# [R-meta] Which method to compute 95% confidence intervals around individual effect sizes (standardized mean differences) ?

Dakis-Yaoba OUEDRAOGO d@k|@-y@ob@@ouedr@ogo @end|ng |rom mnhn@|r
Tue May 25 11:10:35 CEST 2021

```Dear Wolfang,

thank you for your answer, methods 1 and 2 gave indeed the same results, sorry I did not ckeck correctly. Unfortunately confidence intervals computed from method 1 and 3 are different.
Sometimes they are very different one being positive and the other negative (which is my main problem).
Please find below an example from my data with problematic cases highlighted with *!!!*
(cilow1 and ciup1 are lower CI computed with method 1, whereas cilow3 and ciup3 are upper CI computed from method 3 (rma.mv model))

cilow1 cilow3   ciup1   ciup3
1:  0.316  0.600   3.721   3.436
2:  3.758  3.223  11.928  12.463
3:  1.103  1.744   5.284   4.643
4:  3.027  4.369   9.975   8.634
5:  3.029  3.882   9.980   9.127
6: 10.258 15.743  30.346  24.861
7: 11.055 14.887  32.647  28.815
8:  7.519  7.137  22.475  22.857
9: 36.817 31.138 107.667 113.346
10: -0.804 -1.088   2.032   2.317
11:  4.374  4.909  13.613  13.079

12: -0.581 -1.222   2.318   2.959
13:  1.175 -0.166   5.440   6.782 *!!!*
14:  1.921  1.068   7.166   8.019
15:  4.305 -1.180  13.422  18.907 *!!!*
16:  6.964  3.132  20.893  24.725
17:  7.929  8.311  23.649  23.267
18: 42.736 48.415 124.944 119.265

Looking specifically at rows 12 to 18, this is the same experiment testing increasing concentration of a chemical from row 12 to 18 with all compared to the same control. When I look to the raw data, confidence intervals provided with method 1 (cilow1) seem logical because there is an increasing effect of the chemical with increasing concentration, whereas the lack of effect indicated by cilow3 for line 15 seem very strange.
Based on this I think I will finally choose the method 1, but it would be very nice to understand why the model gives different confidence intervals.

Best wishes,
Dakis

----- Mail original -----
De: "Viechtbauer, Wolfgang (SP)" <wolfgang.viechtbauer using maastrichtuniversity.nl>
À: "Dakis-Yaoba OUEDRAOGO" <dakis-yaoba.ouedraogo using mnhn.fr>, "r-sig-meta-analysis" <r-sig-meta-analysis using r-project.org>
Envoyé: Dimanche 23 Mai 2021 19:06:01
Objet: RE: Which method to compute 95% confidence intervals around individual effect sizes (standardized mean differences) ?

Dear Dakis,

All three methods you listed should give you identical results.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Dakis-Yaoba OUEDRAOGO
>Sent: Tuesday, 18 May, 2021 17:00
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Which method to compute 95% confidence intervals around
>individual effect sizes (standardized mean differences) ?
>
>Dear all,
>
>I am gathering studies about effects of various chemicals on corals, and for every
>concentration of a chemical I computed the standardized mean differences for
>several outcomes. My final goal is to know for which maximal concentration of a
>chemical no significant effect is observed, and for which minimal concentration of
>a chemical a significant effect is observed.
>To get this I computed the 95% confidence intervals around the standardized mean
>differences to identify the effect sizes that are significantly/non significantly
>different from zero.
>
>I am quite confused about how to properly compute these condidence intervals. I
>could see 3 different types of CI :
>
>1/ 95% CI assuming a normal distribution
>data\$cilow <- data\$yi - sqrt(data\$vi)*qnorm(0.05/2, lower.tail = FALSE)
>data\$ciup <- data\$yi + sqrt(data\$vi)*qnorm(0.05/2, lower.tail = FALSE)
>
>2/ 95% Wald-type confidence intervals
>These are computed using the summary.escalc() function in metafor
>
>3/ The confidence intervals computed from a multi-level model rma.mv where a
>variance-covariance matrix V is specified to take into account that I have several
>concentrations compared to the same control (Correction of Gleser & Olkin, I
>followed the tutorial in
>http://www.metafor-
>project.org/doku.php/analyses:gleser2009#quantitative_response_variable
>to compute V)
>
>mod <- rma.mv(yi=yi, V=V, mods= ~1, random= ~1 | ID_case, data=data,
>method="REML")
>
>With forest(mod) I can see the individual study 95%CI on the plot and I can get
>them with
>mod\$yi - sqrt(mod\$vi)*qnorm(0.05/2, lower.tail = FALSE)
>mod\$yi + sqrt(mod\$vi)*qnorm(0.05/2, lower.tail = FALSE)
>
>Because the method chosen to compute the 95% CI around the individual standardized
>mean differences will greatly influence the conclusions about the problematic
>chemical concentrations, I will greatly appreciate any help, comment or advise on
>my issue.
>
>Best wishes,
>Dakis

```

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