[R-meta] Comparing estimates of independent subgroups
Martineau, Roger
Roger.Martineau at AGR.GC.CA
Mon Oct 2 16:42:28 CEST 2017
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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