[R-meta] Meta-analyzing gain effects

[Zhouhan Jin]

Dear Wolfgang,

here is a simple example based on my original post (quasi-experimental studies i.e., unequal baselines). Q: Which approach to estimating the gain effects is methodologically more appropriate and common?

# Approach 1: Data to compute SMDs at each time point
smd_dat <- read.table(header=T, text="
study time   nt nc    mt    mc  sdt  sdc
1     pre    28 58  0.89  1.22 1.40 1.76
1     post1  28 58  5.07  3.52 3.20 2.58
1     post2  28 58  3.64  2.86 3.15 2.80
2     pre    38 48  1.89  2.22 0.40 0.76
2     post1  38 48  4.07  2.52 2.20 1.58
")

# Approach 2: Same data reformatted to compute gains before meta-analysis
smcc_dat <- read.table(header=T, text="
study time_interval   group      ni    mpre    mpost  sdpre  sdpost
1     pre-post1       treat      28    .89     5.07   1.40   3.2
1     pre-post2       treat      28    .89     3.64   1.40   3.15
1     pre-post1       contl      58   1.22     3.52   1.76   2.58
1     pre-post2       contl      58   1.22     2.86   1.76   3.15
2     pre-post1       treat      38   2.22     4.07   0.40   2.20
2     pre-post1       contl      48   2.22     1.58   0.76   1.58
")

library(emmeans)

smd <- escalc("SMD", n1i=nt, n2i=nc, m1i=mt, m2i=mc, sd1i=sdt, sd2i=sdc, data=smd_dat)
smcc <- escalc("SMCC", ni=ni, m1i=mpost, m2i=mpre, sd1i=sdpre, sd2i=sdpost, ri=rep(.5,6), data=smcc_dat) # needs ri

# Approach 1
a1 <- rma(yi ~ time-1, vi, data = smd)

gr1 <- emmprep(a1)

# Contrast hypotheses to estimate gains meta-analytically
contrast(gr1, list("gain1"=c(1,0,-1), "gain2"=c(0,1,-1)))

# Approach 2
a2 <- rma(yi ~ time_interval*group, vi, data = smcc)

gr2 <- emmprep(a2)

# Just get the EMMs, don't run hypothesis:
emmeans(gr2, ~ time_interval*group)

Best wishes,

Zhouhan

On Mar 11, 2024 at 10:51 -0400, Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
[????????? wolfgang.viechtbauer using maastrichtuniversity.nl ????????? https://aka.ms/LearnAboutSenderIdentification?????????????]

Dear Zhouhan,

Could you provide a small reproducible toy example illustrating the two different approaches you are contrasting below? I could provide me own interpretation of what it is that you are describing, but it would be a lot easier if you show an example.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
Of Zhouhan Jin via R-sig-meta-analysis
Sent: Monday, March 11, 2024 15:27
To: r-sig-meta-analysis using r-project.org
Cc: Zhouhan Jin <zjin65 using uwo.ca>
Subject: [R-meta] Meta-analyzing gain effects

Dear R meta Community,
(reposting this as I think my first message fell through the cracks)

When meta-analyzing quasi-experimental longitudinal studies, I wonder which
approach I should take to estimate the gains:

1- Meta-analyze the effects (e.g., SMDs) at each time point and then after
modeling, run appropriate hypotheses to estimate treatments' gains meta-
analytically?

OR

2- Compute the gain effects (e.g., SMCCs in escalc) in the dataset, and meta-
analyze them by a model to estimate the treatments' gains directly?

PS. I personally prefer the first approach as it doesn't directly require the
pre-post correlations.

Best wishes,

Zhouhan

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