Package {cdmeta}

Title:	Confidence-Distribution-Based Inference for Random-Effects Meta-Analysis
Version:	1.1-1
Date:	2026-09-07
Maintainer:	Hisashi Noma <noma@ism.ac.jp>
Description:	Computational tools for confidence-distribution-propagation-based inference in random-effects meta-analysis. Implements confidence-distribution propagation for frequentist inference in random-effects meta-analysis. The package samples the between-study variance from a confidence distribution based on the exact distribution of Cochran's Q, samples the average effect conditionally on each draw, and generates the true effect in a future study. It provides prediction intervals and confidence intervals for the average effect, between-study variance, between-study standard deviation, and I2. The methods are described in Noma and Schwarzer (2026) <doi:10.48550/arXiv.2608.26527>.
Depends:	R (≥ 3.5.0)
Imports:	stats, graphics, pimeta (≥ 1.1.3)
Suggests:	metafor
URL:	https://github.com/guido-s/cdmeta
BugReports:	https://github.com/guido-s/cdmeta/issues
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
NeedsCompilation:	no
Config/roxygen2/version:	8.1.0
Packaged:	2026-09-07 10:00:30 UTC; nomah
Author:	Hisashi Noma [aut, cre], Guido Schwarzer [aut]
Repository:	CRAN
Date/Publication:	2026-09-15 11:50:13 UTC

cdmeta: Confidence-Distribution-Based Inference for Random-Effects Meta-Analysis

Description

Computational tools for confidence-distribution-propagation-based inference in random-effects meta-analysis. The package provides prediction intervals for the effect in a future study and interval estimation for the overall mean effect and heterogeneity measures.

Details

The main function is cdmeta. Forest plots are produced by the exported S3 generic forest, which dispatches to forest.cdmeta for objects of class "cdmeta".

Author(s)

Maintainer: Hisashi Noma noma@ism.ac.jp (ORCID)

Authors:

• Hisashi Noma noma@ism.ac.jp (ORCID)

• Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de (ORCID)

References

Higgins, J. P. T., Thompson, S. G., and Spiegelhalter, D. J. (2009). A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A, 172(1), 137–159. doi:10.1111/j.1467-985X.2008.00552.x

Noma, H., and Schwarzer, G. (2026). Frequentist prediction intervals for random-effects meta-analysis via confidence-distribution propagation. arXiv, 2608.26527. doi:10.48550/arXiv.2608.26527

Partlett, C., and Riley, R. D. (2017). Random effects meta-analysis: Coverage performance of 95 percent confidence and prediction intervals following REML estimation. Statistics in Medicine, 36(2), 301–317. doi:10.1002/sim.7140

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. doi:10.18637/jss.v036.i03

See Also

cdmeta, forest.cdmeta

Vitamin K antagonists for prevention of stroke in non-valvular atrial fibrillation

Description

A pairwise subset extracted from a network meta-analysis of antithrombotic treatments for prevention of stroke in patients with non-valvular atrial fibrillation. The dataset includes direct comparisons of vitamin K antagonists versus placebo or control, with study-specific log odds ratios and standard errors for the stroke outcome.

Usage

data(af_vka)

Format

A data frame with 6 rows and 11 variables:

study_id

Study identifier.

study

Trial name.

treatment

Label for the treatment group.

control

Label for the control group.

treatment_events

Number of stroke events in the treatment group.

treatment_total

Number of participants in the treatment group.

control_events

Number of stroke events in the control group.

control_total

Number of participants in the control group.

yi

Study-specific log odds ratio comparing vitamin K antagonists with placebo or control.

sei

Standard error of yi.

vi

Sampling variance of yi, equal to sei^2.

Source

Dogliotti, A., Paolasso, E., and Giugliano, R. P. (2014). Current and new oral antithrombotics in non-valvular atrial fibrillation: a network meta-analysis of 79808 patients. Heart, 100(5), 396–405. doi:10.1136/heartjnl-2013-304347

Confidence-distribution-based inference for random-effects meta-analysis

Description

Performs unified confidence-distribution-based inference for random-effects meta-analysis. The function provides inference for the overall mean effect \mu, heterogeneity variance \tau^2, heterogeneity standard deviation \tau, heterogeneity proportion I^2, and the effect in a future study \theta_{\mathrm{new}}.

Usage

cdmeta(
  y,
  se,
  alpha = 0.05,
  B = 25000,
  seed = NULL,
  parallel = FALSE,
  tau2_samples = NULL,
  i2_method = c("typical_se2", "mean_se2", "harmonic_mean_se2"),
  mu_dist = c("normal", "t"),
  df = NULL,
  qtype = 8,
  transf = NULL,
  transf_name = NULL,
  ...
)

Arguments

Details

The function first obtains Monte Carlo samples of the between-study variance \tau^2. These samples are obtained either from pimeta::pima(..., method = "boot") or from a user-supplied vector tau2_samples.

Given sampled values of \tau^2, the function performs conditional sampling of the overall mean effect. If mu_dist = "normal", then

\mu \mid \tau^2, y \sim N\{\hat{\mu}(\tau^2), V_{\mu}(\tau^2)\}.

If mu_dist = "t", then a t distribution with df degrees of freedom is used instead. The predictive distribution for a future study effect is then generated as

\theta_{\mathrm{new}} \mid \mu, \tau^2 \sim N(\mu, \tau^2).

For I^2, the sampled \tau^2 values are transformed using a reference within-study variance specified by i2_method.

If transf is supplied, all calculations are still performed on the original analysis scale of y. The transformation is applied after Monte Carlo sampling. Heterogeneity measures \tau^2, \tau, and I^2 are not transformed.

Value

An object of class "cdmeta". The main components include the matched call, study and Monte Carlo counts, point estimates, interval estimates, Monte Carlo draws, input data, the pimeta result (when used), and transformation information.

References

Noma, H., and Schwarzer, G. (2026). Frequentist prediction intervals for random-effects meta-analysis via confidence-distribution propagation. arXiv, 2608.26527. doi:10.48550/arXiv.2608.26527

See Also

forest.cdmeta, plot.cdmeta

Examples

data(hf_iron)

fit_hf <- cdmeta(
  y = hf_iron$yi,
  se = hf_iron$sei,
  B = 10000,
  seed = 11111,
  transf = exp,
  transf_name = "exp"
)

fit_hf

forest(
  fit_hf,
  slab = hf_iron$study,
  at = log(c(0.25, 0.5, 1, 2, 4)),
  xlab = "Risk ratio",
  mark_summary_estimate = TRUE,
  mark_prediction_estimate = TRUE
)

Forest plot for cdmeta objects

Description

Draws a forest plot from an object of class "cdmeta". The plot shows study-specific effect estimates and confidence intervals, the confidence-distribution-based summary estimate for the overall mean effect, and optionally the prediction interval for the effect in a future study.

Usage

## S3 method for class 'cdmeta'
forest(
  x,
  slab = NULL,
  order = c("none", "increasing", "decreasing", "precision", "weight"),
  level = NULL,
  summary_stat = c("mean", "median"),
  refline = 0,
  xlab = "Effect size",
  main = NULL,
  atransf = NULL,
  at = NULL,
  alim = NULL,
  xlim = NULL,
  digits = 2,
  ci_digits = digits,
  weight_digits = 1,
  show_weights = TRUE,
  show_pi = TRUE,
  show_het = TRUE,
  header = TRUE,
  annotate = TRUE,
  cex = 0.85,
  psize = NULL,
  pch = 22,
  box_col = "black",
  box_bg = "white",
  ci_col = "black",
  summary_col = "black",
  summary_bg = "gray20",
  pi_col = "gray40",
  refline_col = "gray70",
  grid = TRUE,
  grid_col = "gray90",
  qtype = 8,
  symmetric_shapes = TRUE,
  mark_summary_estimate = FALSE,
  mark_prediction_estimate = FALSE,
  estimate_mark_col = "black",
  estimate_mark_lwd = 1,
  mar = c(4.5, 1, 3, 1),
  ...
)

forest(x, ...)

Arguments

Details

Study-specific confidence intervals are calculated using the normal approximation

y_i \pm z_{1-\alpha/2} se_i,

where \alpha = 1 - level. The summary interval for \mu and the prediction interval are calculated from the Monte Carlo samples in the cdmeta object when available.

If the object was created with transf = exp, forest() uses this transformation automatically when atransf = NULL. Tick marks supplied through at remain on the original analysis scale.

Value

Invisibly returns a data frame containing the plotted study-specific estimates, standard errors, confidence intervals, and weights. Attributes contain the overall, prediction, and heterogeneity summaries on the original analysis scale.

See Also

cdmeta

Examples

data(hf_iron)
fit_hf <- cdmeta(
  y = hf_iron$yi,
  se = hf_iron$sei,
  B = 10000,
  seed = 11111,
  transf = exp,
  transf_name = "exp"
)

forest(
  fit_hf,
  slab = hf_iron$study,
  at = log(c(0.25, 0.5, 1, 2, 4)),
  xlab = "Risk ratio",
  mark_summary_estimate = TRUE,
  mark_prediction_estimate = TRUE
)

Intravenous iron therapy for patients with heart failure and iron deficiency

Description

A dataset from a systematic review and meta-analysis of randomized trials evaluating intravenous iron therapy for patients with heart failure and iron deficiency. The outcome is represented by study-specific log risk ratios and their standard errors.

Usage

data(hf_iron)

Format

A data frame with 6 rows and 5 variables:

study_id

Study identifier.

study

Trial name.

yi

Study-specific log risk ratio.

sei

Standard error of yi.

vi

Sampling variance of yi, equal to sei^2.

Source

Anker, S. D., et al. (2025). Systematic review and meta-analysis of intravenous iron therapy for patients with heart failure and iron deficiency. Nature Medicine, 31, 2640–2646. doi:10.1038/s41591-025-03671-1

Plot the predictive distribution from a cdmeta object

Description

Displays the Monte Carlo predictive distribution of the true effect in a future study and, optionally, its prediction interval.

Usage

## S3 method for class 'cdmeta'
plot(
  x,
  show_interval = TRUE,
  breaks = 40,
  main = NULL,
  xlab = NULL,
  hist_col = "grey85",
  border_col = "white",
  density_lwd = 2,
  pi_col = "firebrick",
  pi_lwd = 3,
  rug = FALSE,
  transf = NULL,
  transf_name = NULL,
  qtype = 8,
  ...
)

Arguments

Value

The input object x, invisibly.

Examples

data(hf_iron)
fit_hf <- cdmeta(hf_iron$yi, hf_iron$sei, B = 10000, seed = 11111)
plot(fit_hf)

Print a cdmeta object

Description

Prints point estimates, confidence intervals, and the prediction interval from an object of class "cdmeta".

Usage

## S3 method for class 'cdmeta'
print(x, digits = 4, transf = NULL, transf_name = NULL, qtype = 8, ...)

Arguments

Value

The input object x, invisibly.