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Fit a Bayesian meta-analysis model across study designs

Source: R/meta_did.R
meta_did.Rd

Fits a hierarchical Bayesian model synthesising treatment effects from studies with different designs: difference-in-differences (DiD), randomised controlled trials (RCT), and pre-post studies. All designs contribute to a shared population treatment effect.

Usage

meta_did(
  summary_data = NULL,
  individual_data = NULL,
  normalise_by_baseline = TRUE,
  robust_heterogeneity = FALSE,
  design_effects = FALSE,
  hierarchical_rho = TRUE,
  covariates = NULL,
  center_covariates = TRUE,
  priors = set_priors(),
  method = c("sample", "optimize"),
  chains = 4L,
  iter_warmup = 1000L,
  iter_sampling = 1000L,
  seed = NULL,
  allow_no_did = FALSE,
  ...
)

Arguments

summary_data

A data frame with one row per study containing summary statistics. Must include columns study_id and design. See validate_summary_data() for the full column specification per design. Valid designs: "did", "did_change", "rct", "pp".

individual_data

A data frame in long format with one row per observation. Must include columns study_id, design, group, time, and value. Valid designs: "did", "rct", "pp". No study_id may appear in both summary_data and individual_data.

normalise_by_baseline

Logical. If TRUE (default), all means and SDs are divided by each study's pre-treatment control mean (or the grand mean for change-only studies), placing outcomes on a common fractional scale.

robust_heterogeneity

Logical. If TRUE, study-level treatment effects are drawn from a Student-t distribution rather than a normal, providing robustness to outlier studies. The degrees-of-freedom parameter is estimated with the prior specified in priors$nu.

design_effects

Logical. If TRUE, additive offsets on the population treatment effect mean are estimated for RCT and Pre-Post studies relative to DiD (the reference). Useful for testing whether designs yield systematically different effect estimates.

hierarchical_rho

Logical. If TRUE (default), the pre-post correlation is modelled hierarchically across studies. Studies with a reported correlation inform the population distribution; studies without one have their correlation imputed.

covariates

An optional one-sided formula specifying study-level covariates for meta-regression on the treatment effect (e.g., ~ dose + year). The named columns must be numeric and present in both summary_data and individual_data (whichever are provided). For individual-level data, covariate values must be constant within each study. Default NULL (no meta-regression).

center_covariates

Logical. If TRUE (default), covariates are mean-centered across all studies before fitting. This ensures that treatment_effect_mean is the population treatment effect at the average covariate values. Set to FALSE to use raw covariate values, in which case treatment_effect_mean is the effect when all covariates equal zero. The covariate coefficients (beta_cov) have the same interpretation regardless of centering: the change in expected treatment effect per unit increase in the covariate.

priors

A did_priors object from set_priors(). Controls the prior distributions on all population-level parameters.

method

Inference method. "sample" (default) runs full MCMC via Stan's HMC-NUTS sampler and returns a posterior distribution. "optimize" finds the maximum a posteriori (MAP) estimate via L-BFGS and is substantially faster, but returns only a point estimate with no uncertainty quantification.

chains

Number of MCMC chains. Ignored when method = "optimize". Default 4.

iter_warmup

Number of warmup iterations per chain. Ignored when method = "optimize". Default 1000.

iter_sampling

Number of sampling iterations per chain. Ignored when method = "optimize". Default 1000.

seed

Integer random seed for reproducibility. Default NULL.

allow_no_did

Logical. If FALSE (default), meta_did() will stop with an error when no DiD studies are present, because the treatment effect is not identified from the data without the double-difference structure. Set to TRUE to override this check if you understand the limitation (the posterior will be prior-driven).

...

Additional arguments passed to the underlying CmdStanModel method: $sample() when method = "sample" (e.g., parallel_chains, adapt_delta) or $optimize() when method = "optimize" (e.g., algorithm, iter).

Value

A meta_did_fit object. See print.meta_did_fit() and summary.meta_did_fit() for extracting results. When method = "optimize", the summary contains MAP point estimates only; sd, lo, and hi columns will be NA.

Details

DiD studies are required for identification of the treatment effect. Without them, the treatment effect is confounded with time trends (pre-post) or baseline group differences (RCT). See vignette("model-details") for a full discussion of the model, normalisation, and identification.

Examples

if (instantiate::stan_cmdstan_exists()) {
  studies <- data.frame(
    study_id            = c("Smith 2020", "Jones 2021"),
    design              = c("did", "rct"),
    n_control           = c(50, 60),
    mean_pre_control    = c(0.45, NA),
    mean_post_control   = c(0.42, 0.48),
    sd_pre_control      = c(0.12, NA),
    sd_post_control     = c(0.11, 0.12),
    n_treatment         = c(55, 65),
    mean_pre_treatment  = c(0.46, NA),
    mean_post_treatment = c(0.30, 0.35),
    sd_pre_treatment    = c(0.13, NA),
    sd_post_treatment   = c(0.10, 0.11),
    rho                 = c(0.75, NA)
  )
  fit <- meta_did(summary_data = studies)
}
#> Running MCMC with 4 sequential chains...
#> 
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#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
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#> Chain 1 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 50, column 2)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
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#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
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#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
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#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
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#> Chain 3 Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/rct_summary_model.stan', line 53, column 8, included from
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#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
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#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/rct_summary_model.stan', line 53, column 8, included from
#> Chain 3 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 52, column 2)
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#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 7, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 26, column 6, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 50, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 7, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 26, column 6, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 50, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 7, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 26, column 6, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 50, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 7, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 26, column 6, included from
#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 50, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
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#> Chain 4 '/tmp/RtmpSwKEab/model-1a82616f6e06.stan', line 50, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
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#> 
#> All 4 chains finished successfully.
#> Mean chain execution time: 6.7 seconds.
#> Total execution time: 26.9 seconds.
#> 
#> Warning: 375 of 4000 (9.0%) transitions ended with a divergence.
#> See https://mc-stan.org/misc/warnings for details.
#> Warning: 3098 of 4000 (77.0%) transitions hit the maximum treedepth limit of 10.
#> See https://mc-stan.org/misc/warnings for details.