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Fit a naive meta-analysis model (no borrowing across designs)

Source: R/meta_did.R
meta_did_naive.Rd

Deprecated. meta_did_naive() is deprecated in favour of meta_did_general() with time_trend = "fixed_zero" and baseline_imbalance = "fixed_zero", which provides the same behaviour with more explicit control.

This function imposes the "naive" assumptions typically made when analysing each design in isolation:

  • RCT: Baseline means are assumed equal across treatment and control groups (randomisation assumption), so the baseline difference \(\gamma\) is fixed to zero.

  • Pre-post: The time trend \(\beta\) is fixed to zero, so the pre-post change is attributed entirely to the treatment effect.

Usage

meta_did_naive(
  summary_data = NULL,
  individual_data = NULL,
  normalise_by_baseline = TRUE,
  robust_heterogeneity = FALSE,
  design_effects = FALSE,
  hierarchical_rho = TRUE,
  covariates = NULL,
  multiplicative_covariate = 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,
  allow_unidentified_kappa = 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. The reported treatment_effect_mean is then the population mean of the per-study proportional effects, \(E[\theta_i / b_i]\) (a percentage-scale effect, each study expressed as a fraction of its own baseline), which is the appropriate estimand when studies are on heterogeneous scales. Note this is not \(E[\theta] / E[b]\): when baselines vary across studies the two differ by the between-study baseline coefficient of variation squared (Jensen's inequality).

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).

multiplicative_covariate

Optional specification of one or two categorical study-level covariates that modify the population treatment effect multiplicatively rather than additively. Either a single column name (character of length 1) for one covariate, or a one-sided formula naming one or two columns (~ a or ~ a + b). At most two are allowed. One factor is estimated per non-reference level of each covariate: studies at a covariate's reference level keep their population-mean linear predictor \(\mu_\theta + X_{\mathrm{cov},i}^{\top}\beta_{\mathrm{cov}}\) unchanged (factor fixed at 1), while studies at level \(k\) have it multiplied by the estimated effect_multiplier[k]. With two covariates the study's overall factor is the product of the two per-covariate factors, \(\alpha_{a(i)} \cdot \beta_{b(i)}\) — i.e. each covariate scales the effect independently (a log-additive structure). The reference level is the first factor level (declare the column as a factor to control it, with identical levels declared in every data frame), the lowest value for numeric input, or the alphabetically first value for character input. A numeric {0, 1} indicator is the simplest case: 0 is the reference (factor fixed at 1) and 1 selects the single estimated multiplier. Useful when a study attribute attenuates or amplifies the underlying effect by a shared factor — e.g. how an intervention was delivered, optionally crossed with a second attribute such as how long it ran. Each column must contain no NAs, be constant within study for individual-level data, must not also appear in covariates, and must take at least two distinct values across studies for its multipliers to be identified; the two columns must be distinct. Numeric columns with more than 5 distinct values are rejected as likely continuous (convert genuinely categorical numeric codes to a factor). The same multiplier prior from set_priors() is applied independently to every estimated factor. On the returned object, fit$multiplicative_covariate is a list with elements name and levels (reference first) for one covariate, or a list of two such descriptors for two covariates. Default NULL (no multiplicative structure).

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).

allow_unidentified_kappa

Logical. If FALSE (default), kappa = "estimate" errors when no randomised study carries pre-treatment data, because \(\kappa\) is then not identified by anything. Set to TRUE to sample it anyway (the posterior for \(\kappa\) will reproduce its prior).

Doing so is a modelling choice rather than an estimate. Sampling \(\kappa\) instead of fixing it makes the marginal prior on \(\gamma_i\) a scale mixture of normals rather than a normal – simultaneously more peaked at zero and much heavier-tailed than any fixed \(\kappa\). That is a better description of "most randomised trials achieved balance, occasionally one badly did not" than a single scale can give, and it propagates the uncertainty in \(\kappa\) into the pooled effect rather than conditioning on one value. What it does not do is learn \(\kappa\) from the data, which is why it must be asked for explicitly.

...

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, identical in structure to the return value of meta_did().

See also

meta_did_general() for independent control over assumptions.