[R-meta] Data Extraction
Viechtbauer, Wolfgang (SP)
wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Mon Aug 24 10:16:16 CEST 2020
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)
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.
>From: t.saueressig using gmx.de [mailto:t.saueressig using gmx.de]
>Sent: Sunday, 23 August, 2020 19:05
>To: Viechtbauer, Wolfgang (SP)
>Subject: RE: RE: [R-meta] Data Extraction
>One more question from me. From which equation does one derive this? Ist
>there a citation for this?
>Thank you in advance.
>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
>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.
>>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
>>you are my hero. Thank you.
>>I am a bit sad that I cannot include the study because it is based on
>>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
>>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
>>SD <- SE / sqrt(1/30 + 1/36)
>>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
>>to d-values that use the SD of a single time point for the standardization.
>>>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-
>>>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
>>>I have a problem to extract data from one study. I want to calculate
>>>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
>>>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?
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