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:

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")
install.packages("MAIVE", repos = c('https://petrcala.r-universe.dev', 'https://cloud.r-project.org'))

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:

Column Label Description
1 bs Primary estimates (effect sizes)
2 sebs Standard errors (must be > 0)
3 Ns Sample sizes (must be > 0)
4 study_id Study identification (optional, for clustering/fixed effects)

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. A column already mapped as estimate, se, or n is never picked: the single remaining column is used instead, and when several remain an error asks for study_id. With study fixed effects (studylevel 1 or 3), 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

Weighting Schemes

Robust Inference

Output

The function returns:

Documentation

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:

License

MIT License - see LICENSE file for details.

Authors

Questions? Contact the maintainer or visit our project website.