Analyzing change with linear mixed effects models

[Lucy Hiscox]

Hi,

I am hoping someone can help me.

I am looking at the effect of acute exercise on brain structure over time.

I have 30 subjects, split into 2 groups: Exercise (N=20) and Control (N=10)

In all subjects, there was a MRI scan (and cognitive tests) (1) immediately before, (2) immediately after, and (3) 1 hour after the Activity Block (exercise, or rest for controls).

In my first aim, I wanted to see whether brain changes were different between groups (Exercise vs control) over time (scan [factor variable, time1,2,and 3]) and ran a linear mixed model:

xtmixed whole_brain_mu group##scan i.sex c.age || id:, var noconst residuals(unstr, t(scan)) reml
contrast group##scan

This provides a significant interaction between group and time, as expected: F_2,39.22 = 13.31, p = .0010

I then wanted to see whether there was an interaction between group and time on cognitive performance:

xtmixed flanker_inc_rt group##scan i.sex c.age || id:, var noconst residuals(unstr, t(scan)) reml
contrast group##scan

which there was: F_2,35.30 = 11.00, p = .0041

What I now want to do, is analyse whether the changes observed in brain structure are related to the changes observed in cognition, and whether this differs by group.

One option was to perform a regression and calculate difference scores between scan 1 and scan 2 in brain structure, and calculate difference scores between scan 1 and scan 2 in cognition. But then I am missing the effects of scan 3 (presumably everything returning to baseline).
I also am not sure how this design would consider between-subject and within-subject effects (as in the first lines of code).

Any advice would be much appreciated.

Thanks,
Lucy

[Lucy Hiscox]

Data below:

[Lucy Hiscox]

input byte(id group sex) double age byte scan double whole_brain_mu int flanker_inc_rt
 1 1 1 19.65 1  2.779 611
 1 1 1 19.65 2 2.8865   .
 1 1 1 19.65 3  2.938 552
 2 1 0 19.79 1 2.8303 515
 2 1 0 19.79 2  2.706   .
 2 1 0 19.79 3 2.8309 534
 3 1 0 22.47 1 2.8026 509
 3 1 0 22.47 2 2.6632   .
 3 1 0 22.47 3 2.8266 459
 4 1 1 20.53 1 3.0665 597
 4 1 1 20.53 2 2.9192   .
 4 1 1 20.53 3 2.8305 560
 5 0 1 20.54 1 2.8067 577
 5 0 1 20.54 2 2.9067   .
 5 0 1 20.54 3 2.7982 597
 6 1 1 24.39 1 2.7701 649
 6 1 1 24.39 2 2.5172   .
 6 1 1 24.39 3 2.7511 542
 7 1 1 22.34 1 2.6797 586
 7 1 1 22.34 2 2.5227   .
 7 1 1 22.34 3   2.71 576
 8 1 0  19.1 1  2.847 525
 8 1 0  19.1 2 2.7707 482
 8 1 0  19.1 3 2.8263 521
 9 1 0 19.63 1 2.7862 561
 9 1 0 19.63 2 2.7173 519
 9 1 0 19.63 3 2.8551 525
10 1 1 23.38 1 2.6764 635
10 1 1 23.38 2   2.51   .
10 1 1 23.38 3 2.6415 612
11 1 1  24.8 1 2.8238 808
11 1 1  24.8 2 2.6421 669
11 1 1  24.8 3 2.8527 652
12 1 1 24.27 1 2.7843 502
12 1 1 24.27 2  2.678 490
12 1 1 24.27 3 2.7973 478
13 0 1 21.33 1 2.7188 526
13 0 1 21.33 2 2.6568 495
13 0 1 21.33 3 2.7556 506
14 1 1 21.18 1 2.6368 454
14 1 1 21.18 2 2.5191 484
14 1 1 21.18 3 2.6911 468
15 0 1 21.96 1  2.515 534
15 0 1 21.96 2 2.5181 477
15 0 1 21.96 3 2.5438 459
16 1 1 21.84 1  2.708 530
16 1 1 21.84 2 2.5153 517
16 1 1 21.84 3 2.7338 505
17 1 0 23.21 1 2.8715 487
17 1 0 23.21 2 2.6165 424
17 1 0 23.21 3 2.8309 463
18 1 0 26.42 1 2.7411 552
18 1 0 26.42 2 2.6225 491
18 1 0 26.42 3 2.8017 480
19 0 0  23.3 1 2.9521 593
19 0 0  23.3 2 2.7254 585
19 0 0  23.3 3 2.8178 514
20 0 0 20.99 1 2.5776 640
20 0 0 20.99 2 2.6514 676
20 0 0 20.99 3 2.6365 621
21 0 0 27.13 1 2.6038 514
21 0 0 27.13 2 2.6092 506
21 0 0 27.13 3 2.6431 557
22 1 0 19.42 1 2.6777 540
22 1 0 19.42 2 2.4152 464
22 1 0 19.42 3 2.5506 515
23 0 1 21.33 1 2.4942 537
23 0 1 21.33 2 2.5842 559
23 0 1 21.33 3 2.5922 546
24 1 0 20.15 1  2.723 593
24 1 0 20.15 2 2.7915 517
24 1 0 20.15 3 2.7408 522
25 0 0 30.36 1 2.9172 534
25 0 0 30.36 2 2.8434 536
25 0 0 30.36 3  2.871 510
26 1 0 26.49 1 2.9862 523
26 1 0 26.49 2 2.8391 454
26 1 0 26.49 3 2.9984 508
27 1 1 22.32 1 2.6267 508
27 1 1 22.32 2 2.6333 484
27 1 1 22.32 3 2.8271 483
28 1 1 25.21 1 2.6864 465
28 1 1 25.21 2 2.6786 463
28 1 1 25.21 3  2.717 533
29 0 0 23.04 1 2.6642 480
29 0 0 23.04 2 2.6514 493
29 0 0 23.04 3 2.6606 489
30 0 0 25.84 1 2.8856 514
30 0 0 25.84 2 2.8253 494
30 0 0 25.84 3 2.8116 456
end
label values group labels0
label def labels0 0 "Control", modify
label def labels0 1 "Exercise", modify
label values sex labels1
label def labels1 0 "Male", modify
label def labels1 1 "Female", modify
[/CODE]