory results I've obtained with CONN (14p).
I have modeled an analysis that examines differences pre/post intervention between groups with the assumption that one group (X) would perform worse post-intervention than the other group (Y).
Between Subjects Contrast
Group X (1), Group Y (-1)
Between Conditions Contrast (Pre/Post intervention scans)
Baseline (1), Followup (-1)
Using AAL and the graph theory viewer with cost function set to 0.20 (one-sided), I obtained the following for the contrast above:
Global Efficiency (p-FDR 0.05, one-sided):
network 0.01 1.28 10 0.114778
(10) 0.17 6.98 10 0.000019 0.002043 (left inferior frontal gyrus, pars triangularis)
(2) 0.13 4.41 10 0.000653 0.034935 (left frontal pole)
Local Efficiency
-nothing survives p-FDR correction
Betweenness Centrality
-nothing survives p-FDR correction
Cost (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 0.18 6.08 10 0.000059 0.006320
(2) 0.11 5.11 10 0.000228 0.012220
Average Path Length
-nothing survives p-FDR correction
Clustering Coefficient
-nothing survives p-FDR correction
Degree (p-FDR 0.05, one-sided):
network 0.00 0.00 10 0.500000
(10) 19.50 6.08 10 0.000059 0.006320
(2) 11.67 5.11 10 0.000228 0.012220
So, essentially, I have statistically significant results for these two closely located nodes for global efficiency, cost and degree. How should I interpret this? And, any recommendations on how to follow-up on these observations? I have no prior research support to suggest a direction of examination, which is why I opted for voxel-to-voxel and graph theory analyses. BTW - the voxel-to-voxel analyses found differences in intrinsic connectivity and integrated local correlation in very proximal areas as those popping as significant in the Graph theory nodes (e.g., left PFC).
Thanks for any pointers or assistance.
Jeff
Jan 22, 2015 03:01 AM | Jeff Browndyke
RE: Graph Theory Interpretation of Repeated Meas?
Thanks, Alfonso. As usual, quite helpful.
I know how to obtain 10;01 group and 10;01 condition data in the seed-to-voxel analyses, which I can then use to display values in a 1 -1 and -1 1 interaction analysis to look at the direction of mean betas for each condition and group, but how does one do this within the context of the Graph Theory viewer?
Also, what significance threshold is appropriate for a post-hoc ROI-to-ROI or seed-to-voxel investigation if I'm originally guided by p-FDR significant voxel-to-voxel or graph theory analyses.
I had another idea, which I'm not certain is correct, to save the voxel-to-voxel intrinsic and local correlation results as ROIs, which I could then feed into a seed-to-voxel analysis. I figure this may not be too helpful with the local correlation ROI result, but maybe appropriate for the intrinsic ROI?
Warm regards,
Jeff
I know how to obtain 10;01 group and 10;01 condition data in the seed-to-voxel analyses, which I can then use to display values in a 1 -1 and -1 1 interaction analysis to look at the direction of mean betas for each condition and group, but how does one do this within the context of the Graph Theory viewer?
Also, what significance threshold is appropriate for a post-hoc ROI-to-ROI or seed-to-voxel investigation if I'm originally guided by p-FDR significant voxel-to-voxel or graph theory analyses.
I had another idea, which I'm not certain is correct, to save the voxel-to-voxel intrinsic and local correlation results as ROIs, which I could then feed into a seed-to-voxel analysis. I figure this may not be too helpful with the local correlation ROI result, but maybe appropriate for the intrinsic ROI?
Warm regards,
Jeff