[R-meta] Combining studies with different within-subject designs

[Pablo Grassi]

Dear all,

Maybe some of you can help me out with the following design-conundrum. I 
am currently performing a series of meta-analysis investigating the 
effect on an intervention in closely related outcomes. Most of the 
reviewed studies are within-subject designs (one group of participants), 
for which the standardized mean differences (SMD; Hedge's g) are 
differences of change scores divided by the SD of the difference (with 
change score standardization), as follows:

     SMD = M_diff / SDdiff   (for simplicity in this E-mail without the 
bias-correction factor)

Unfortunately, there is a huge variability in the control measurements 
used. Roughtly following the nomenclature from Morris 2008, I have the 
following different design-cases:

     Case 1) Within-subject desing, pre-post-control (WS_PPC):

                M_diff_ws_pcc = (post_Treatment - pre_Treatment) - 
(post_Control - pre_Control)

However, some others had no baseline pre-intervention measurement (i.e. 
only report post-intervention measurements), i.e. Post-test only with 
control design (WS_POWC)

     Case 2) M_diff_ws_powc = (post_Treatment - post_Control)

And some few others just have a post-pre measurement but no control 
(i.e. only report a change score, single-group pre-post, SGPP), so that:

     Case 3) M_diff_ws_sgpp = (post_Treatment - pre_Treatment)

Then, while the M_diff if Case 1 and 2 is measuring +/- the same effect, 
their SDdiffs (and thus SMDs) are not really comparable as they reflect 
different things.

Thus:

  * What would be the "standard" approach to include the within-subject
    design studies (Case 1, 2, 3) in the same meta-analysis, if this is
    possible at all? (Please consider that most of the publications
    report ONLY the SD of the change scores and NOT the SD of the pre
    and post conditions separately or in case 2 of the post-interventions).

Best,

Pablo




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