Separate covariance patterns for each treatment group

Sometimes measurements on different treatments will have different variances and covariances. For example, it may be the case that measurements are more variable on an active treatment than on a placebo. This can be allowed for by using separate sets of covariance parameters for each treatment group. For example, if the first three patients in a trial received treatments A, B and A and were each measured at three time points, then the R matrix for these patients with separate compound symmetry structures for each treatment would be

(-1

Oa

Oa

0

0

0

0

0

0

Oa

-A

Oa

0

0

0

0

0

0

0A

Oa

-A

0

0

0

0

0

0

0

0

0

-B2

Ob

Ob

0

0

0

0

0

0

Ob

-B2

Ob

0

0

0

0

0

0

Ob

Ob

-b2

0

0

0

0

0

0

0

0

0

-A

Oa

Oa

0

0

0

0

0

0

Oa

-A

Oa

0

0

0

0

0

0

Oa

Oa

-D

Alternatively, if a general structure were used for each treatment group, then the R matrix would be

If most of the covariances were small or negative, then observations on the same patient could be made uncorrelated, while different variances were still allowed for each treatment:

-A, 1

oa, 12

oa, 13

0

0

0

0

0

0

oa, 12

-A,2

0a,23

0

0

0

0

0

0

0A, 13

0A,23

-A2,3

0

0

0

0

0

0

0

0

0

-B,1

ob,12

ob, 13

0

0

0

0

0

0

ob, 12

-B,2

ob,23

0

0

0

0

0

0

ob, 13

ob,23

-B,3

0

0

0

0

0

0

0

0

0

-A,1

oa, 12

oa, 13

0

0

0

0

0

0

oa, 12

-A2,2

0a,23

0

0

0

0

0

0

oa, 13

0a,23

-A,3

-A2

0

0

0

0

0

0

0

0

0

-A2

0

0

0

0

0

0

0

0

0

-A2

0

0

0

0

0

0

0

0

0

-B2

0

0

0

0

0

0

0

0

0

-B2

0

0

0

0

0

0

0

0

0

-B2

0

0

0

0

0

0

0

0

0

-A2

0

0

0

0

0

0

0

0

0

-A2

0

0

0

0

0

0

0

0

0

-A2

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