[R-meta] Mismatch between output from sub-group analysis and forest plot

[Joao Afonso]

Dear all,

Once again I am sorry for posting this message again but I forgot to
send the outputs.

Again I am conducting a meta-analysis on prevalence and incidence
data. As there is plenty of heterogeneity I am doing a sub-group
analysis. However I
am finding the output of the same and forest plots produced to have
different values for the pooled estimates. I am using the double
arcsine transformation and then have the data back-transformed to
produce the estimates. I have amended the model following Wofgang's
reply, but the problem still remains.The updated model is the
following:

ies.da.lcmbi<-ies.da %>%
  filter(is.na(lcmbi)==FALSE)

subganal.lcmbi=rma(yi, vi, data=ies.da.lcmbi, mods=~lcmbi, method="DL")
pes.da.lcm=rma(yi, vi, data=ies.da.lcmbi, subset = lcmbi=="Records",
method="DL")
pes.da.records=rma(yi, vi, data=ies.da.lcmbi, subset =
lcmbi=="Locomotion Scoring Method", method="DL")
pes.subg.lcmbi=predict(subganal.lcmbi,
transf=transf.ipft.hm,
targ=list(ni=prevalence_2020_cow_nomv$ssizeanimal))
dat.samevar=data.frame(estimate=c((pes.da.lcm$b)[1], (pes.da.records$b)[1]),
stderror=c((pes.da.lcm$se)[1], (pes.da.records$se)[1]),
tau2=subganal.lcmbi$tau2)
pes.da.lcmbi=rma(estimate, sei=stderror,
method="DL",
data=dat.samevar)
pes.lcmbi=predict(pes.da.lcmbi, transf=transf.ipft.hm,
targ=list(ni=prevalence_2020_cow_nomv$ssizeanimal))
print(pes.da.lcm, digits=3) #display subgroup 1 summary effect size
print(pes.da.records, digits=3) #display subgroup 2 summary effect size
print(subganal.lcmbi, digits=3) #display subgroup analysis results
print(pes.lcmbi, digits=3) #display recomputed summary effect size

Which produces the following output:

Random-Effects Model (k = 11; tau^2 estimator: DL)

tau^2 (estimated amount of total heterogeneity): 0.027 (SE = 0.021)
tau (square root of estimated tau^2 value):      0.164
I^2 (total heterogeneity / total variability):   99.93%
H^2 (total variability / sampling variability):  1428.81

Test for Heterogeneity:
Q(df = 10) = 14288.143, p-val < .001

Model Results:

estimate     se   zval   pval  ci.lb  ci.ub
   0.506  0.051  9.905  <.001  0.406  0.606  ***

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> print(pes.da.records, digits=3) #display subgroup 2 summary effect size

Random-Effects Model (k = 22; tau^2 estimator: DL)

tau^2 (estimated amount of total heterogeneity): 0.011 (SE = 0.007)
tau (square root of estimated tau^2 value):      0.104
I^2 (total heterogeneity / total variability):   99.23%
H^2 (total variability / sampling variability):  130.14

Test for Heterogeneity:
Q(df = 21) = 2732.942, p-val < .001

Model Results:

estimate     se    zval   pval  ci.lb  ci.ub
   0.600  0.024  25.359  <.001  0.553  0.646  ***

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> print(subganal.lcmbi, digits=3) #display subgroup analysis results

Mixed-Effects Model (k = 33; tau^2 estimator: DL)

tau^2 (estimated amount of residual heterogeneity):     0.022 (SE = 0.013)
tau (square root of estimated tau^2 value):             0.148
I^2 (residual heterogeneity / unaccounted variability): 99.82%
H^2 (unaccounted variability / sampling variability):   549.07
R^2 (amount of heterogeneity accounted for):            29.36%

Test for Residual Heterogeneity:
QE(df = 31) = 17021.085, p-val < .001

Test of Moderators (coefficient 2):
QM(df = 1) = 2.899, p-val = 0.089

Model Results:

              estimate     se    zval   pval   ci.lb  ci.ub
intrcpt          0.601  0.033  18.449  <.001   0.537  0.665  ***
lcmbiRecords    -0.096  0.056  -1.703  0.089  -0.207  0.015    .

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> print(pes.lcmbi, digits=3) #display recomputed summary effect size

  pred ci.lb ci.ub cr.lb cr.ub
 0.283 0.206 0.368 0.168 0.415


And to produce the forest plot I use the following code:

subganal.lcmbi=rma(yi, vi, data=ies.da.lcmbi, mods=~lcmbi, method="DL")
pes.summary=metaprop(nlameanimal, ssizeanimal, author, data=ies.da.lcmbi,
                     sm="PFT",
                     method.tau="DL",
                     method.ci="NAsm",
                     byvar=lcmbi,
                     tau.common=TRUE,
                     tau.preset=sqrt(subganal.lcmbi$tau2))
precision=sqrt(ies.da.lcmbi$vi)
jpeg(file="forest_cow_cow_lcmbi.jpeg", width=11, height=12, units="in", res=300)
forest(pes.summary,
       xlim=c(0,1),
       pscale=1,
       rightcols=FALSE,
       leftcols=c("studlab", "effect", "ci"),
       leftlabs=c("Study", "Prevalence", "95% C.I."),
       text.random="Prevalence of Lameness in British Dairy Cattle",
       bylab = "Lameness Data Source",
       print.byvar = TRUE,
       xlab="Prevalence of Lameness", smlab="",
       weight.study="random", squaresize=0.5, col.square="navy",
       col.diamond="maroon", col.diamond.lines="maroon",
       pooled.totals=FALSE,
       comb.fixed=FALSE,
       fs.hetstat=10,
       print.tau2=TRUE,
       print.Q=TRUE,
       print.pval.Q=TRUE,
       print.I2=TRUE,
       digits=2,
       sortvar = precision)
dev.off()

The forest plot follows attached.

Again I will be extremely grateful for any help
or guidance.

Wishing all a great day,

Joao

-
João Afonso
DVM, MSc Veterinary Epidemiology
PhD Student
Department of Infection and Global Health
University of Liverpool
+351914812305

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