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Nov 12, 2022 03:11 PM | Marius Gruber
Testing for associations in longitudinal changes of structural connectivity and metric variables
Dear Andrew,
We are currently working on a longitudinal analysis with two time points (T1 and T2). We want to test the association between longitudinal changes in structural connectivity and longitudinal changes in a metric predictor, namely depression symptom severity (measured via Hamilton Depression Rating Scale).
Our first idea is to use a standard ANCOVA model to test the association between the difference in connectivity matrices (T2-T1) and the differences in HAMD scores (T2-T1) while correcting for baseline values of age and sex. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -9 35 0
1 -5 22 1
with the first column modeling the intercept, the second column modeling the difference in HAMD scores, the third column modeling the age at baseline, and the fourth column modeling the participants' sex.
An alternative we thought of would be to use a repeated measures ACNOVA with a design matrix containing a constant (1), the time points (-1 or 1), and the interaction of time and either the HAMD score at T1 or the HAMD score at T2, and the columns that model each participant's random intercept. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -1 -15 1 0
1 -1 -20 0 1
1 1 6 1 0
1 1 10 0 1
Is the second design matrix correctly specified in this way? And which of the two alternatives would be more sensible in your view?
Thank you very much in advance!
Marius
We are currently working on a longitudinal analysis with two time points (T1 and T2). We want to test the association between longitudinal changes in structural connectivity and longitudinal changes in a metric predictor, namely depression symptom severity (measured via Hamilton Depression Rating Scale).
Our first idea is to use a standard ANCOVA model to test the association between the difference in connectivity matrices (T2-T1) and the differences in HAMD scores (T2-T1) while correcting for baseline values of age and sex. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -9 35 0
1 -5 22 1
with the first column modeling the intercept, the second column modeling the difference in HAMD scores, the third column modeling the age at baseline, and the fourth column modeling the participants' sex.
An alternative we thought of would be to use a repeated measures ACNOVA with a design matrix containing a constant (1), the time points (-1 or 1), and the interaction of time and either the HAMD score at T1 or the HAMD score at T2, and the columns that model each participant's random intercept. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -1 -15 1 0
1 -1 -20 0 1
1 1 6 1 0
1 1 10 0 1
Is the second design matrix correctly specified in this way? And which of the two alternatives would be more sensible in your view?
Thank you very much in advance!
Marius
Nov 14, 2022 06:11 AM | Andrew Zalesky
RE: Testing for associations in longitudinal changes of structural connectivity and metric variables
Hi Marius,
Both design options are quite sensible, but they will not necessarily give the same result.
However, the second option will give a rank deficient error/warning in its current form. For the second option, a column of ones is not required because the mean (i.e., random intercept) of each subject is modelled. Furthermore, regressors that remain constant between the two time points (e.g. sex) should not be included for the same reason. Finally, if you include the interaction between time and HAMD, the column modelling the main effect of HAMD should be removed. So, we would have one column for time, one column for interaction between time and HAMD and N columns for random intercepts, where N is the number of subjects.
One thing that you may want to consider in first option is controlling for baseline HAMD scores. This may be important, depending on the context.
Andrew
Originally posted by Marius Gruber:
Both design options are quite sensible, but they will not necessarily give the same result.
However, the second option will give a rank deficient error/warning in its current form. For the second option, a column of ones is not required because the mean (i.e., random intercept) of each subject is modelled. Furthermore, regressors that remain constant between the two time points (e.g. sex) should not be included for the same reason. Finally, if you include the interaction between time and HAMD, the column modelling the main effect of HAMD should be removed. So, we would have one column for time, one column for interaction between time and HAMD and N columns for random intercepts, where N is the number of subjects.
One thing that you may want to consider in first option is controlling for baseline HAMD scores. This may be important, depending on the context.
Andrew
Originally posted by Marius Gruber:
Dear Andrew,
We are currently working on a longitudinal analysis with two time points (T1 and T2). We want to test the association between longitudinal changes in structural connectivity and longitudinal changes in a metric predictor, namely depression symptom severity (measured via Hamilton Depression Rating Scale).
Our first idea is to use a standard ANCOVA model to test the association between the difference in connectivity matrices (T2-T1) and the differences in HAMD scores (T2-T1) while correcting for baseline values of age and sex. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -9 35 0
1 -5 22 1
with the first column modeling the intercept, the second column modeling the difference in HAMD scores, the third column modeling the age at baseline, and the fourth column modeling the participants' sex.
An alternative we thought of would be to use a repeated measures ACNOVA with a design matrix containing a constant (1), the time points (-1 or 1), and the interaction of time and either the HAMD score at T1 or the HAMD score at T2, and the columns that model each participant's random intercept. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -1 -15 1 0
1 -1 -20 0 1
1 1 6 1 0
1 1 10 0 1
Is the second design matrix correctly specified in this way? And which of the two alternatives would be more sensible in your view?
Thank you very much in advance!
Marius
We are currently working on a longitudinal analysis with two time points (T1 and T2). We want to test the association between longitudinal changes in structural connectivity and longitudinal changes in a metric predictor, namely depression symptom severity (measured via Hamilton Depression Rating Scale).
Our first idea is to use a standard ANCOVA model to test the association between the difference in connectivity matrices (T2-T1) and the differences in HAMD scores (T2-T1) while correcting for baseline values of age and sex. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -9 35 0
1 -5 22 1
with the first column modeling the intercept, the second column modeling the difference in HAMD scores, the third column modeling the age at baseline, and the fourth column modeling the participants' sex.
An alternative we thought of would be to use a repeated measures ACNOVA with a design matrix containing a constant (1), the time points (-1 or 1), and the interaction of time and either the HAMD score at T1 or the HAMD score at T2, and the columns that model each participant's random intercept. For two participants with HAMD scores 15 and 20 at T1 and 6 and 10 at T2, our design matrix would look like this:
1 -1 -15 1 0
1 -1 -20 0 1
1 1 6 1 0
1 1 10 0 1
Is the second design matrix correctly specified in this way? And which of the two alternatives would be more sensible in your view?
Thank you very much in advance!
Marius