Source code and materials for ‘Subgroup comparisons within and across studies in meta-analysis’ (Panaro et al., 2025) https://doi.org/10.48550/arXiv.2508.15531
Large data files generated during the analyses are not included in
this repository due to GitHub’s file size limitations.
Researchers interested in accessing these data can contact me to request a copy.
All files directly related to the article (e.g., analysis scripts, figures, and supplementary materials) are included in this repository.
This README demonstrates how to apply the same or user-chosen weighting scheme across multiple meta-analytic analyses (Difference of Averages and Average Difference) using aggregate data (AgD).
The goal is to approximate IPD-level inference under a consistent information structure while allowing flexible comparison of different weighting options.
Here we begin by loading an example dataset to illustrate the SWADA concept with real numbers.
steroids <- read.csv("data/steroids.csv")
print(steroids)
#> trial drug ventilation treat.events treat.total
#> 1 CAPE COVID Hydrocortisone IV 10 61
#> 2 CAPE COVID Hydrocortisone NIV 1 14
#> 3 CoDEX Dexamethasone IV 69 128
#> 4 CoDEX Dexamethasone NIV 0 0
#> 5 COVID STEROID Hydrocortisone IV 4 7
#> 6 COVID STEROID Hydrocortisone NIV 2 8
#> 7 DEXA-COVID 19 Dexamethasone IV 2 7
#> 8 DEXA-COVID 19 Dexamethasone NIV 0 0
#> 9 RECOVERY Dexamethasone IV 95 324
#> 10 RECOVERY Dexamethasone NIV 0 0
#> 11 REMAP-CAP Hydrocortisone IV 18 68
#> 12 REMAP-CAP Hydrocortisone NIV 8 37
#> 13 Steroids-SARI Methylprednisolone IV 10 13
#> 14 Steroids-SARI Methylprednisolone NIV 3 11
#> cont.events cont.total
#> 1 17 59
#> 2 3 14
#> 3 76 128
#> 4 0 0
#> 5 0 6
#> 6 2 8
#> 7 2 12
#> 8 0 0
#> 9 283 683
#> 10 0 0
#> 11 10 49
#> 12 19 43
#> 13 9 14
#> 14 4 9Next, we compute log-odds ratios and their variances for each subgroup comparison within trials, preparing the data for meta-analysis.
agd <- escalc(measure = "OR",
ai = treat.events, bi = treat.total - treat.events,
ci = cont.events, di = cont.total - cont.events,
data = steroids) |>
mutate(
subgroup = ifelse(ventilation == "IV", 0, 1),
ni = treat.total + cont.total,
subgroup12 = as.numeric(subgroup) - 0.5
)
print(agd)
#>
#> trial drug ventilation treat.events treat.total
#> 1 CAPE COVID Hydrocortisone IV 10 61
#> 2 CAPE COVID Hydrocortisone NIV 1 14
#> 3 CoDEX Dexamethasone IV 69 128
#> 4 CoDEX Dexamethasone NIV 0 0
#> 5 COVID STEROID Hydrocortisone IV 4 7
#> 6 COVID STEROID Hydrocortisone NIV 2 8
#> 7 DEXA-COVID 19 Dexamethasone IV 2 7
#> 8 DEXA-COVID 19 Dexamethasone NIV 0 0
#> 9 RECOVERY Dexamethasone IV 95 324
#> 10 RECOVERY Dexamethasone NIV 0 0
#> 11 REMAP-CAP Hydrocortisone IV 18 68
#> 12 REMAP-CAP Hydrocortisone NIV 8 37
#> 13 Steroids-SARI Methylprednisolone IV 10 13
#> 14 Steroids-SARI Methylprednisolone NIV 3 11
#> cont.events cont.total yi vi subgroup ni subgroup12
#> 1 17 59 -0.7248 0.2022 0 120 -0.5
#> 2 3 14 -1.2657 1.5012 1 28 0.5
#> 3 76 128 -0.2229 0.0638 0 256 -0.5
#> 4 0 0 0.0000 8.0000 1 0 0.5
#> 5 0 6 2.8163 2.6618 0 13 -0.5
#> 6 2 8 0.0000 1.3333 1 16 0.5
#> 7 2 12 0.6931 1.3000 0 19 -0.5
#> 8 0 0 0.0000 8.0000 1 0 0.5
#> 9 283 683 -0.5338 0.0209 0 1007 -0.5
#> 10 0 0 0.0000 8.0000 1 0 0.5
#> 11 10 49 0.3393 0.2012 0 117 -0.5
#> 12 19 43 -1.0542 0.2538 1 80 0.5
#> 13 9 14 0.6162 0.7444 0 27 -0.5
#> 14 4 9 -0.7577 0.9083 1 20 0.5We now define a helper function to choose the study weights according to different strategies—equal, inverse-variance, by study size, or by smaller subgroup size.
choose_weights <- function(type, agd, uni = NULL) {
switch(
type,
"equal" = rep(2 / length(agd$vi), length(agd$vi)),
"inverse_variance" = 1 / agd$vi,
"study_size" = rep(agd$ni[agd$subgroup == 0] + agd$ni[agd$subgroup == 1], each = 2),
"smaller_subgroup" = rep(apply(cbind(agd$ni[agd$subgroup == 0],
agd$ni[agd$subgroup == 1]), 1, min), each = 2),
stop("Unknown weighting type.")
)
}We select one weighting scheme (e.g., inverse-variance) and fit a
random-effects meta-analytic model using rma.mv() from metafor.
weight_type <- "inverse_variance" # try "equal", "study_size", "smaller_subgroup"
wi <- choose_weights(weight_type, agd)
W_common <- diag(wi)
fit_common <- rma.mv(
yi = yi,
V = diag(vi),
W = W_common,
random = list(~ -1 + subgroup | trial, ~ 1 | trial),
struct = c("ID", "CS"),
method = "REML",
data = agd
)
summary(fit_common)
#>
#> Multivariate Meta-Analysis Model (k = 14; method: REML)
#>
#> logLik Deviance AIC BIC AICc
#> -17.7302 35.4604 41.4604 43.1553 44.1271
#>
#> Variance Components:
#>
#> estim sqrt nlvls fixed factor
#> sigma^2 0.0000 0.0000 7 no trial
#>
#> outer factor: trial (nlvls = 7)
#> inner factor: subgroup (nlvls = 2)
#>
#> estim sqrt fixed
#> tau^2 0.0252 0.1587 no
#>
#> Test for Heterogeneity:
#> Q(df = 13) = 13.2662, p-val = 0.4275
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> -0.4150 0.1472 -2.8191 0.0048 -0.7034 -0.1265 **
#>
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Now we compare how each weighting approach affects the interaction estimate—showing the sensitivity of results to the assumed information structure.
weight_options <- c("equal", "inverse_variance", "study_size", "smaller_subgroup")
res_list <- lapply(weight_options, function(wt) {
wi <- choose_weights(wt, agd)
fit <- rma.mv(yi = yi, V = diag(vi), W = diag(wi),
mods = ~ 1 + subgroup12,
random = list(~ -1 + subgroup | trial, ~ 1 | trial),
struct = c("ID", "CS"),
method = "REML", data = agd)
tibble(weight_type = wt, b1 = -fit$beta[2], se = sqrt(vcov(fit)[2,2]))
})
bind_rows(res_list) %>%
ggplot(aes(weight_type, exp(b1))) +
geom_point(size = 3) +
geom_errorbar(aes(ymin = exp(b1 - 1.96*se), ymax = exp(b1 + 1.96*se)), width = 0.1) +
coord_flip() +
theme_minimal() +
labs(
y = "Interaction estimate (95% CI)",
x = "Weighting scheme",
title = "Impact of Weighting Scheme on Interaction Estimate"
)
Finally, we interpret and summarize how the choice of weighting affects inference and what each option represents conceptually.
| Scheme | Description |
|---|---|
| Equal weights | Treats all studies equally; ignores precision and size |
| Inverse-variance | Standard approach emphasizing interaction precision |
| Study-size | Reflects total study sample size; design-based |
| Smaller subgroup | Rewards balanced subgroups; penalizes imbalance |
Panaro, R., Röver, C., & Friede, T. (2025). Subgroup comparisons within and across studies in meta-analysis. arXiv preprint arXiv:2508.15531.