help > Design matrix for a few repeat scans
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Jan 30, 2021  03:01 PM | jdc77
Design matrix for a few repeat scans
Hi Dr. Zalesky,

First of all, thank you for providing researchers with this very useful tool.

I wanted to write a contrast that compares two groups A and B. A subset of the subjects were scanned twice. I have 200 data sets, and 25 were from the same subject . I was wondering how to account for the repeat scans in the design matrix and include this as a covariate in the contrast. My other covariates are age and gender.

I did:
1 0 1 24
1 0 2 18
1 0 1 35
1 0 1 42
0 1 2 16
0 1 2 18
0 1 1 29
0 1 1 32

Where
Column 1 = group A
Column 2 = group B
Column 3 = gender (1 = male)
Column 4 = age

In the example above, rows 3 and 4 are the same subject, scanned twice at age 35 and 42. Rows 7 and 8 are also the same individual, scanned at different times.

I plan to do a [-1 1 0 0] contrast to compare the two groups. May I ask what is the proper way to add repeat scans in the design matrix?
Thank you!

Best,
Jay
Jan 30, 2021  10:01 PM | Andrew Zalesky
RE: Design matrix for a few repeat scans
Hi Jay,

to model repeat scans, add an additional column to the design matrix to represent each individual. So you would have an extra column with a one at rows 3 and 4, and zeros everywhere else. And another extra column with a one at rows 7 and 8, and zeros elsewhere.

Note that if you end up adding an extra column for all subjects then you will need to remove either column 1 or 2. In this case, your contrast will be [1 0 0 ...] or [-1 0 0 ...]

A more principled (but complex) approach is to use a mixed effects model.

Andrew

Originally posted by jdc77:
Hi Dr. Zalesky,

First of all, thank you for providing researchers with this very useful tool.

I wanted to write a contrast that compares two groups A and B. A subset of the subjects were scanned twice. I have 200 data sets, and 25 were from the same subject . I was wondering how to account for the repeat scans in the design matrix and include this as a covariate in the contrast. My other covariates are age and gender.

I did:
1 0 1 24
1 0 2 18
1 0 1 35
1 0 1 42
0 1 2 16
0 1 2 18
0 1 1 29
0 1 1 32

Where
Column 1 = group A
Column 2 = group B
Column 3 = gender (1 = male)
Column 4 = age

In the example above, rows 3 and 4 are the same subject, scanned twice at age 35 and 42. Rows 7 and 8 are also the same individual, scanned at different times.

I plan to do a [-1 1 0 0] contrast to compare the two groups. May I ask what is the proper way to add repeat scans in the design matrix?
Thank you!

Best,
Jay
Jan 31, 2021  12:01 AM | jdc77
RE: Design matrix for a few repeat scans

So, that means my design matrix will be:
1 1 0 0 1 24
1 0 1 0 2 18
1 0 0 1 1 35
1 0 0 1 1 42
0 1 0 0 2 16
0 0 1 0 1 18
0 0 0 1 1 29
0 0 0 1 1 32

I added a column for all subjects including those with single scans only. Or do I only add for those with 2 scans?

My contrast will be [1 0 0 0 0 0] if I wanted to compare group A vs B (A > B).

Would these be correct?

Thank you again! I appreciate your help.

Jay
Jan 31, 2021  01:01 AM | Andrew Zalesky
RE: Design matrix for a few repeat scans
Hi Jay,

With this design, ideally you should have repeat scans in all subjects. If you only have repeat scan in some subjects, but not others, you may want to consider a linear mixed effects model, which is a better option in this case (but a lot more complex and slower). There is an R package called NBR which implements NBS in a mixed effects model.

If you stick with the current model, I would add a column for all subjects, not just those with repeat scans. Once again though, this is not an optimal model when not all subjects have repeat scans.

When modeling sex, use 0 and 1, rather than 1 and 2.

Yes - the contrast is correct.

Andrew
Originally posted by jdc77:

So, that means my design matrix will be:
1 1 0 0 1 24
1 0 1 0 2 18
1 0 0 1 1 35
1 0 0 1 1 42
0 1 0 0 2 16
0 0 1 0 1 18
0 0 0 1 1 29
0 0 0 1 1 32

I added a column for all subjects including those with single scans only. Or do I only add for those with 2 scans?

My contrast will be [1 0 0 0 0 0] if I wanted to compare group A vs B (A > B).

Would these be correct?

Thank you again! I appreciate your help.

Jay
Jan 31, 2021  02:01 PM | jdc77
RE: Design matrix for a few repeat scans
Thank you!

I will take a look at the R package you suggested.

Jay