Fit a meta-analysis model with explicit control over design assumptions

A flexible interface for controlling how nuisance parameters are handled for non-DiD study designs. By default, behaves identically to meta_did(). Users can independently control whether time trends and baseline imbalances are estimated or fixed to zero for RCT and pre-post studies.

Usage

meta_did_general(
  summary_data = NULL,
  individual_data = NULL,
  normalise_by_baseline = TRUE,
  robust_heterogeneity = FALSE,
  design_effects = FALSE,
  hierarchical_rho = TRUE,
  correlated_effects = FALSE,
  baseline_imbalance = c("by_randomisation", "estimated", "fixed_zero"),
  mu_gamma = c("zero", "estimated"),
  kappa = 0.5,
  cluster_deff_default = 2,
  covariates = NULL,
  multiplicative_covariate = NULL,
  center_covariates = TRUE,
  priors = set_priors(),
  time_trend = c("pooled", "fixed_zero"),
  pp_likelihood = c("differenced", "bivariate"),
  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.

correlated_effects

Logical. If TRUE, study-level treatment effects and time trends are drawn jointly from a bivariate normal with a shared correlation parameter, rather than independently. The correlation is parameterised via a Cholesky factor of a 2×2 correlation matrix with an LKJ prior (see set_priors()). Cannot be combined with robust_heterogeneity = TRUE. Default FALSE.

baseline_imbalance

How the per-study baseline difference $\gamma_i$ is modelled: "by_randomisation" (default), "estimated", or "fixed_zero". Identical in meaning and default to the meta_did() argument of the same name – see there for the full description, and for mu_gamma, kappa and cluster_deff_default, which this function also accepts.

mu_gamma

Whether the population mean baseline imbalance among non-randomised studies is estimated. One of:

"zero": (Default) $\mu_\gamma = 0$. The magnitude of selection-driven imbalance is pooled across non-randomised studies, but its direction is not transported between them.
"estimated": $\mu_\gamma$ is estimated, with the prior from baseline_difference_mean in set_priors().

The default is deliberate. Whether a treated group starts above or below its control is a property of each programme's targeting rule – some interventions go to high-need (high-baseline) populations, others to easy-to-reach (low-baseline) ones – not of the outcome or the intervention. Estimating a single $\mu_\gamma$ asserts that a whole literature shares a direction of selection, and then applies that direction to every post-only study, whose own data cannot contradict it. Worse, the resulting bias does not shrink with more data: it sharpens, because $\mu_\gamma$ is estimated more precisely. Set to "estimated" only when the studies plausibly share a targeting mechanism – for example, several evaluations of the same programme.

kappa

Excess-imbalance factor for randomised studies. Either a single non-negative number (default 0.5) or the string "estimate".

$\kappa^2$ is the variance inflation of a randomised study's baseline contrast beyond simple random sampling, so $\kappa^2 = $DEFF$ - 1$ and $\kappa = 0$ is perfect randomisation. Note $\kappa = 0$ is not the same as ignoring finite-sample imbalance: the realised imbalance of a randomised allocation is already carried by the likelihood's $\sigma^2/n$ terms (and, for DiD, propagated into the post period by the pre-post correlation). $\kappa$ governs only the extra allowance for randomisation not having held exactly – imperfect allocation, attrition, post-randomisation selection.

Because $s_i$ scales as $1/\sqrt{n_i}$, this automatically down-weights small randomised studies more than large ones. For a post-only randomised study, where $\gamma_i$ is unidentified, the mechanism is equivalent to inflating that study's standard error by $\sqrt{1 + \kappa^2}$.

"estimate" samples $\kappa$ with the prior from kappa in set_priors(), but by default is only permitted when at least one randomised study carries pre-treatment data (a randomised DiD). Post-only randomised studies constrain $\kappa$ not at all. With no such anchor, either fix $\kappa$ or set allow_unidentified_kappa = TRUE. The default of 0.5 is a reasonable central choice rather than a value to trust on its own, so it is worth refitting at a few values to see whether any conclusion turns on it.

cluster_deff_default

Design effect assumed for studies with randomisation = "cluster" that do not supply cluster_size and icc columns. Default 2, which corresponds to roughly 50 units per cluster at an ICC of 0.02. When both columns are supplied, the study's own $1 + (m - 1)\rho_{ICC}$ is used instead. The design effect inflates $s_i$ so that $\kappa$ keeps one meaning across designs.

This corrects the baseline contrast only. A cluster-randomised study's likelihood still uses $\sigma^2/n$ for the post-treatment period, so it remains over-precise about its own treatment effect. Correcting that needs cluster identifiers and a random effect, which this model does not carry.

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.

time_trend

How to handle the time trend $\beta_i$ for non-DiD studies. One of:

"pooled": (Default) Estimate study-level time trends with a hierarchical prior shared across designs. Information from DiD studies informs the RCT and pre-post time trends. This is the same behaviour as meta_did().
"fixed_zero": Fix $\beta_i = 0$ for RCT and pre-post studies. For pre-post studies, this means the pre-post change is attributed entirely to treatment. For RCT studies, the reparameterised time trend correction is bypassed.

pp_likelihood

Likelihood form for pre-post studies. One of:

"differenced": (Default) Use the differenced (post minus pre) likelihood. The pre/post correlation $\rho_i$ is not separately estimable and the baseline cancels algebraically. This is the same behaviour as meta_did().
"bivariate": Use the full bivariate normal likelihood for the (pre, post) pair. This retains the pre/post correlation $\rho_i$ as an estimable parameter, contributing to the hierarchical $\rho$ model, at the cost of estimating additional nuisance 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().

Details

DiD studies always estimate both time trends and baseline differences regardless of these settings, since they provide the identifying information for these parameters.

Examples