Is a t-based BIC Bayes factor approximation reasonable for three-level meta-regression?

SzTy

Hello,

I am conducting a meta-analysis that aims to compare mean values of a continuous variable X between two study types, A and B. The variable ranges roughly from 10 to 100. I also have a few study-level moderators, such as mean age and proportion of females.

I ran a meta-regression using metafor. The model is three-level, with samples nested in studies (although only a few studies include more than one sample). It is a random-effects model, fitted with REML and based on t-statistics:

res <- rma.mv(
  yi = yi,
  V = vi,
  mods = ~ Group + other_moderators,
  random = ~ 1 | Study_ID/Sample_ID,
  method = "REML",
  test = "t",
  dfs = "contain",
  data = dat
)

Group is coded as a factor comparing study type A vs B.

Since I received mostly null findings, I would like to add a simple Bayesian framework to help interpret them. I am thinking about using a BIC-based Bayes factor approximation:

BF_10 ≈ exp((t^2 - log(k)) / 2)

where (t) would be the t-statistic for the group coefficient from my model, and (k) would be the number of samples.

Do you think this is reasonable in this context? Are there any important pitfalls?

Thank you