help > 2x2 design, contrasts and interpretation
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Jul 16, 2021  07:07 PM | Ramiro Salas - Baylor College of Medicine
2x2 design, contrasts and interpretation
Dear Conners, 

I want to do a 2x2 study with controls (C) and depression (D), with genotypes X and Y. Say we have 8 people, so we have these vectors: 
Allsubjects [1 1 1 1 1 1 1 1]
GroupD [1 1 1 1 0 0 0 0]
GroupC [0 0 0 0 1 1 1 1]
GenotypeX [1 1 0 0 1 1 0 0]
GenotypeY [0 0 1 1 0 0 1 1]

And I can create vectors for the depression/genotypeX, etc:
DepX (1 1 0 0 0 0 0 0]
DepY [0 0 1 1 0 0 0 0]
ConX [0 0 0 0 1 1 0 0]
ConY [0 0 0 0 0 0 1 1]

I also want to correct for age, so I have 

Age [age1 age2 age3 age4 age5 age6 age7 age8]

Assuming I have one condition (rest) and care about one seed only.

First contrast: Is there a difference in seed to voxel in depression vs controls? The contrast should be: 
[0 1 -1 0] (all subjects, groupC, groupD, age). Would this be the same as [1 -1 0] since I am using them all anyway? 

Second contrast: Is there a difference between the two genotypes?

[0 1 -1 0] (now they are all subjects, genotypeX, genotypeY, age)

third contrast: is there an interaction between depression group and genotype? 
[1 -1 -1 1 0] (using DepX, DepY, ConX, ConY, age)

Question 1: Now, when I see the results, the first two are pretty straight forward, but the interaction: if I see a significative cluster, it means there is an interaction, correct? How do I know what type of interaction? Do I need to extract the cluster data? How do I check how do they interact?  

Question 2: what I am comparing if I do [1 -1 0 0 0 ; 0 0 1 -1 0] using groupD, groupC, genotypeX, genotypeY, age]? And If I see a cluster, what does that mean? 

Thank you, 
Ramiro
Jul 18, 2021  09:07 AM | Alfonso Nieto-Castanon - Boston University
RE: 2x2 design, contrasts and interpretation
Dear Ramiro,

Re: first contrast; yes, that looks perfectly fine, a couple of suggestions would be: a) removing the 'all subjects' factor (just for simplicity, as you should get exactly the same results), since it is co-linear with the group factors, e.g. [1 -1 0] (groupC, groupD, age); and b) consider controlling for genotype effects (e.g. using [.5 .5 -.5 -.5 0] (ConX ConY DepX DepY age]) particularly if your groups show prevalence difference in depression with genotype (same comments apply to your second contrast)

Re: question 1; the interaction results simply indicate that the difference in connectivity between depression and control groups is itself different in genotypeX vs in genotypeY subjects (or equivalently, that the difference between genX&genY is different in Dep vs. Con). One simple way to interpret the directionality of those interaction results is to use the 'plot effects' button (the button with a barplot image) in the second-level results explorer window to display connectivity within each cluster and within each of the 4 Con/Dep X/Y subgroups. You may also extract the values within each cluster (e.g. using the 'Import values' button) and perform additional post-hoc analyses (e.g. in the main CONN gui Tools.Calculator menu)

Re: question 2; that test ([1 -1 0 0 0 ; 0 0 1 -1 0] using groupD, groupC, genotypeX, genotypeY, age]) is evaluating areas that show either depression or genotype effects (e.g. and OR conjunction on your first and second contrast)

Hope this helps
Alfonso

Originally posted by Ramiro Salas:
Dear Conners, 

I want to do a 2x2 study with controls (C) and depression (D), with genotypes X and Y. Say we have 8 people, so we have these vectors: 
Allsubjects [1 1 1 1 1 1 1 1]
GroupD [1 1 1 1 0 0 0 0]
GroupC [0 0 0 0 1 1 1 1]
GenotypeX [1 1 0 0 1 1 0 0]
GenotypeY [0 0 1 1 0 0 1 1]

And I can create vectors for the depression/genotypeX, etc:
DepX (1 1 0 0 0 0 0 0]
DepY [0 0 1 1 0 0 0 0]
ConX [0 0 0 0 1 1 0 0]
ConY [0 0 0 0 0 0 1 1]

I also want to correct for age, so I have 

Age [age1 age2 age3 age4 age5 age6 age7 age8]

Assuming I have one condition (rest) and care about one seed only.

First contrast: Is there a difference in seed to voxel in depression vs controls? The contrast should be: 
[0 1 -1 0] (all subjects, groupC, groupD, age). Would this be the same as [1 -1 0] since I am using them all anyway? 

Second contrast: Is there a difference between the two genotypes?

[0 1 -1 0] (now they are all subjects, genotypeX, genotypeY, age)

third contrast: is there an interaction between depression group and genotype? 
[1 -1 -1 1 0] (using DepX, DepY, ConX, ConY, age)

Question 1: Now, when I see the results, the first two are pretty straight forward, but the interaction: if I see a significative cluster, it means there is an interaction, correct? How do I know what type of interaction? Do I need to extract the cluster data? How do I check how do they interact?  

Question 2: what I am comparing if I do [1 -1 0 0 0 ; 0 0 1 -1 0] using groupD, groupC, genotypeX, genotypeY, age]? And If I see a cluster, what does that mean? 

Thank you, 
Ramiro