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.

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)

Arguments

Details

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 method chosen

• SE_standard: standard error from the method chosen

• 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

• 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
)

WAIVE: Weighted Adjusted Instrumental Variable Estimator

Description

WAIVE extends MAIVE by applying exponential-decay weights that downweight studies with spurious precision or extreme outlier behavior.

Usage

waive(dat, method, weight, instrument, studylevel, SE, AR, first_stage = 0L)

Arguments

Details

Computes robust downweighting based on first-stage residuals. Studies with negative residuals (spurious precision) or extreme residuals (outliers) receive reduced influence in the meta-analytic estimate.

Value

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

See Also

maive

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
)