[R-meta] Data Extraction

[Viechtbauer, Wolfgang (SP)]

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 using gmx.de [mailto:t.saueressig using 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 using 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 using 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 using maastrichtuniversity.nl>
>>An: "Tobias Saueressig" <t.saueressig using gmx.de>, "r-sig-meta-analysis using r-
>>project.org" <r-sig-meta-analysis using 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 using r-
>>project.org]
>>>On Behalf Of Tobias Saueressig
>>>Sent: Monday, 17 August, 2020 12:03
>>>To: r-sig-meta-analysis using 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
>E
>>>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