POEMED: Power Enhancement for High-Dimensional Mediation Analysis

POEMED implements powerful global tests for high-dimensional mediation analysis, for continuous, binary, and count outcomes. It answers the question “is there any active mediator among a large set of candidate mediators?” and, when the answer is yes, reports which individual mediators its screen identifies as active. The name comes from POwer-Enhanced MEDiation and is pronounced “POE-med”.

Why Power Enhancement

The conventional high-dimensional mediation test targets the total indirect effect beta = Gamma_x' alpha_m, the sum of every mediator’s individual indirect effect. When some indirect effects are positive and others negative they can cancel, making beta = 0 even though active mediators exist, and a test built on beta is then powerless. The power-enhanced (PE) test adds a component J_m that accumulates the marginal signal from each individual mediator. Because J_m sums magnitudes, opposite-signed effects reinforce rather than cancel, so the test stays powerful under heterogeneous and contrasting mediation. Under the global null the enhancement is built to vanish: as the sample size and the number of candidate mediators grow, the test’s Type I error rate approaches the nominal level, as the benchmark’s does, and in finite samples it rejects slightly more often than the benchmark.

When to Use POEMED

POEMED answers the global question, “is there any active mediator among many candidates?”, and then names the mediators it identifies as active. Reach for it when the candidate mediators number in the dozens or more (p may exceed n), the outcome is continuous, binary, or a count, and the individual mediation effects may differ in sign. For a single mediator, or a few mediators fit as one structural model (indirect effects with confidence intervals, likelihood ratio tests of arbitrary indirect effects, moderated mediation), use DMAR instead. Among high-dimensional global tests, POEMED implements the power-enhanced tests of Yu and Kelley (in press) and the HDMM benchmark they extend; HILMA, GlobalTest, HDMT, and DACT are separate methods in their own packages. The vignette poemed-vs-competitors shows how to run HILMA and GlobalTest beside a POEMED fit and where to find HDMT and DACT. The guided-tour vignette and ?pe_mediation state the method’s practical limits (a sample size small relative to log(p) and to the signal, strongly correlated mediators, the screen’s asymptotic error rate control in finite samples, rare binary outcomes, overdispersed counts, and missing values).

Installation

Once POEMED is on CRAN:

install.packages("POEMED")

The development version, from GitHub:

# install.packages("remotes")
remotes::install_github("yelleKneK/POEMED", build_vignettes = TRUE)

POEMED imports glmnet and ncvreg; knitr and rmarkdown build the vignettes. After installing, browseVignettes("POEMED") opens the guides.

Quick Start

library(POEMED)

# A contrasting setting: active mediators whose indirect effects cancel,
# so the total indirect effect is zero.
set.seed(113)
d <- simulate_mediation_data(n = 200, p = 60, outcome = "continuous",
                             pattern = "contrasting", c1 = 1)

# One call reports the benchmark Wald test and the power-enhanced test
# side by side, and names the active mediators the screen identified.
pe_mediation(d$X, d$Y, d$M, outcome = "continuous")

The benchmark test (pval_hdmm) does not reject the (zero) total indirect effect; the power-enhanced test (pval_pe) rejects decisively, and the screen identifies three of the four truly active mediators as active (the footer reads “Active mediators identified (3): 2, 3, 4”). The footer also reports the tuning parameter the high-dimensional BIC chose and the grid it was chosen from, seq(0.05, 10, length.out = 100) by default for every outcome type; the grid can be shortened to save time or extended when the value chosen sits at an end of it, which the fit warns about (see ?pe_mediation). Run as printed, this fit chooses 0.05, the smallest value, and warns; a grid extended below it and spaced more finely (seq(0.01, 10, length.out = 200)) chooses an interior value and identifies the same three mediators as active.

Reproducing the Article

All data needed to rerun the article’s analyses ship with the package; nothing is downloaded at run time. The vignette reproducing-the-article reruns the empirical analysis cell by cell; the table below maps each article result to the function that runs its analysis.

The Monte Carlo studies use the article’s n = 300, p = 500, and 1,000 replications (the supplement’s real-data-motivated setting its case-study n = 85 and p = 1008), and each panel takes hours; set cores > 1 to parallelize (near-linear). The real-data analyses are deterministic: under its default tuning grid, WHO_mediation_analysis() reproduces the active mediators identified in Tables 1, 2, and S.8 to S.12 (every identified set but one BH set) and their benchmark p-values to the printed four decimals, apart from a few cells that differ in the fourth decimal or below 0.0001 and six cells it does not fit: four in which two indicators are exactly collinear and two in which the outcome is constant. The reproduction vignette names those six cells, shows how to fit the four collinear ones by hand, and shows why the two constant-outcome cells cannot be fit. The package’s test suite pins every global, region, and income row of Tables 1 and 2 (tests/testthat/test-benchmark.R) and checks every populated cell of Tables 1, 2, and S.8 to S.12 against the printed values (tests/testthat/test-who_article_tables.R).

# The global, region, and income models of the article's infant-mortality
# analysis (Table 1); add "region_income" to groupings for the
# region-by-income cells.
WHO_mediation_analysis("imr", groupings = c("global", "region", "income"))

Vignettes

browseVignettes("POEMED")

• POEMED: a guided tour of the method and the package.
• reproducing-the-article: the empirical analysis rerun cell by cell.
• poemed-vs-competitors: a head-to-head against the benchmark test.

Main Functions

Every test reports the benchmark Wald test and the power-enhanced test side by side, plus the estimated total indirect effect. No confidence interval is reported: the article reports none, and the Wald interval built on the penalized estimate under-covers in finite samples. report_all_methods = TRUE adds the identified active set and the PE p-value under all three multiplicity methods, drop_constant = TRUE tolerates zero-variance mediators, and cores parallelizes the Monte Carlo and benchmark routines. For a continuous outcome, pe_mediation_linear() also takes lambda_grid_reduced, the tuning grid for the reduced model it fits beside the full one (by default the same grid as lambda_grid).

Data

• WHO_health_mediation: the empirical panel analyzed in the article: 91 World Health Organization member states over 2000–2021, with GDP per capita growth as the exposure, 57 WHO Global Health Expenditure Database indicators as candidate mediators, and five World Bank health outcomes (infant and under-five mortality, life expectancy, low birthweight, undernourishment).
• WHO_indicator_codebook: definitions of the 57 indicators.
• guo_calibration: constants for the real-data-motivated heterogeneous simulation.
• example_continuous, example_binary, example_count: small simulated data sets, one per outcome type, each with three confounders and stored with the truth that generated it (the truly active mediators and every coefficient).

Reference

Yu, X., & Kelley, K. (in press). Power Enhancement in High-Dimensional Heterogeneous Mediation Analysis. Journal of the American Statistical Association.

If you use POEMED in published work, please cite the article. Run citation("POEMED") for the BibTeX entry.

Authors

• Xiufan Yu, Department of Applied and Computational Mathematics and Statistics, University of Notre Dame.
• Ken Kelley (maintainer), Department of IT, Analytics, and Operations, University of Notre Dame (kkelley@nd.edu).

License

GPL (>= 3).