Estimate a treatment-by-subgroup interaction using the Average-Difference construction

Average Difference (AD) first forms the within-trial treatment-by-subgroup difference and then meta-analyzes those differences. For binary subgroups with reference \(A\) and non-reference \(B\), \(g_j = y_{Bj} - y_{Aj}\) with \(\sigma_{gj}^2 = \sigma_{Aj}^2 + \sigma_{Bj}^2\) (within-trial subgroup covariance assumed zero), and \(\gamma_{\mathrm{AD}}\) is a random-effects meta-analysis of the \(g_j\).

Usage

ad(
  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).

Value

An object of class "interactmeta_ad".

Details

AD is a different construction from da() (Panaro, Röver & Friede 2026), not an inference framework. It may be fitted with engine = "metafor" (REML/ML) or engine = "bayesmeta" (Bayesian RE-MA of \(g_j\)). The CAMS manuscript’s BIM (Bayesian interaction meta-analysis) is the Bayesian analogue of this construction. A Bayesian AD fit is internally complete: it does not borrow uncertainty or heterogeneity from Bayesian DA or CAMS. It still does not use CAMS information fractions.

Study weights are those of the interaction series, \(w_j \propto 1/(\sigma_{gj}^2 + \tau_g^2)\). They generally differ from the subgroup-specific weights used by da(). swada() replaces those analysis-specific weights with one common vector. cams() is a different object: the CAMS statistical model.

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

Panaro RV, Röver C, Friede T (2025). Consistent Bayesian meta-analysis on subgroup specific effects and interactions. arXiv:2512.18785. https://doi.org/10.48550/arXiv.2512.18785