# Integrating different types of error/intervals in meta-analysis

Dear brms/stan community,

I have a dataset of publications with estimates, some have Standard Errors, other Confidence Intervals, some have Credible Intervals and there are still those without error estimates.
The last set I’ve removed from my analysis.
The Confidence Intervals I’ve transformed into Standard Errors, by using the formula SE = (UL - LL) / 3.92
But I am not sure how to integrate the estimates with credible intervals in the meta-analysis. What is the standard way to tackle this issue? Any ideas would be welcome.

``````ma\$v <- ifelse(
ma\$ErrorMetric == "ConfInt", # rule selects
(ma\$Max - ma\$Min)/3.92, # convert Confidence Interval
# else SE
(ma\$Max - ma\$Min)/2 # Get Standard Error from mean of max and min
)

mod <- brm(
ESTIMATION | se(v) ~ 1 + (1|Author),
family = gaussian(),
prior = priors,
data = ma,
cores = 4
)
``````
• Operating System: Win 11
• brms Version: 2.16.3

I thought about 1) do a similar transformation as the one from Conf. Int. to S.E, 2) separate the meta-analysis into 2 (one dealing with papers that have only credible intervals available, the other with frequentist estimates), 3) ignore the studies with credible intervals since they are the minority (64 out of 193).

But I am really not happy with any of these solutions. There must be a better way… I can’t be the first to deal with this.

1 Like

Hi!

Why would you not just convert the credible intervals to S.E.s (your 1)? That seems like a good way to go about this.

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Hi @matii thanks!

This was what I did first. But I asked some colleagues if they thought it was ok, and they were skeptical because credible intervals have a different nature. So, I can apply the same logic of converting confidence intervals, i.e. SE = (UL - LL) / 3.92 to credible intervals? How do I justify doing this though, since they are not the same? Maybe something like “Assuming a Gaussian shape for the posterior, the credible intervals were transformed into standard errors using the following formula SE = (UL - LL) / 3.92” etc. is enough?

Best,
J

Yeah. If the original studies didn’t use strong priors the credible intervals would be the same as confidence intervals, given the assumption you outlined.

1 Like