Run a Bayesian Meta-Analysis in Stan

Fits a Bayesian meta-analysis model via Stan. Use stan_code(model) to inspect the generated Stan program after fitting. Supply custom_model to use your own Stan program instead.

Usage

bayesma(
  data,
  studyvar,
  event_ctrl = NULL,
  event_int = NULL,
  mean_ctrl = NULL,
  mean_int = NULL,
  sd_ctrl = NULL,
  sd_int = NULL,
  n_ctrl = NULL,
  n_int = NULL,
  likelihood = c("binomial", "gaussian", "poisson"),
  model_type = c("random_effect", "common_effect", "bias_corrected", "bc_bnp",
    "selection_copas", "selection_weight", "pet_peese", "mixture_model"),
  stage = c("one_stage", "two_stage"),
  re_dist = c("normal", "t", "skew_normal", "mixture"),
  small_sample = c("none", "t_approx", "hjsk"),
  multi_arm = NULL,
  rho_prior = NULL,
  mu_prior = NULL,
  tau_prior = NULL,
  gamma_prior = NULL,
  nu_prior = NULL,
  alpha_prior = NULL,
  mixture_priors = NULL,
  b_prior = NULL,
  p_bias_prior = NULL,
  w_bias_prior = NULL,
  mu_beta_prior = NULL,
  tau_beta_prior = NULL,
  bnp_concentration_max = NULL,
  bnp_K_max = NULL,
  use_known_bias = FALSE,
  selection_priors = NULL,
  p_cutoffs = c(0.025, 0.05),
  n_components = 2L,
  robust = FALSE,
  robust_prior = NULL,
  robust_df = 4,
  robust_weight = NULL,
  custom_model = NULL,
  custom_data = NULL,
  estimand = NULL,
  cate_covariate = NULL,
  baseline_risk = NULL,
  re_min_k = NULL,
  sample_prior = FALSE,
  chains = 4,
  iter_warmup = 1000,
  iter_sampling = 1000,
  adapt_delta = 0.95,
  seed = 1234,
  ...
)

Arguments

data: A data frame with one row per study (or per arm for multi-arm studies).
studyvar: Character. Column name for study identifiers.
event_ctrl, event_int: Character (binomial/poisson). Event counts.
mean_ctrl, mean_int: Character (gaussian). Arm means.
sd_ctrl, sd_int: Character (gaussian). Arm SDs.
n_ctrl, n_int: Character. Arm sample sizes.
likelihood: Character. "binomial", "gaussian", or "poisson".
model_type: Character. "random_effect", "common_effect", "bias_corrected", "bc_bnp" (Bias-Corrected Bayesian Non-Parametric; Verde 2025), "selection_copas" (Robust Bayesian Copas; Bai 2020), "selection_weight", "pet_peese", or "mixture_model" (Bayesian meta-analytic mixture; Maier 2024).
stage: Character. "one_stage" or "two_stage".
re_dist: Character. "normal", "t", "skew_normal", or "mixture". For model_type = "selection_copas", only "normal" and "t" are supported; pass "t" for the Bai (2020) Robust Bayesian Copas (RBC) formulation with heavy-tailed random effects (recommended; see nu_prior).
small_sample: Character. "none", "t_approx", or "hjsk".
multi_arm: Character or NULL. Column name indicating multi-arm study grouping. Only used with stage = "one_stage".
rho_prior: Prior on the within-study correlation for multi-arm studies.
mu_prior: Prior on the pooled effect mu.
tau_prior: Prior on the RE standard deviation tau.
gamma_prior: Prior on study baselines gamma. One-stage only.
nu_prior: Prior on RE degrees of freedom nu. re_dist = "t" only.
alpha_prior: Prior on RE skewness shape. re_dist = "skew_normal" only.
mixture_priors: Named list of priors for mixture components.
b_prior: Prior on bias shift B. model_type = "bias_corrected" only.
p_bias_prior: Prior on proportion of biased studies. Used by bias_corrected and bc_bnp.
w_bias_prior: Prior on per-study bias weight. bias_corrected only.
mu_beta_prior: Prior on the bias-component location (DP base). Used by bc_bnp only. Default uniform(-15, 15).
tau_beta_prior: Prior on the bias-component scale (DP base). Used by bc_bnp only. Default half_cauchy(0, 1).
bnp_concentration_max: Numeric. Upper bound for the DP concentration alpha ~ Uniform(0.5, bnp_concentration_max). bc_bnp only. Default NULL resolves from data via Verde (2025) eqn (20).
bnp_K_max: Integer. Truncation level for the stick-breaking approximation. bc_bnp only. Default NULL resolves to 1 + ceiling(5 * bnp_concentration_max).
use_known_bias: Logical. If TRUE, data must contain a biased column.
selection_priors: Named list of priors for selection model parameters.
p_cutoffs: Numeric vector. One-sided p-value cutpoints for the weight-function selection model.
n_components: Integer. Number of mixture components.
robust: Logical. Adds a two-component outlier mixture.
robust_prior: Prior on the outlier component location.
robust_df: Degrees of freedom for the outlier component.
robust_weight: Prior on the mixing weight for the main component.
custom_model: Optional Stan program (character scalar). When non-NULL, code generation is bypassed and the user's program is used verbatim.
custom_data: Optional named list of Stan data entries that override or augment the automatically built data list.
estimand: Character. The user-facing target effect: "OR", "RR", "HR", "IRR", "MD", "SMD" (relative-effect / mean-difference estimands; behave as today), or "RD" / "ARR", "ATE", "ATT", "CATE" (marginal estimands; computed from posterior draws via bayesma_marginal() and attached to the output as $marginal). Default NULL infers from likelihood.
cate_covariate: Character. Column name of a study-level covariate to condition on for estimand = "CATE". Required when CATE is requested.
baseline_risk: Numeric, between 0 and 1, or "study_mean". Reference baseline risk used to back-transform relative effects to absolute scale for two-stage binomial fits with estimand in c("RD","ARR","ATE","ATT"). Default NULL falls back to the observed control-arm event rate.
re_min_k: Optional numeric. If set and model_type = "random_effect", the model is downgraded to "common_effect" with a warning when the number of unique studies is below re_min_k. Default NULL (no enforcement). Useful for subgroup analyses where some strata have too few studies for stable random-effects estimation.
sample_prior: Logical. If TRUE, samples from the prior predictive distribution by fitting the model without conditioning on the data likelihood. The result can be passed to pp_check() to verify that the prior places mass on plausible observable values. Use this for prior elicitation and sanity-checking — not for calibrating priors against the analysis dataset itself (which would be circular). Default FALSE.
chains, iter_warmup, iter_sampling, adapt_delta, seed: MCMC settings.
...: Passed to cmdstanr::sample().

Value

A list of class "bayesma".