[R-meta] Comparing estimates of independent subgroups

[Martineau, Roger]

Hi list members,

Dr Viechtbauer used the BCG vaccine meta-analysis to illustrate how the difference between estimates from independent meta-analyses (or subgroups)  can be tested: http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates

In this example, 2 RE models were fitted separately to each subset of the “alloc” variable (i.e., random/other) using the rma ( ) function. Then, the 2 estimates were compared using a FE model. This example was for a simple 2-level model. I would like to know if the example could be extended to a 3-level model?

Therefore, let’s create a new variable “publication” (A, B, C, D and E) and assume that “trial” (1 to 13) is nested within “publication”:

library(metafor)
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
dat$alloc <- ifelse(dat$alloc == "random", "random", "other")
dat$publication <- ifelse(dat$trial<=4, "A",
                          ifelse(dat$trial>4&dat$trial<=6, "B",
                                 ifelse(dat$trial>6&dat$trial<=9, "C",
                                        ifelse(dat$trial>9&dat$trial<=11, "D", "E"))))

The 2 separate RE multilevel models would be:
(res1a <- rma.mv(yi, vi, data=dat, subset=alloc=="random",random = ~1|publication/trial))
(res2a <- rma.mv(yi, vi, data=dat, subset=alloc=="other",random = ~1|publication/trial))

(dat.comp.a <- data.frame(estimate = c(coef(res1a), coef(res2a)),
                        stderror = c(res1a$se, res2a$se),
                        meta = c("random","other"),
                        sigma2.1 = round(c(res1a$sigma2[1], res2a$sigma2[1]),3),
                        sigma2.2 = round(c(res1a$sigma2[2], res2a$sigma2[2]),3)))
    estimate  stderror   meta sigma2.1 sigma2.2
1 -0.9386383 0.4183251 random    0.246    0.238
2 -0.4757994 0.2266656  other    0.016    0.204

(rma(estimate, sei=stderror, mods = ~ meta, method="FE", data=dat.comp.a, digits=3))
Model Results:
            estimate     se    zval   pval   ci.lb   ci.ub
intrcpt       -0.476  0.227  -2.099  0.036  -0.920  -0.032  *
metarandom    -0.463  0.476  -0.973  0.331  -1.395   0.470
The difference between the 2 estimates is not significant (z-value = -0.973 with P-value = 0.331).

Fitting a meta-regression multilevel model using all studies with different amount of residual heterogeneity in each each subset of “alloc”:
(rma.mv(yi, vi, mods = ~ alloc, random = ~alloc|publication/trial, struct="DIAG", data=dat, digits=3))

Model Results:

             estimate     se    zval   pval   ci.lb  ci.ub

intrcpt        -0.449  0.460  -0.975  0.330  -1.351  0.453

allocrandom    -0.487  0.666  -0.732  0.464  -1.793  0.818
The z-value, P-value, coefficients and SE do not match the results obtained in the 2 separate RE multilevel models.

Any assistance would be greatly appreciated,

Roger ☺

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