MAIVE: Meta-Analysis Instrumental Variable Estimator

Spurious Precision in Meta-Analysis of Observational Research
by Zuzana Irsova, Pedro R. D. Bom, Tomas Havranek, and Heiko Rachinger

Project Website: https://meta-analysis.cz/maive/

Overview

MAIVE addresses a fundamental problem in meta-analysis of observational research: spurious precision.

Traditional meta-analysis assigns more weight to studies with lower standard errors, assuming higher precision. However, in observational research, precision can be manipulated through p-hacking and other questionable research practices, invalidating:

• Inverse-variance weighting schemes
• Traditional bias-correction methods (funnel plots, trim-and-fill)
• Selection models for publication bias

MAIVE implements an instrumental variable approach to limit bias caused by spurious precision in meta-analysis.

Installation

From CRAN

install.packages("MAIVE")

Development version

install.packages("devtools")
devtools::install_github("PetrCala/MAIVE")

Load package

library(MAIVE)

Quick Start

# Prepare your data
data <- data.frame(
  bs = c(...),        # Effect sizes
  sebs = c(...),      # Standard errors
  Ns = c(...),        # Sample sizes
  study_id = c(...)   # Study IDs (optional)
)

# Run MAIVE with defaults (PET-PEESE, instrumented SEs, no weights)
result <- maive(
  dat = data,
  method = 3,      # PET-PEESE (default)
  weight = 0,      # No weights (default)
  instrument = 1,  # Instrument SEs (default)
  studylevel = 2,  # Cluster-robust (default)
  SE = 3,          # Wild bootstrap (default)
  AR = 1           # Anderson-Rubin CI (default)
)

# View results
print(result$beta)        # MAIVE estimate
print(result$SE)          # Standard error
print(result$Hausman)     # Hausman test
print(result$`F-test`)    # First-stage F-test

Data Structure

The maive() function expects a data frame with:

Other column names can be mapped with the estimate, se, n, and study_id arguments. A column named study_id is used as the study identifier wherever it sits. If there is no such column and no study_id argument, the fourth column is used with a warning that names it, so a moderator or year kept in column four does not silently drive the study dummies and clustering. With a study identifier, the data needs at least the number of unique studies plus three rows.

Using metafor objects

If your effect sizes already live in a metafor escalc() data frame or an rma() fit, convert them with maive_from_metafor() rather than rebuilding the frame by hand. It takes sqrt(vi) as the standard error (pasting metafor’s variance into sebs raises no error but shifts the estimate) and reads sample sizes from the object, never from the variance:

dat <- metafor::escalc(measure = "SMD", m1i = ..., sd1i = ..., n1i = ...,
                       m2i = ..., sd2i = ..., n2i = ...)
result <- maive(maive_from_metafor(dat), method = 3, weight = 0, instrument = 1,
                studylevel = 0, SE = 3, AR = 1)

Rows of an rma.uni fit are taken through the fit’s subset and missing-value masks, so a study_id vector for the original data stays aligned. rma.mv and rma.glmm fits are refused rather than flattened.

Key Features

Methods

• PET (Precision-Effect Test)
• PEESE (Precision-Effect Estimate with Standard Error)
• PET-PEESE (Conditional method, default)
• EK (Endogenous Kink)

Weighting Schemes

• No weights (recommended when spurious precision is a concern)
• Inverse-variance weights
• MAIVE-adjusted weights (using instrumented SEs)
• WAIVE (more aggressive correction via waive() function - downweights spurious precision and outliers) - Details

Robust Inference

• Study-level correlation (fixed effects, clustering, or both)
• Multiple SE estimators (CR0, CR1, CR2, wild bootstrap)
• Anderson-Rubin confidence intervals for weak instruments
• First-stage specification options (levels or log transformation)

Output

The function returns:

• MAIVE point estimate and standard error
• Standard (non-IV) estimate for comparison
• Hausman-type test statistic
• First-stage F-test of instrument strength
• Anderson-Rubin confidence interval
• Publication bias test p-value
• Instrumented standard errors

Documentation

• Getting Started Guide: See vignette("introduction")
• Function Reference: ?maive and ?waive
• Guided interactive workflow: https://www.easymeta.org
• Development Workflow: .github/DEVELOPMENT-WORKFLOW.md
• CRAN Submission: .github/CRAN-SUBMISSION.md
• Project Page: https://meta-analysis.cz/maive/

Example

# Create example data
set.seed(123)
Ns <- sample(100:1000, 50, replace = TRUE)
data <- data.frame(
  bs = rnorm(50, mean = 0.3, sd = 0.2),
  sebs = 2 / sqrt(Ns) * runif(50, min = 0.8, max = 1.2),  # precision driven by sample size
  Ns = Ns,
  study_id = rep(1:10, each = 5)
)

# Run MAIVE
result <- maive(data, method = 3, weight = 0, instrument = 1, 
                studylevel = 2, SE = 3, AR = 1)

# Compare with standard estimate
cat("MAIVE Estimate:", result$beta, "\n")
cat("Standard Estimate:", result$beta_standard, "\n")
cat("Hausman Test:", result$Hausman, "\n")

# Use WAIVE for more aggressive correction (downweights spurious precision + outliers)
result_waive <- waive(data, method = 3, weight = 0, instrument = 1,
                      studylevel = 2, SE = 3, AR = 1)
cat("WAIVE Estimate:", result_waive$beta, "\n")

Citation

If you use MAIVE in your research, please cite:

Irsova, Z., Bom, P.R.D., Havranek, T., & Rachinger, H. (2025). Spurious precision in meta-analysis of observational research. Nature Communications, 16, 8454. https://doi.org/10.1038/s41467-025-63261-0

References

Keane, M., & Neal, T. (2023). Instrument strength in IV estimation and inference: A guide to theory and practice. Journal of Econometrics, 235(2), 1625-1653. https://doi.org/10.1016/j.jeconom.2022.12.009

Tipton, E. (2015). Small sample adjustments for robust variance estimation with cluster-correlated data. Psychological Methods, 20(3), 375–389. https://doi.org/10.1037/met0000019

Contributing

We welcome contributions! Please see our GitHub repository for:

• Bug reports and feature requests (use Issues)
• Code contributions (submit Pull Requests)
• Questions and discussions

License

MIT License - see LICENSE file for details.

Authors

• Zuzana Irsova - Charles University, Prague
• Pedro R. D. Bom - University of Deusto, Bilbao
  
• Tomas Havranek - Charles University, Prague; CEPR, London; METRICS, Stanford
• Petr Cala (Maintainer) - Charles University, Prague
• Heiko Rachinger - University of the Balearic Islands, Palma

Questions? Contact the maintainer or visit our project website.