Title:	Design-Robust Meta-Analysis via Variance-Function Models
Version:	0.1.0
Description:	Implements Design-Robust Meta-Analysis (DR-Meta), a variance-function random-effects framework in which between-study heterogeneity is modelled as a function of a study-level design robustness index, allowing heterogeneity to depend systematically on study quality or design strength rather than being treated as a single nuisance parameter. The package provides profiled restricted maximum likelihood (REML) estimation of the overall effect and variance-function parameters, study-specific weights, heterogeneity diagnostics (tau-squared, I-squared), influence and leave-one-out analysis, and graphical tools including forest plots and influence plots. The DR-Meta framework nests classical fixed-effects and standard random-effects meta-analysis as special cases, making it a strict generalisation of existing approaches.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.1.0)
Imports:	grDevices, graphics, stats, utils
Suggests:	ggplot2 (≥ 3.4.0), knitr, metafor (≥ 4.0.0), rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
URL:	https://github.com/causalfragility-lab/drmeta
BugReports:	https://github.com/causalfragility-lab/drmeta/issues
NeedsCompilation:	no
Packaged:	2026-04-01 22:48:08 UTC; Subir
Author:	Subir Hait [aut, cre]
Maintainer:	Subir Hait <haitsubi@msu.edu>
Repository:	CRAN
Date/Publication:	2026-04-08 18:40:03 UTC

drmeta: Design-Robust Meta-Analysis

Description

Fits the DR-Meta variance-function random-effects model (Hait, 2025), where between-study heterogeneity is a monotone-decreasing function of each study's design robustness index.

Author(s)

Maintainer: Subir Hait haitsubi@msu.edu (ORCID)

See Also

Useful links:

• https://github.com/causalfragility-lab/drmeta

• Report bugs at https://github.com/causalfragility-lab/drmeta/issues

Extract Coefficients from a drmeta Object

Description

Returns a named numeric vector of the three model parameters: mu, tau0sq, and gamma.

Usage

## S3 method for class 'drmeta'
coef(object, ...)

Arguments

Value

A named numeric vector of length 3 with the estimated model parameters: mu (pooled effect estimate), tau0sq (baseline between-study variance at DR = 0), and gamma (variance-function decay rate).

Confidence Interval for a drmeta Object

Description

Returns a data frame with the estimate and 95% confidence interval for the pooled effect \hat\mu.

Usage

## S3 method for class 'drmeta'
confint(object, parm = NULL, level = 0.95, ...)

Arguments

Value

A data frame with one row (mu) and three columns: estimate (the pooled effect \hat\mu), lower, and upper (confidence interval bounds at the requested level, default 95\

Forest Plot for DR-Meta

Description

Draws a forest plot for a fitted "drmeta" model using base graphics. Studies are ordered by design robustness (largest DR at top by default). Point sizes are proportional to DR-Meta weights; a vertical reference line and summary diamond are included.

Usage

dr_forest(
  object,
  order_by = c("dr", "yi", "none"),
  xlab = "Effect size",
  main = "DR-Meta Forest Plot",
  col_point = "#2166AC",
  col_diamond = "#D6604D",
  col_dr = "#4DAC26",
  show_dr = TRUE,
  xlim = NULL,
  cex_study = 0.8,
  ...
)

Arguments

Value

Invisibly returns the data frame used for plotting (ordered studies).

Examples

set.seed(42)
k <- 10
dr <- runif(k, 0.1, 0.9)
vi <- runif(k, 0.01, 0.05)
yi <- rnorm(k, 0.3, sqrt(vi + 0.04 * exp(-2 * dr)))
fit <- drmeta(yi, vi, dr)
dr_forest(fit)

Design Robustness from Study Design Type

Description

Maps a vector of study design type labels to a numeric design robustness score in [0,1], using a pre-specified hierarchy of causal credibility. This is a convenient starting point for operationalising the DR index when only design type is available.

Usage

dr_from_design(
  design,
  custom_map = NULL,
  default_score = 0.25,
  warn_unknown = TRUE
)

Arguments

Details

The default hierarchy follows the causal inference literature (Rubin, 2008; Rosenbaum, 2010; Imbens & Rubin, 2015):

Users can override or extend this table via the custom_map argument.

Value

A numeric vector of design robustness scores in [0,1], the same length as design.

See Also

dr_score, drmeta

Examples

designs <- c("RCT", "DiD", "OLS", "IV", "matching", "unknown_design")
dr_from_design(designs)

# Custom override
dr_from_design(designs, custom_map = c(unknown_design = 0.35))

Funnel Plot for DR-Meta

Description

Creates a funnel plot for a fitted "drmeta" model. The horizontal axis shows effect-size estimates; the vertical axis shows standard errors. Point sizes are proportional to DR-Meta weights and point colour encodes design robustness.

Usage

dr_funnel(
  object,
  contours = TRUE,
  xlab = "Effect size",
  ylab = "Standard error",
  main = "DR-Meta Funnel Plot",
  col_low = "#D6604D",
  col_high = "#2166AC"
)

Arguments

Value

Invisibly returns NULL.

Examples

set.seed(42)
k <- 15
dr <- runif(k)
vi <- runif(k, 0.01, 0.06)
yi <- rnorm(k, 0.3, sqrt(vi + 0.04 * exp(-1.5 * dr)))
fit <- drmeta(yi, vi, dr)
dr_funnel(fit)

Heterogeneity Diagnostics for DR-Meta

Description

Computes a suite of heterogeneity statistics for a fitted "drmeta" model, including Cochran's Q (with DR-Meta weights), I^2, H^2, the design-residual variance decomposition of Proposition 6 (Hait, 2025), and per-study contributions to Q.

Usage

dr_heterogeneity(object)

Arguments

Value

A list with three elements:

summary

A one-row data frame with: k, Q, df, pval, tau2_mean (mean design-specific heterogeneity), I2, H2.

decomposition

A one-row data frame with the Proposition 6 decomposition: tau2_design_explained, tau2_residual, tau2_total, R2_DR (proportion explained by design).

contributions

A data frame with per-study Q contributions: study, DR, tau2_i, q_i, pct_Q.

Design-Residual Decomposition (Proposition 6)

The total between-study heterogeneity can be decomposed as:

\tau^2_{\text{total}} = \mathbb{E}[\tau^2(\mathrm{DR}_i)] + \mathrm{Var}(u_i \mid \mathrm{DR}_i),

where the first term is the design-explained heterogeneity (captured by the variance function) and the second is the design-residual heterogeneity (unexplained by DR). This decomposition is analogous to R-squared in meta-regression.

The design-explained proportion is

R^2_{\mathrm{DR}} = \frac{\mathbb{E}[\tau^2(\mathrm{DR}_i)]}{\tau^2_{\mathrm{total}}}.

References

Hait, S. (2025). Design-Robust Meta-Analysis: A Variance-Function Framework for Causal Credibility. Proposition 6.

Examples

set.seed(42)
k <- 15
dr <- runif(k, 0.1, 0.9)
vi <- runif(k, 0.01, 0.05)
tau2_true <- 0.04 * exp(-2 * dr)
yi <- rnorm(k, 0.3, sqrt(vi + tau2_true))

fit <- drmeta(yi, vi, dr)
het <- dr_heterogeneity(fit)
het$summary
het$decomposition
het$contributions

Leave-One-Out Influence Diagnostics for DR-Meta

Description

For each study, re-fits the DR-Meta model after excluding that study and records how the pooled estimate, confidence interval, variance-function parameters, and heterogeneity change. Studies with large absolute \Delta\hat\mu or large shifts in \hat\tau_0^2/\hat\gamma are considered influential.

Usage

dr_loo(object, parallel = FALSE, mc.cores = NULL)

Arguments

Value

A list with:

summary

A data frame with one row per study and columns: study, DR, est_loo (LOO pooled estimate), ci.lb_loo, ci.ub_loo, tau0sq_loo, gamma_loo, delta_mu (change in estimate), delta_tau0sq, delta_gamma, influential (logical: |delta_mu| > 2 * SE of full model).

full

The original full-model "drmeta" object.

Examples

set.seed(7)
k  <- 12
dr <- runif(k, 0.1, 0.9)
vi <- runif(k, 0.01, 0.05)
tau2_true <- 0.04 * exp(-2 * dr)
yi <- rnorm(k, 0.3, sqrt(vi + tau2_true))

fit <- drmeta(yi, vi, dr)
loo <- dr_loo(fit)
loo$summary

Weight Diagnostic Plot for DR-Meta

Description

Plots DR-Meta study weights against design robustness (\mathrm{DR}_i), illustrating the monotone ordering of Lemma 3 (Hait, 2025). An overlaid curve shows the theoretical weight function holding sampling variance at its median value.

Usage

dr_plot(
  object,
  col_pts = "#2166AC",
  col_curve = "#D6604D",
  xlab = expression(paste("Design robustness (", DR[i], ")")),
  ylab = "DR-Meta weight (normalised, %)",
  main = "DR-Meta Weight vs Design Robustness",
  show_labels = TRUE,
  ...
)

Arguments

Value

Invisibly returns a data frame with study-level weight information.

Examples

set.seed(42)
k <- 12
dr <- runif(k, 0.1, 0.9)
vi <- runif(k, 0.01, 0.05)
yi <- rnorm(k, 0.3, sqrt(vi + 0.04 * exp(-2 * dr)))
fit <- drmeta(yi, vi, dr)
dr_plot(fit)

Variance Function Plot for DR-Meta

Description

Plots the fitted variance function \tau^2(\mathrm{DR};\,\hat\psi) as a curve from DR = 0 to DR = 1, with study-level \hat\tau^2_i overlaid as points.

Usage

dr_plot_vfun(
  object,
  col_curve = "#D6604D",
  col_pts = "#2166AC",
  xlab = expression(paste("Design robustness (", DR[i], ")")),
  ylab = expression(paste("Between-study variance ", tau^2)),
  main = "DR-Meta Variance Function"
)

Arguments

Value

Invisibly returns a data frame with the plotting grid.

Examples

set.seed(1)
fit <- drmeta(rnorm(12, 0.3), runif(12, 0.01, 0.04), runif(12))
dr_plot_vfun(fit)

Publication Bias Assessment for DR-Meta (PET/PEESE/Egger/Funnel)

Description

Performs a suite of publication-bias and small-study-effects tests adapted for DR-Meta weights. PET and PEESE regressions use w_i = 1/\hat\sigma_i^2 = 1/(v_i + \hat\tau^2(\mathrm{DR}_i)) as regression weights, so precision is design-adjusted.

Usage

dr_pub_bias(object, test = c("PET", "PEESE", "Egger"), alpha = 0.05)

Arguments

Details

PET (Precision Effect Test): regresses y_i on se_i = \sqrt{v_i}, with DR-Meta weights. A significant slope implies small-study bias; the intercept estimates the publication-bias-corrected effect.

PEESE (Precision Effect Estimate with Standard Error): regresses y_i on v_i, with DR-Meta weights. Generally preferred when the true effect is non-zero.

Egger test: Egger-type regression using the standardised effect y_i / se_i on 1 / se_i, with DR-Meta weights.

Funnel asymmetry: classic funnel plot with DR-Meta summary.

Value

A list with elements:

PET

Summary of PET regression (data frame with intercept, slope, SE, z, p).

PEESE

Summary of PEESE regression.

Egger

Summary of Egger regression.

recommendation

Character string: use PET intercept if PET slope is significant and effect is small; use PEESE intercept otherwise.

Examples

set.seed(99)
k  <- 20
dr <- runif(k, 0.1, 0.9)
vi <- runif(k, 0.005, 0.08)
# Introduce small-study effect: smaller studies overestimate
yi <- rnorm(k, 0.3 + 0.5 * sqrt(vi), sqrt(vi + 0.03 * exp(-1.5 * dr)))
fit <- drmeta(yi, vi, dr)
pb  <- dr_pub_bias(fit)
pb$PET
pb$PEESE
pb$recommendation

Construct a Design Robustness Index (DR_i)

Description

Computes a scalar design robustness index \mathrm{DR}_i \in [0,1] for each study by forming a weighted composite of user-supplied sub-scores. This is the recommended way to operationalise the DR index described in Section 3.1 of Hait (2025).

Usage

dr_score(..., weights = NULL, warn_range = TRUE)

Arguments

Details

Sub-scores are first clipped to [0,1] and then combined as a normalised weighted average:

\mathrm{DR}_i = \sum_j \tilde{w}_j\, s_{ij}, \qquad \tilde{w}_j = w_j / \sum_j w_j.

The result is therefore guaranteed to lie in [0,1].

Typical sub-score dimensions for quasi-experimental studies include:

• Balance: covariate balance between treatment and control (e.g., standardised mean difference < 0.1 scores 1.0).

• Overlap: common-support / propensity-score overlap.

• Design: study design type — see dr_from_design.

• Transparency: pre-registration, data/code availability.

Value

A numeric vector of length k with values in [0,1]. The vector carries an attribute "subscores" containing a data frame of the clipped sub-scores and the final DR index.

See Also

dr_from_design, drmeta

Examples

k <- 5
balance  <- c(0.9, 0.6, 0.4, 0.8, 0.3)
overlap  <- c(0.8, 0.7, 0.5, 0.9, 0.4)
design   <- c(1.0, 0.5, 0.5, 0.75, 0.25)

# Equal weights
dr <- dr_score(balance = balance, overlap = overlap, design = design)
dr

# Down-weight transparency
transp <- c(1, 0, 0, 1, 0)
dr_w <- dr_score(balance = balance, overlap = overlap,
                 design = design, transparency = transp,
                 weights = c(2, 2, 3, 1))
dr_w

Evaluate the DR-Meta Variance Function

Description

Evaluates \tau^2(\mathrm{DR};\,\psi) for a grid of DR values or for the study-level DR indices from a fitted "drmeta" model. Useful for visualising how heterogeneity varies with design robustness.

Usage

dr_variance(dr, tau0sq = NULL, gamma = NULL, vfun = c("exponential", "linear"))

Arguments

Value

A numeric vector of \tau^2(\mathrm{DR}_i) values.

See Also

drmeta, dr_weights

Examples

# Evaluate on a grid
grid <- seq(0, 1, by = 0.1)
tau2 <- dr_variance(grid, tau0sq = 0.04, gamma = 1.5)
plot(grid, tau2, type = "l", xlab = "DR", ylab = expression(tau^2))

# Extract from a fitted model
set.seed(1)
fit <- drmeta(yi = rnorm(10, 0.3), vi = runif(10, 0.01, 0.05),
              dr = runif(10))
dr_variance(fit)

Compute DR-Meta Study Weights

Description

Returns the DR-Meta inverse-total-variance weights

w_i = \frac{1}{v_i + \hat\tau^2(\mathrm{DR}_i)},

given estimated variance-function parameters. Optionally normalises weights to sum to 1 or to 100.

Usage

dr_weights(
  vi,
  dr,
  tau0sq,
  gamma,
  vfun = c("exponential", "linear"),
  normalise = c("none", "sum1", "pct")
)

Arguments

Details

This function is primarily a utility for diagnostics and visualisation; weights are also returned as part of the "drmeta" object produced by drmeta.

Value

A numeric vector of weights, the same length as vi.

See Also

drmeta, dr_variance

Examples

vi  <- c(0.02, 0.03, 0.015, 0.025, 0.01)
dr  <- c(0.9,  0.4,  0.7,   0.2,   1.0)
dr_weights(vi, dr, tau0sq = 0.04, gamma = 1.5)
dr_weights(vi, dr, tau0sq = 0.04, gamma = 1.5, normalise = "pct")

Fit a Design-Robust Meta-Analysis (DR-Meta) Model

Description

Fits a random-effects meta-analysis model in which between-study heterogeneity is a monotone-decreasing function of each study's design robustness index \mathrm{DR}_i \in [0,1]. Studies with higher design robustness receive less heterogeneity weight, implementing Proposition 1 of Hait (2025).

Usage

drmeta(
  yi,
  vi,
  dr = NULL,
  vfun = c("exponential", "linear"),
  method = c("REML", "ML"),
  slab = NULL,
  control = list()
)

Arguments

Value

An object of class "drmeta" (a named list). Key components: mu (pooled estimate), se, ci.lb, ci.ub, zval, pval, tau0sq, gamma, tau2_i, sigma2_i, weights, loglik, reml_loglik, AIC, BIC, k, yi, vi, dr, slab, vfun, method, converged, optim_out, call.

References

Hait, S. (2025). Design-Robust Meta-Analysis: A Variance-Function Framework for Causal Credibility.

See Also

dr_heterogeneity, dr_loo, dr_pub_bias, dr_forest, dr_score, dr_from_design

Examples

set.seed(42)
k  <- 20
dr <- runif(k, 0.1, 0.9)
vi <- runif(k, 0.01, 0.05)
tau2_true <- 0.04 * exp(-2 * dr)
yi <- rnorm(k, 0.3, sqrt(vi + tau2_true))

fit <- drmeta(yi, vi, dr)
print(fit)
summary(fit)

Fitted Values for a drmeta Object

Description

Returns a vector of length k where every element equals the pooled estimate \hat\mu (the model has a single intercept, so all fitted values are identical).

Usage

## S3 method for class 'drmeta'
fitted(object, ...)

Arguments

Value

A numeric vector of length k where every element equals the pooled estimate \hat\mu. Because DR-Meta has a single intercept, all studies share the same fitted value.

Log-Likelihood for a drmeta Object

Description

Log-Likelihood for a drmeta Object

Usage

## S3 method for class 'drmeta'
logLik(object, REML = FALSE, ...)

Arguments

Value

An object of class "logLik". The numeric value is the maximised log-likelihood (ML or REML, depending on REML). The object carries two attributes: df (number of parameters, always 3: mu, tau0sq, gamma) and nobs (number of studies k).

Normalise a Numeric Vector to the [0, 1] Interval

Description

Linearly rescales a numeric vector to the [0,1] interval. Useful for standardising individual sub-score components before aggregation with dr_score.

Usage

normalize_01(x)

Arguments

Value

A numeric vector rescaled to [0,1]. If all non-missing values are equal, returns a zero vector (to avoid division by zero).

Examples

normalize_01(c(2, 5, 8))   # returns c(0, 0.5, 1)
normalize_01(c(1, 1, 1))   # returns c(0, 0, 0)

Print Method for drmeta Objects

Description

Print Method for drmeta Objects

Usage

## S3 method for class 'drmeta'
print(x, digits = 4, ...)

Arguments

Value

Invisibly returns the original drmeta object x, unchanged. This function is called for its side effect of printing a formatted summary of the fitted DR-Meta model to the console.

Residuals for a drmeta Object

Description

Residuals for a drmeta Object

Usage

## S3 method for class 'drmeta'
residuals(object, type = c("raw", "standardised"), ...)

Arguments

Value

A numeric vector of length k of residuals. When type = "raw" (default), returns observed minus fitted values (y_i - \hat\mu). When type = "standardised", each residual is divided by \sqrt{\hat\sigma^2_i} (the square root of the total study variance under the fitted model).

Summary Method for drmeta Objects

Description

Summary Method for drmeta Objects

Usage

## S3 method for class 'drmeta'
summary(object, digits = 4, ...)

Arguments

Value

Invisibly returns the fitted drmeta object object, unchanged. Called for its side effect of printing a detailed formatted summary — including the pooled estimate, confidence interval, z-test, variance-function parameters, and model fit statistics — to the console.