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

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Tue Jun 1 19:35:10 CEST 2021

```Dear Dakis,

Method 3 should give the same results. The yi and vi elements in 'mod' are just the original data -- these are not modified or changed by the model that is fitted.

Here is a fully reproducible example (using one of the Gleser & Olkin, 2009, examples) showing that all three methods give the exact same CIs:

library(metafor)

dat <- data.frame(study=c(1,1,2,3,3,3), trt=c(1,2,1,1,2,3),
ai=c( 40, 40, 10,150,150,150), n1i=c(1000,1000,200,2000,2000,2000),
ci=c(100,150, 15, 40, 80, 50), n2i=c(4000,4000,400,1000,1000,1000))
dat\$pti <- with(dat, ci / n2i)
dat\$pci <- with(dat, ai / n1i)
dat <- escalc(measure="OR", ai=ai, ci=ci, n1i=n1i, n2i=n2i, data=dat)

calc.v <- function(x) {
v <- matrix(1/(x\$n1i[1]*x\$pci[1]*(1-x\$pci[1])), nrow=nrow(x), ncol=nrow(x))
diag(v) <- x\$vi
v
}

V <- bldiag(lapply(split(dat, dat\$study), calc.v))

res <- rma.mv(yi, V, mods = ~ factor(trt) - 1, data=dat)
res

cbind(dat\$yi - sqrt(dat\$vi)*qnorm(0.05/2, lower.tail=FALSE),
dat\$yi + sqrt(dat\$vi)*qnorm(0.05/2, lower.tail=FALSE))

cbind(summary(dat)\$ci.lb, summary(dat)\$ci.ub)

cbind(res\$yi - sqrt(res\$vi)*qnorm(0.05/2, lower.tail = FALSE),
res\$yi + sqrt(res\$vi)*qnorm(0.05/2, lower.tail = FALSE))

Best,
Wolfgang

>-----Original Message-----
>From: Dakis-Yaoba OUEDRAOGO [mailto:dakis-yaoba.ouedraogo using mnhn.fr]
>Sent: Tuesday, 25 May, 2021 11:11
>To: Viechtbauer, Wolfgang (SP)
>Cc: r-sig-meta-analysis
>Subject: Re: Which method to compute 95% confidence intervals around individual
>effect sizes (standardized mean differences) ?
>
>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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