CODEWITHSUNDEEP
rmetafor
J_B
J_B

Reputation: 11

Metafor: How to get confidence interval for I^2 in fixed-effect meta-analysis

I'm trying to get a confidence interval for the I^2 heterogeneity statistic from a fixed-effect meta-analysis I've run using the R package metafor.

It seems like the confint() function doesn't work for fixed effect meta-analyses?

Appreciate any pointers!

Upvotes: 1

Views: 765

Answers (2)

retodomax
retodomax

Reputation: 615

Newer versions of metafor (> 4.6) seem to include I^2 in the output of equal/fixed-effects models. It uses the formula based on the Q statistics included in the metafor FAQ.

I^2 = 100% * (Q-(k-1))/Q

The Q statistic measures the amount of heterogeneity (even if you don't model the heterogeneity in a fixed effects model). If you really need confidence intervals, you could use the bootstrap approach (as explained here for R^2). However, as mentioned by @Emily Kothe, if you think I^2 is very relevant for your data, then a random effects model would probably make more sense (which returns confidence intervals much simpler):

library(metafor)
dat <- escalc(measure="OR", ai=xTi, n1i=nTi, ci=xCi, n2i=nCi, add=1/2,
              to="all", data=dat.viechtbauer2021)
fit <- rma(yi, vi, data=dat, method="REML")
confint(fit)
#> 
#>        estimate   ci.lb   ci.ub 
#> tau^2    0.2943  0.1270  0.6863 
#> tau      0.5425  0.3563  0.8284 
#> I^2(%)  80.5415 64.1003 90.6119 
#> H^2      5.1392  2.7855 10.6518

Created on 2024-12-11 with reprex v2.1.1

Upvotes: 1

Emily Kothe
Emily Kothe

Reputation: 872

The assumption of fixed effects meta-analysis is that there is no heterogeneity in the effect. All differences in the observed effects are assumed to be due to sampling variance. As I^2 is the proportion of observed variance attributable to heterogeneity rather than sampling variance, metafor does not estimate an I^2 value when you use a fixed effect model (see below for sample output using fixed and random effects). This is why you cannot obtain the confidence interval around the I^2 value. 

library(metafor)
#> Warning: package 'metafor' was built under R version 3.5.2
#> Loading required package: Matrix
#> Loading 'metafor' package (version 2.0-0). For an overview 
#> and introduction to the package please type: help(metafor).

rma(yi = yi, vi = vi, data = dat.bangertdrowns2004, method = "FE")
#> 
#> Fixed-Effects Model (k = 48)
#> 
#> Test for Heterogeneity: 
#> Q(df = 47) = 107.1061, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se    zval    pval   ci.lb   ci.ub     
#>   0.1656  0.0269  6.1499  <.0001  0.1128  0.2184  ***
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

rma(yi = yi, vi = vi, data = dat.bangertdrowns2004)
#> 
#> Random-Effects Model (k = 48; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of total heterogeneity): 0.0499 (SE = 0.0197)
#> tau (square root of estimated tau^2 value):      0.2235
#> I^2 (total heterogeneity / total variability):   58.37%
#> H^2 (total variability / sampling variability):  2.40
#> 
#> Test for Heterogeneity: 
#> Q(df = 47) = 107.1061, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se    zval    pval   ci.lb   ci.ub     
#>   0.2219  0.0460  4.8209  <.0001  0.1317  0.3122  ***
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Created on 2019-02-16 by the reprex package (v0.2.0).

Upvotes: 1

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