[R-meta] Data Extraction - R-SIG-meta-analysis

Mon, Aug 24, 2020 1:16 AM #

This is easily derived based on basic principles (e.g., https://en.wikipedia.org/wiki/Algebra_of_random_variables#Variance_algebra_for_random_variables). In particular, we know:

SD[x1-x2]^2 = SD[x1]^2 + SD[x2]^2 - 2*r*SD[x1]*SD[x2]

and now if we assume SD[x1] = SD[x2] = SD, we get

SD[x1-x2]^2 = 2*SD^2 - 2*r*SD^2
            = SD^2 * 2 * (1-r)

so:

SD[x1-x2] = SD * sqrt(2*(1-r))

If you need a reference, you could cite:

Morris, S. B., & DeShon, R. P. (2002). Combining effect size estimates in meta-analysis with repeated measures and independent-groups designs. Psychological Methods, 7(1), 105-125.

Best,
Wolfgang

-----Original Message-----
From: t.saueressig at gmx.de [mailto:t.saueressig at gmx.de]
Sent: Sunday, 23 August, 2020 19:05
To: Viechtbauer, Wolfgang (SP)
Cc: R-sig-meta-analysis
Subject: RE: RE: [R-meta] Data Extraction

Hello,

One more question from me. From which equation does one derive this? Ist
there a citation for this?

Thank you in advance.

Regards

Tobias

Am 18.08.2020 08:24 schrieb "Viechtbauer, Wolfgang (SP) "
<wolfgang.viechtbauer at maastrichtuniversity.nl>:
Please always cc the mailing list.

You can include the study if you know (or can guestimate) the pre-post
correlation.

SD of the change scores = SD * sqrt(2*(1-r)),

where SD is the pre or post treatment SD (this assumes that the SD is the
same before and after the treatment). So if you know r, you can easily
recover the SD and standardize in the usual manner.

Best,
Wolfgang

-----Original Message-----
From: Tobias Saueressig [mailto:t.saueressig at gmx.de]
Sent: Tuesday, 18 August, 2020 7:40
To: Viechtbauer, Wolfgang (SP)
Subject: Aw: RE: [R-meta] Data Extraction

Dear Wolfgang,

you are my hero. Thank you.

I am a bit sad that I cannot include the study because it is based on

change

scores and I have used postintervention only.

Gesendet:?Montag, 17. August 2020 um 22:33 Uhr
Von:?"Viechtbauer, Wolfgang (SP)"
<wolfgang.viechtbauer at maastrichtuniversity.nl>
An:?"Tobias Saueressig" <t.saueressig at gmx.de>, "r-sig-meta-analysis at r-
project.org" <r-sig-meta-analysis at r-project.org>
Betreff:?RE: [R-meta] Data Extraction
Dear Tobias,

The difference between the upper and lower CI bounds divided by the
appropriate critical t-value should be *twice* the SE. So:

SE <- (9.3 - -5.7) / (2*1.99)

should be the SE of the difference in the mean change between the two
groups. Dividing this by sqrt(1/n1 + 1/n2) should give you the SD of the
change scores (assuming homoscedasticity of the change variances in the two
groups), so:

SD <- SE / sqrt(1/30 + 1/36)

Hence:

1.8/SD

yields approximately 0.12. Sure you can apply the bias correction, but this
is hardly relevant here.

More importantly, this d-value standardizes the difference between the two
groups based on the (pooled) SD of the change scores. This is not

comparable

to d-values that use the SD of a single time point for the standardization.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-

project.org]

On Behalf Of Tobias Saueressig
Sent: Monday, 17 August, 2020 12:03
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] Data Extraction

Hello,

I have a problem to extract data from one study.? I want to calculate

hedges

g.

I have the following information (2 groups):

Between-group change score from baseline to follow-up (9?months) is?1.8(-
5.7,9.3) (mean and 95%CI) and p-value 0.64

Sample size is n1 = 30; n2 = 36?(two group RCT).

Link:?https://linkinghub.elsevier.com/retrieve/pii/S1063458420309882?(TABL

2 HOOS ADL)

I would do it the following way:

Calculate a SD for both group from the CI. _> SE = (Upper limit-lower
limit)/t-statistic (~2) => SD = SE/squ(1/n1?+ 1/n2)

Then g = d = MD/SD

g* = (1-3/(4*(n1+n2)-9) * g

e.g.

SE = (9.3+5.7)/1.99 = 7.54 => SD = 7.54/squ(1/30+1/36) = 7.54/0.25 = 30.16

g = 1.8/30.16 = 0.06

g* = 0.06 * (1-3/255) = 0.06 * 0.99 = 0.0594

Is that correct?

Best regards

Tobias