[R-meta] HKSJ adjusted error by hand

[James Pustejovsky]

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> 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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>
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