Compute a marginal estimand from a bayesma fit — bayesma

Post-processes the posterior draws of a fitted bayesma() model to return a marginal estimand on the natural scale: risk difference (RD/ARR), average treatment effect (ATE), average treatment effect on the treated (ATT), or a conditional average treatment effect (CATE).

Usage

bayesma_marginal(fit, spec)

Arguments

fit: A bayesma_fit object (or the cmdstanr fit inside one).
spec: The matching bayesma_spec.

Value

A list with elements:

estimand: The estimand label.
draws: A numeric vector of posterior draws on the natural scale.
summary: A tibble with median, 95\ of being above zero.

Details

For relative-effect estimands ("OR", "RR", "HR", "IRR", "MD", "SMD") this function is unnecessary — bayesma() already returns the pooled effect on the appropriate scale.

Methods by estimand and stage

RD / ARR / ATE — binomial, one-stage: Computed via marginal standardisation (g-computation) over posterior draws of the per-study baseline logit (gamma[s]) and the pooled log-OR (mu), optionally shifted by study-level random effects (epsilon[s]). The per-study RD is plogis(gamma[s] + mu + epsilon[s]) - plogis(gamma[s]), averaged across studies weighted by the harmonic mean of arm sample sizes. This corresponds to a population-weighted ATE over the observed study mix and requires no external baseline assumption.
RD / ARR / ATE — binomial, two-stage: Back-transforms posterior draws of the pooled log-OR using a baseline risk drawn per-iteration from a Beta distribution fitted (method-of-moments) to the observed control-arm event rates. Propagates baseline uncertainty into the posterior RD. A fixed scalar baseline_risk bypasses this and uses the supplied value directly (old behaviour).
ATE — gaussian: Equivalent to MD. Returns the pooled posterior on the absolute scale.
ATT: One-stage: weighted by intervention-arm sample size (n_int / sum(n_int)). Two-stage: same back-transform as ATE but with intervention-size-weighted baseline. Without IPD this is an arm-size-weighted ATE on the treated, not a true causal ATT — interpret with caution.
CATE: Routes to meta_reg() with moderators = cate_covariate. Reports the meta-regression effect; the user is expected to evaluate it at a specific covariate value downstream.