Meta-analysis to calculate mean paired difference between groups (if data extracted from papers already summarised as overall mean/SD)

[Dil Singh]

Hi

I want to take data from several studies that have been published to examine the effect of a drug vs. placebo on renal function. Renal function is measured on day 1 after an operation and again on day 4. The data presented by the authors has it so that the mean and SD of each group is presented on days 1 and 4. Typically they have seemingly not presented these as paired data as she should have, but do present the mean, SD and number in each group on each day.

Is there a way of analysing data from these pooled data to end up with an appropriately analysed summary mean difference? This is assuming that there is no way to obtain the raw data.

Many thanks

[Clyde Schechter]

Well, with paired data, the mean difference is the same as the difference of the means (so long as there are no missing values). But, the standard deviation of the difference cannot be calculated from what you have described. If, however, the correlation coefficient between the day1 and day4 observations is available, then the standard deviation of the difference can be calculated:

SD(day1 - day4) = sqrt(Var(day1) + Var(day4) - 2*r*SD(day1)*SD(day4))

If all you have are the means and standard deviations, but no correlations, and no access to the underlying paired data, then the SD of the pairwise difference cannot be calculated.

[Dil Singh]

Hi

Thank you very much for taking the time to reply with an informative response - it's much appreciated.

Further to the last post and as a relative novice, I just wanted to confirm what the means means of analysis was for some data I have for an informal local project I am doing.

Attached is a screenshot of the data I have, which as I mentioned take various treatments from various studies where the renal function is measured at either day 1 after an operation or day 4 after an operation. Most (but not all) of those who have day 4 measurements also have day 1 measurements.

I have the N in each group, as well as the mean and SD where available.

In this case, if I wanted to pool the results by a treatment group, assuming that both groups had similar values before their operation and that any measured effect was due to the treatment group they were placed in, would it be appropriate to treat them as independent (i.e. non-paired) data and examine them separately, if I pointed out the reasons for doing so and limitations in not having the original data.

Essentially is it appropriate to say, "This is the summary pooled result of day 1 and this is the summary pooled result of day 4". This is in effect ignoring any pairwise differences being calculated as has been pointed out to me in the earlier post, given the coefficients between the values for day 1 and days 4 are not present nor readily available, that these cannot be calculated.

Or would any analyses simply not be possible and/or appropriate with the data I have?

Any help would be gratefully received.

Many thanks in advance.

[Clyde Schechter]

You can certainly present the day 1 results and the day 4 results separately. But if you want to in some way compare the day 1 and day 4 results to each other, you are limited to statistics that do not require a standard deviation or standard error. So you can point out what each mean is, and you can say what the confidence interval around each mean is. You can also give a point estimate of the mean difference. But you cannot give any interval estimate for the mean difference, nor any estimate of the precision of your estimate of the mean difference. And you cannot do any statistical tests of hypotheses about the mean difference.

If you do this in a manuscript intended for publication, I would certainly include an explanation that this was done due to the unavailability of the necessary information.

[Dil Singh]

Hi

Thank you so much again for taking the time for your detailed reply - it's genuinely much appreciated.

It's for a small diploma by distance learning that I'm doing and your advice has been very useful.

Regards