[R-meta] mean-variance relationships introduces additional heterogeneity, how?

[Luke Martinez]

Hello All,

I wanted to follow up on an answer
(https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-October/003354.html)
on the list that, in a nutshell, says:

Existence of a relationship between the Mean and SD for a given study
group (e.g., Treatment), over a couple of time points, can potentially
introduce additional heterogeneity in the SMD effect sizes across the
studies.

I was wondering how exactly this heterogeneity comes about?

A part of me says that such a Mean-SD relationship for a given study
group over time is indicative of what Hedges' (1981;
https://doi.org/10.3102/10769986006002107) refers to as
"subject-treatment interaction"?

Another part of me says, no, "subject-treatment interaction" is
controllable by adding a random effect for individuals, and thus it is
different.

I highly appreciate your insights regarding HOW Mean-SD relationship
for study groups over time can potentially introduce additional
heterogeneity in SMDs across studies?

Luke

PS:
Here are the relation I see between mean and sd of a study group
across 3 time points:
group1_Ms = c(.39, .18, .13)
group1_SDs = c(.25, .16, .13)
plot(group1_Ms, group1_SDs, type="l")