# Meta Analysis with continues outcome - appropriate effect calculation

I am conducting a meta analysis with studies on psychological treatments with continues outcome variables. The included studies use two different scales (either 0-20 or 0-100) for each study i have the following data:

Pre treatment: Treatment group: N, mean outcome, SD outcome Control group: N, mean outcome, SD outcome

Post treatment: TG: N,mean outcome, SD outcome CG: N,mean outcome, SD outcome

From literature i learned, that in this case i could use the difference of difference as effect size i.e.:

(mean_post_tg-mean_pre_tg)-(mean_post_cg-mean_pre_cg)

Now i am trying to conduct the meta analysis with RevMan, i choose Random Effect model on continues data. It asks me for mean,sd and N for TG and CG, what exact values do i need to provide? Only the post_treatment values?

Further: What if studies use different control groups, e.g. waiting list vs. treatment as usual?

If you want to use this outcome/effect size measure, you also need to know the pre-post correlation of the outcome scores within groups. The standard deviation/error of $\bar{x}_{post} - \bar{x}_{pre}$ within a group is a function of the group size $n$, the standard deviations $\mbox{SD}_{pre}$ and $\mbox{SD}_{post}$, and the pre-post correlation $r_{pre, post}$. To be precise: $$\mbox{SD}(\bar{x}_{post} - \bar{x}_{pre}) = \sqrt{\frac{\mbox{SD}_{pre}^2 + \mbox{SD}_{post}^2 - 2 r_{pre, post}\mbox{SD}_{pre}\mbox{SD}_{post}}{n}}.$$ Note that the numerator is the SD of the change scores, so if that is reported, you have what you need. In fact, what you plug into RevMan are the mean change (i.e., $\bar{x}_{post} - \bar{x}_{pre}$), the SD of the change scores, and the group size (for each group).

If you don't know the pre-post correlations (likely), then you could make a "guestimate" and do a bit of a sensitivity analysis afterwards to see if it matters what you plug in.

Alternatively, you could just focus on the post-test results. If these are randomized trials, then any baseline differences are purely due to chance anyway (assuming that the randomization was properly carried out within trials).

That aside, if you want to combine studies using the two different scales, you need to think about how you can put the results on a common scale. Usually, a standardized measure of effect will be needed (i.e., the standardized mean difference).

• And if the studies used different control groups you could add that as a binary moderator variable. I would recommend doing something about this as Barth et al 2013 PLoS Medicine vol 10 (5) did a network meta-analysis and showed differences between different control groups. – mdewey May 23 '16 at 9:21
• I also have similar data, without information about correlation between "pre" and "post" scores. Do you aware of any paper that uses post-hoc sensitivity analysis? – Andrej Jan 13 '17 at 14:43