GFisher: Generalized Fisher’s Combination Tests Under Dependence

Overview

GFisher is an R package that provides accurate and computationally efficient methods for computing p-values for a general family of Fisher-type statistics (GFisher), including Fisher’s combination, Good’s statistic, Lancaster’s statistic, and weighted Z-score combinations. It supports flexible weighting schemes and an omnibus procedure that adapts the weights and degrees of freedom to the data. The p-value calculation methods used in the testing procedure are based on moment-ratio matching and joint distribution approximations. The new version includes both pure R implementations and optimized C++ code via RcppArmadillo to improve performance on large-scale data. Based on Zhang, H. and Wu, Z. (2022) ``The generalized Fisher’s combination and accurate p-value calculation under dependence”, Biometrics, 79(2), 1159-1172.

Key Features

  • Generalized Fisher’s combination tests: Implements the GFisher family of tests with flexible degrees of freedom and weighting schemes
  • Omnibus testing (oGFisher): Adapts test weights and degrees of freedom to the data for increased power
  • Multiple calculation methods: Supports moment ratio matching (MR), hybrid quadratic approximation (HYB), and Brown’s method (GB)
  • Handles dependence: Accounts for correlation structure among input test statistics through correlation matrices
  • Independent case optimization: Special fast implementations when input p-values are independent
  • C++ acceleration: High-performance implementations using RcppArmadillo achieving 2-400x speedups with caching
  • CRAN compliant: Follows all R package development standards with comprehensive documentation and tests
  • Cross-platform: Works on Windows, macOS, and Linux

Installation 

# install.packages("remotes")
remotes::install_github("ZWuLab/GFisher")

From source 

# requires a C++ compiler
install.packages("devtools")
devtools::install_local("path/to/GFisher")

System Requirements

  • R >= 4.3.0
  • C++11 compiler
  • RcppArmadillo (automatically installed)

Optional Dependencies

For optimized calculations under independence (*_ind functions), install the ‘coga’ package:

# Check if coga is available
GFisher::check_coga()

# Install coga from CRAN
install.packages("coga")

# Or use the helper function
GFisher::check_coga(install = TRUE)

Note: If ‘coga’ is not installed, you can still perform calculations under independence using the general functions with M = diag(n), though this will be slower than the specialized *_ind functions.

Quick Start 

library(GFisher)

# Example: Combine p-values under independence
set.seed(123)
pvals <- c(0.01, 0.03, 0.05, 0.1, 0.2)

# Calculate GFisher statistic (standard Fisher's method: df=2, equal weights)
stat <- stat.GFisher(pvals, df = 2, w = 1)

# Calculate p-value (fast method for independent p-values)
p_value <- p.GFisher_ind_w1(stat, df = rep(2, length(pvals)))
print(p_value)
# Calculate p-value using other functions
p.GFisher_ind(stat, df=rep(2, length(pvals)), w=rep(1, length(pvals)))
p.GFisher(stat, df=2, w=1, M=diag(length(pvals)))

# Example: Account for dependence with correlation matrix
n <- 5
M <- matrix(0.3, n, n) + diag(0.7, n, n)  # Correlation matrix
p_dependent <- p.GFisher(stat, df = 2, w = 1, M = M, method = "HYB")
print(p_dependent)

Package Structure 

GFisher/
├── R/                  # R function implementations
├── src/                # C++ source code
├── tests/testthat/     # Unit tests
├── vignettes/          # Documentation and examples
└── inst/               # Additional package files

Development Status

Version 0.3.0

This version includes fully implemented GFisher methodology with both R and optimized C++ implementations.

Main Functions

Basic GFisher Tests: - stat.GFisher(): Calculate GFisher test statistic - p.GFisher(): Calculate p-value under dependence (methods: HYB, MR, GB)

Omnibus Tests: - stat.oGFisher(): Calculate multiple GFisher statistics with different configurations - pval.oGFisher(): Combined p-value using Cauchy combination or minimum p-value

Independent Case (Optimized, require ‘coga’ package): - p.GFisher_ind(): Fast p-value calculation for independent inputs (requires coga) - p.GFisher_ind_w1(): Fastest method for equal weights (no coga needed) - stat.oGFisher_ind(): Omnibus test for independent inputs (requires coga) - pval.oGFisher_ind(): Combined p-value for independent inputs (requires coga)

Helper Functions: - check_coga(): Check and optionally install ‘coga’ package for independent functions - getGFisherGM(): Calculate covariance of GFisher statistic - getGFisherlam(): Calculate eigenvalues for moment matching - getGFisherCOR(): Calculate correlation among multiple GFisher tests - getGFishercov(): Calculate covariance matrix - getGFishercoef(): Calculate coefficients for variance calculation

Documentation

Testing

The package includes comprehensive unit tests using testthat:

devtools::test()

Performance Benchmarks

The C++ implementations provide substantial speedups over pure R code:

  • 2-10x speedup: Basic coefficient and covariance calculations
  • 50-400x speedup: With caching enabled for repeated calculations
  • Moment ratio method: C++ implementation handles large simulations efficiently

Recent Optimization (2025-10-16): Refactored getGFisherGM() to eliminate code duplication and integrate with the caching system. Both R and C++ versions now share coefficient calculations, providing: - Eliminated ~80 lines of duplicated code - 2-4x speedup on repeated calls with same degrees of freedom - 30-70% time reduction for typical genomic pipelines analyzing thousands of gene sets - Automatic caching with negligible memory overhead (<2 KB)

Contributing

For issues or contributions, please file an issue on GitHub or contact the package maintainer.

License

GPL-3

Citation

If you use GFisher in your research, please cite:

Zhang, H. and Wu, Z. (2022). The generalized Fisher's combination and accurate p-value calculation under dependence. *Biometrics*, 79(2), 1159-1172. doi:10.1111/biom.13634

Contact

Maintainer: Hong Zhang (). Please file bugs and questions at https://github.com/ZWuLab/GFisher/issues.

Authors

GFisher is also used as the combination-test backend of the GLOW software family.

Developed with AI assistance; see AI-USE.md.