library(metafor)
dat <- get(data(dat.berkey1998))
V <- bldiag(lapply(split(dat[,c("v1i", "v2i")], dat$trial), as.matrix))
res <- rma.mv(yi, V, mods = ~ outcome - 1, random = ~ outcome | trial, struct="UN", data=dat, method="ML")
print(res, digits=3)
> dat
trial author year ni outcome yi vi v1i v2i
1 1 Pihlstrom et al. 1983 14 PD 0.4700 0.0075 0.0075 0.0030
2 1 Pihlstrom et al. 1983 14 AL -0.3200 0.0077 0.0030 0.0077
3 2 Lindhe et al. 1982 15 PD 0.2000 0.0057 0.0057 0.0009
4 2 Lindhe et al. 1982 15 AL -0.6000 0.0008 0.0009 0.0008
5 3 Knowles et al. 1979 78 PD 0.4000 0.0021 0.0021 0.0007
6 3 Knowles et al. 1979 78 AL -0.1200 0.0014 0.0007 0.0014
7 4 Ramfjord et al. 1987 89 PD 0.2600 0.0029 0.0029 0.0009
8 4 Ramfjord et al. 1987 89 AL -0.3100 0.0015 0.0009 0.0015
9 5 Becker et al. 1988 16 PD 0.5600 0.0148 0.0148 0.0072
10 5 Becker et al. 1988 16 AL -0.3900 0.0304 0.0072 0.0304
I am trying to understand this example documented here. Each study has 2 correlated outcomes (PD and AL). And the goal of this analysis is to estimate a combined effect size fo PD, and to estimate a combined effect size for AL, correct?
What exactly are the grey diamonds overlapping the effect size & CI for each study? And why is there no combined effect at the bottom of the forest plot? In my mind I was expecting 2 forest plots: 1 for the combined effect size of PD, and one of the combined effect size of AL, am I understanding the analysis correctly?
res2
Multivariate Meta-Analysis Model (k = 10; method: ML)
Variance Components:
outer factor: trial (nlvls = 5)
inner factor: outcome (nlvls = 2)
estim sqrt k.lvl fixed level
tau^2.1 0.0261 0.1617 5 no AL
tau^2.2 0.0070 0.0837 5 no PD
rho.AL rho.PD AL PD
AL 1 0.6992 - no
PD 0.6992 1 5 -
Test for Residual Heterogeneity:
QE(df = 8) = 128.2267, p-val < .0001
Test of Moderators (coefficient(s) 1,2):
QM(df = 2) = 155.7733, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
outcomeAL -0.3379 0.0798 -4.2368 <.0001 -0.4943 -0.1816 ***
outcomePD 0.3448 0.0495 6.9721 <.0001 0.2479 0.4418 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
A quick look at the summary of res
shows me an estimate of AL and PD. Are these the combined effect sizes for AL, and PD, respectively? And what exactly does mods = ~ outcome - 1
do?
outcomeAL
as the overall effect of AL across all 5 studies? And similarly foroutcomePD
$\endgroup$