[R-meta] HKSJ adjusted error by hand

[Yefeng Yang]

Hi James,

Thank you for you quick and helpful code.

Interesting to see the scale factor (S_sq  in you notation) is just the heterogeneity measure H^2, which is equal to Q / df. If this is the case, I am wondering why this adjustment has not been extended to multilevel/multivariate meta-analysis, given that one can also derive the scale factor from these relative complex meta-analyses?

Best,
Yefeng


________________________________
From: James Pustejovsky <jepusto using gmail.com>
Sent: Friday, September 27, 2024 0:41
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Yefeng Yang <yefeng.yang1 using unsw.edu.au>
Subject: Re: [R-meta] HKSJ adjusted error by hand

The adjustment is just a scalar that can be calculated "by hand" from the weights and residuals of the model. Here's an example, which could be turned into a function:

library(metafor)

dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

rma_fit <- rma(yi, vi, mods = ~ ablat + year, data=dat)

# Calculate variance factor
wi <- 1 / (rma_fit$vi + rma_fit$tau2)
ri <- residuals(rma_fit)
df <- rma_fit$k - rma_fit$p
S_sq <- sum(wi * ri^2) / df

# Scale the variance-covariance matrix
V_hksj <- S_sq * vcov(rma_fit)

# Check against rma.uni()
rma_hksj <- update(rma_fit, test = "hksj")
all.equal(V_hksj, vcov(rma_hksj))

Depending on your preferred settings, you might need to adjust by taking max(S_sq, 1).

James

On Thu, Sep 26, 2024 at 9:03 AM Yefeng Yang via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org<mailto:r-sig-meta-analysis using r-project.org>> wrote:
Dear community,

I am wondering whether there is a post-hoc way to calculate sampling variances of the estimated regression coefficients from meta-analysis models based on the Hartung-Knapp-Sidik-Jonkman method.

To be more precise,

  1.
I first fit a normal random-effect meta-analysis via `rma()` in metafor package:

library(metafor)
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
mod <- rma(yi, vi, data=dat),


  1.
then, how can I get the adjusted standard error of the estimated coefficients (in this case, it is an intercept) based on the model object `mod`?

Of course, we can get it using an on-the-fly way:
rma(yi, vi, data=dat, test = "hksj")

But I have a couple of big datasets and want to report both the original standard and adjusted errors. I do not have a high-performance PC and I would like to avoid 're-fitting' the meta-analysis.

Best,
Yefeng





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