Package {MAIVE}

MAIVE: Meta Analysis Instrumental Variable Estimator

Description

Meta-analysis traditionally assigns more weight to studies with lower standard errors, assuming higher precision. However, in observational research, precision must be estimated and is vulnerable to manipulation, such as p-hacking, to achieve statistical significance. This can lead to spurious precision, invalidating inverse-variance weighting and bias-correction methods like funnel plots. Common methods for addressing publication bias, including selection models, often fail or exacerbate the problem. This package introduces an instrumental variable approach to limit bias caused by spurious precision in meta-analysis. Methods are described in 'Irsova et al.' (2025) doi:10.1038/s41467-025-63261-0.

Author(s)

Maintainer: Petr Cala cala.p@seznam.cz (Charles University, Prague)

Authors:

• Zuzana Irsova (Charles University, Prague)

• Pedro R. D. Bom (University of Deusto, Bilbao)

• Tomas Havranek (Charles University, Prague; CEPR, London; METRICS, Stanford)

• Heiko Rachinger (University of the Balearic Islands, Palma)

See Also

Useful links:

• https://meta-analysis.cz/maive/

• https://github.com/meta-analysis-es/maive

• Report bugs at https://github.com/meta-analysis-es/maive/issues

Joint Anderson-Rubin CI computation

Description

Computes AR confidence intervals using a 2D grid search over (b0, b1) with chi^2_2 critical value. For the slope (Egger) coefficient under weak instruments, use method = "slope_only" instead.

Usage

compute_AR_CI_optimized(
  model,
  adjust_fun,
  bs,
  sebs,
  invNs,
  g,
  type_choice,
  weights = NULL,
  method = "joint"
)

Arguments

Subset Anderson-Rubin CI for the slope coefficient

Description

Computes weak-instrument-robust AR confidence interval for the slope (Egger) coefficient by treating the intercept as a nuisance parameter.

Usage

compute_AR_CI_slope_only(
  model,
  adjust_fun,
  bs,
  sebs,
  invNs,
  g,
  type_choice,
  weights = NULL
)

Details

This method is robust under weak instruments and avoids the "banana projection" artifact that can produce spuriously narrow CIs when projecting from 2D joint AR regions.

Algorithm (per tjhavranek, Nov 2025): 1. For each candidate slope b1, form residuals: r_i = y_i - b1 * x_i 2. Run auxiliary regression: r ~ 1 + z (intercept absorbs b0) 3. Use cluster-robust (CR2) variance for the z coefficient 4. Test statistic: t_z^2 from the clustered test 5. Accept b1 if t_z^2 <= qchisq(0.95, df = 1) = 3.84

References: - Guggenberger, P., Kleibergen, F. (2012). Econometrica. - Andrews, D. W. K., & Mikusheva, A. (2016). Econometrica.

Draw a funnel plot (base graphics)

Description

High-level wrapper that accepts the original input data and the result returned by 'maive()' / 'waive()', prepares the necessary vectors/metadata, and draws the funnel plot on the currently active graphics device.

Usage

get_funnel_plot(dat, result, instrument = NULL, model_type = "MAIVE")

Arguments

Details

Device management (PNG/SVG/PDF, resolution, base64 encoding) is intentionally left to the caller.

Value

Invisibly returns 'NULL'.

R code for MAIVE

Description

R package for MAIVE: "Spurious Precision in Meta-Analysis of Observational Research" by Zuzana Irsova, Pedro Bom, Tomas Havranek, Petr Cala, and Heiko Rachinger.

Usage

maive(
  dat,
  method,
  weight,
  instrument,
  studylevel,
  SE,
  AR,
  first_stage = 0L,
  estimate = NULL,
  se = NULL,
  n = NULL,
  study_id = NULL,
  seed = 123
)

Arguments

Details

Guided, interactive workflow available at https://www.easymeta.org.

Data dat can be imported from an Excel file via: dat <- read_excel("inputdata.xlsx") or from a csv file via: dat <- read.csv("inputdata.csv") It should contain:

• Estimates: bs

• Standard errors: sebs

• Number of observations: Ns

• Optional: study_id

Default option for MAIVE: MAIVE-PET-PEESE, unweighted, instrumented, cluster SE, wild bootstrap, AR.

Value

• beta: MAIVE meta-estimate

• SE: MAIVE standard error

• F-test: heteroskedastic robust F-test of the first step instrumented SEs

• beta_standard: point estimate from the conventional (non-instrumented, inverse-variance weighted) fit of the method chosen

• SE_standard: standard error from the same conventional fit as beta_standard

• Hausman: Hausman type test: comparison between MAIVE and standard version

• Chi2: 5

• SE_instrumented: instrumented standard errors

• AR_CI: Anderson-Rubin confidence interval for weak instruments

• pub bias p-value: p-value of test for publication bias / p-hacking based on instrumented FAT

• egger_coef: Egger Coefficient (PET estimate)

• egger_se: Egger Standard Error (PET standard error)

• egger_boot_ci: Confidence interval for the Egger coefficient using the selected resampling scheme

• egger_ar_ci: Anderson-Rubin confidence interval for the Egger coefficient (when available)

• is_quadratic_fit: Details on quadratic selection and slope behaviour

• ek_structure: Structure of the fitted EK model when method=4: "kink", "linear", or "intercept" (intercept-only degenerate fit); NA for other methods

• boot_result: Boot result

• slope_coef: Slope coefficient

• petpeese_selected: Which model (PET or PEESE) was selected when method=3 (NA otherwise)

• peese_se2_coef: Coefficient on SE^2 when PEESE is the final model (NA otherwise)

• peese_se2_se: Standard error of the PEESE SE^2 coefficient (NA otherwise)

Examples

dat <- data.frame(
  bs = c(0.5, 0.45, 0.55, 0.6),
  sebs = c(0.25, 0.2, 0.22, 0.27),
  Ns = c(50, 80, 65, 90)
)

result <- maive(dat,
  method = 3, weight = 0, instrument = 1,
  studylevel = 0, SE = 0, AR = 0, first_stage = 0
)

Convert metafor objects into MAIVE input data

Description

Builds the data frame that maive() and waive() expect (columns bs, sebs, Ns, and optionally study_id) from a metafor escalc data frame or an rma.uni model fit.

Usage

maive_from_metafor(x, ni = NULL, study_id = NULL)

Arguments

Details

The conversion takes the standard error as sqrt(vi), so metafor's sampling variance cannot end up in the sebs slot by mistake. Sample sizes are never inferred from the variances; doing so would reintroduce the spurious precision that MAIVE corrects for. They are resolved, in order, from the ni argument, an ni column (or the fit's ni), the ni attribute that escalc() stamps on the effect size column, and finally the exact two-group total n1i + n2i. When none of these is available the function stops and names what it needs.

For rma.uni fits the effect sizes, variances, sample sizes, and any vector supplied through ni or study_id are taken through the same subset and missing-value masks the fit applied, so the rows stay aligned. Multivariate (rma.mv), GLMM (rma.glmm), and other rma subclasses are refused rather than silently flattened.

Value

A data frame with columns bs, sebs, Ns, and, when identifiers were supplied, study_id, ready for maive() or waive().

Examples

dat <- metafor::escalc(
  measure = "SMD",
  m1i = c(2.1, 2.5, 1.9, 2.4, 2.2, 2.6),
  sd1i = c(1.0, 1.2, 0.9, 1.1, 1.0, 1.3),
  n1i = c(40, 50, 30, 45, 60, 35),
  m2i = c(1.8, 2.0, 1.7, 2.1, 1.9, 2.2),
  sd2i = c(1.0, 1.1, 1.0, 1.0, 1.1, 1.2),
  n2i = c(42, 55, 33, 48, 58, 37)
)
maive_dat <- maive_from_metafor(dat)
head(maive_dat)

fit <- metafor::rma(yi, vi, data = dat)
identical(maive_from_metafor(fit), maive_dat)

result <- maive(maive_dat,
  method = 3, weight = 0, instrument = 1,
  studylevel = 0, SE = 0, AR = 0
)

Funnel plot (base graphics)

Description

Components provided: - 'get_funnel_plot()' as the public high-level entrypoint - internal helpers to validate and map '(dat, result)' into plot inputs - an internal base-graphics engine that draws onto the current device

Details

Device management (PNG/SVG/PDF), resolution, and any base64 encoding are the caller's responsibility.

WAIVE: More Aggressive Correction for P-Hacking and Spurious Precision

Description

WAIVE (Weighted Adjusted Instrumental Variable Estimator) provides a more aggressive correction for p-hacking and spurious precision by extending MAIVE with exponential-decay weights that downweight both spuriously precise estimates and extreme outliers.

Usage

waive(
  dat,
  method,
  weight,
  instrument,
  studylevel,
  SE,
  AR,
  first_stage = 0L,
  estimate = NULL,
  se = NULL,
  n = NULL,
  study_id = NULL,
  seed = 123
)

Arguments

Details

Guided, interactive workflow available at https://www.easymeta.org.

For technical details on WAIVE methodology, see: https://meta-analysis.cz/waive_ottawa.pdf

WAIVE combines variance instrumentation (as in MAIVE) with robust downweighting based on first-stage residuals. Studies with negative residuals (spurious precision) or extreme residuals (outliers) receive exponentially reduced influence in the meta-analytic estimate. This makes WAIVE more aggressive than standard MAIVE at correcting for p-hacking and handling outliers.

Value

List with the same structure as maive(). See ?maive for details.

Examples

dat <- data.frame(
  bs = c(0.5, 0.45, 0.55, 0.6),
  sebs = c(0.25, 0.2, 0.22, 0.27),
  Ns = c(50, 80, 65, 90)
)

result <- waive(dat,
  method = 3, weight = 0, instrument = 1,
  studylevel = 0, SE = 0, AR = 0, first_stage = 0
)