Estimate a treatment-by-subgroup interaction using the Difference-of-Averages construction

Difference of Averages (DA) synthesizes each subgroup series separately and takes the difference of those pooled treatment effects. Study inverse-variance weights generally differ across the two subgroup analyses, so DA need not equal ad(). Panaro, Röver and Friede (2026) treat DA and AD as different constructions.

Usage

da(
  data,
  reference,
  modifier = NULL,
  trial = "study",
  subgroup = "level",
  yi = "yi",
  vi = "vi",
  method = "Bayesian",
  tau.prior = NULL,
  mu.prior = NULL,
  ...
)

Arguments

data: A data frame with trial, subgroup, yi, and vi.
reference: Reference subgroup label.
modifier: Column of the two levels. Overrides subgroup when set. The default column remains "subgroup".
trial, subgroup, yi, vi: Column names.
method: Inferential method. NULL (default) is "REML" for metafor and "bayes" for bayesmeta. metafor also accepts "ML". If engine is omitted, "bayes" uses bayesmeta and "REML" / "ML" use metafor.
tau.prior, mu.prior: Bayesian priors when engine = "bayesmeta" (defaults: improper uniform on \(\tau\), matching bayesmeta; \(N(0,10)\) on \(\mu\). AD uses the same tau default as CAMS interaction). Ignored by metafor.
...: Computational options passed to metafor::rma() or bayesmeta::bayesmeta() (including engine_args).
engine: Computational backend. "metafor" (default) or "bayesmeta". CAMS backends are not DA backends. "bayes" is accepted as a synonym of "bayesmeta".
approach: Inferential approach. "bayes" uses engine = "bayesmeta" when engine is omitted; "frequentist", "REML", or "ML" use engine = "metafor". NULL (default) follows engine / method.

Value

An object of class "interactmeta_da".

Details

For binary subgroups with reference \(A\) and non-reference \(B\), \(\mu_A\) and \(\mu_B\) are independent random-effects meta-analyses of the subgroup series, and \(\gamma_{\mathrm{DA}} = \mu_B - \mu_A\).

DA is an analysis construction, not an inference framework. It may be fitted with frequentist inference (engine = "metafor", REML/ML) or Bayesian inference (engine = "bayesmeta"). Bayesian DA fits two independent univariate bayesmeta::bayesmeta() models and forms \(\mu_B - \mu_A\) by Cartesian-product Gaussian-mixture (and optional convolution). It does not use quantile matching, and it does not acquire CAMS information-fraction functionality merely because a posterior exists.

Fisher et al. (2017) discussed a related across-trial contrast of subgroup averages as the “deluded” approach. That paper does not define the DA/AD pair used here. DA is not the joint bivariate mixed model of van Houwelingen, Arends and Stijnen (2002). That joint model remains a related reference for modelling two subgroup series together with a heterogeneity matrix \(\Sigma\); da() uses separate univariate pooling instead.

ad() meta-analyses the within-trial differences. swada() imposes the same study weights on both constructions. cams() is a different object: the CAMS statistical model, which is the analysis family that uses the information-fraction construction.

References

Panaro RV, Röver C, Friede T (2026). Subgroup comparisons within and across studies in meta-analysis. Research Synthesis Methods (in press). arXiv:2508.15531. https://doi.org/10.48550/arXiv.2508.15531

Fisher DJ, Carpenter JR, Morris TP, Freeman SC, Tierney JF (2017). Meta-analytical methods to identify who benefits most from treatments: daft, deluded, or deft approach? BMJ, 356, j573. https://doi.org/10.1136/bmj.j573

van Houwelingen HC, Arends LR, Stijnen T (2002). Advanced methods in meta-analysis: multivariate approach and meta-regression. Statistics in Medicine, 21(4), 589–624. https://doi.org/10.1002/sim.1040

van Houwelingen HC, Zwinderman KH, Stijnen T (1993). A bivariate approach to meta-analysis. Statistics in Medicine, 12(24), 2273–2284. https://doi.org/10.1002/sim.4780122405