Power Enhancement for High-Dimensional Mediation Analysis (POEMED)

Powerful global tests for high-dimensional mediation analysis, for continuous, binary, and count outcomes, implementing the power-enhanced tests of Yu and Kelley (in press). The package 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 the screen identifies as active. The name comes from POwer-Enhanced MEDiation and is pronounced “POE-med”.

The Problem POEMED Solves

A mediation analysis asks how an exposure \(X\) affects an outcome \(Y\) through intermediate variables (mediators) \(M\). With many candidate mediators, the standard approach tests the total indirect effect \(\beta = \Gamma_x \alpha_m\), the sum of every mediator's individual indirect effect, with the partially penalized Wald test of Guo et al. (2022, 2023, 2024). That test has a blind spot: when some mediators carry positive indirect effects and others carry negative ones, the individual effects can cancel and the total indirect effect is zero even though active mediators plainly exist. A test built on the total indirect effect is then powerless, by construction, against exactly the heterogeneous mediation that is common in practice.

The power enhancement (PE) tests of Yu and Kelley (in press), which follow the power enhancement principle of Fan, Liao, and Yao (2015), add a component \(J_m\) that accumulates the marginal signal from each individual mediator. Because \(J_m\) is a sum of magnitudes, opposite-signed indirect effects reinforce rather than cancel, so the PE test detects active mediators whether their effects are homogeneous, heterogeneous, or exactly contrasting. Under the global null of no mediation the PE test has the same chi-square limit as the original test, so its Type I error rate is controlled asymptotically; in finite samples it can reject somewhat more often than the original test (see pe_mediation()).

Main Functions

pe_mediation(): The front end. Give it the exposure, outcome, mediators, and optional confounders, name the outcome type (continuous, binary, or count), and it returns a tidy table with the benchmark Wald test, the power-enhanced test, the estimated total indirect effect, and the active mediators the screen identified.
pe_mediation_linear(), pe_mediation_logistic(), pe_mediation_poisson(): The outcome-specific workers that pe_mediation() dispatches to. Call them directly when the outcome type is known.
simulate_mediation_data(): Generates mediation data under the homogeneous and contrasting patterns studied in the article, for any of the three outcome types.
simulate_guo_mediation() and guo_calibration: The article's real-data-motivated heterogeneous setting (Section S.4.4 of its supplement), a continuous-outcome design with eleven active mediators of mixed sign, and the constants that calibrate it.
pe_power_curve(): Runs the article's Monte Carlo size and power study: it sweeps a signal-strength grid and returns the empirical rejection rate of the benchmark and power-enhanced tests at each point.
pe_mediate(): A data-frame / formula front end to pe_mediation() for users who prefer naming columns to matrices.
pe_mediators() and pe_selection(): The per-mediator screen detail behind a fit, and the active mediators identified under each multiplicity method.
pe_simulation_study() and ss_power_pe_mediation(): Run the size and power study across patterns, and plan the sample size for a target power.
pe_identification_study(): Runs the article's Monte Carlo study of mediator identification: the familywise error rate, false discovery rate, precision, and recall of the identified active set under each multiplicity method.
plot.poemed_tbl(), tidy.poemed_tbl(), glance.poemed_tbl(): A base-graphics plot and broom verbs for POEMED results.
mediation_ar1_cov(): The autoregressive mediator covariance used throughout the simulations, exported as a reusable utility.
WHO_health_mediation, WHO_mediation_design(), and WHO_mediation_analysis(): The article's empirical data (economic growth, 57 health-expenditure mediators, five health outcomes for 91 WHO members), a helper that assembles an analysis design from it, and a function that runs the article's subgroup analyses (global, by region, by income group, and by region and income group) with the preprocessing and the tuning grid of the analysis behind the article's tables (standardized exposure and mediators, centered outcome, unscaled region, income, and year confounders, and the grid seq(0.1, 2, length.out = 100); the article's text says that covariates are standardized). Its country counts match the article's tables in every cell, except that the function reports NA for the cells the article lists with 0 countries. Under its default grid it reproduces the article's Tables 1, 2, and S.8 to S.12 in every cell it fits: every identified active set but one BH set, and the benchmark p-values to four decimals in all but a few cells. Six region-by-income cells are reported as NA instead; the reproduction vignette, vignette("reproducing-the-article"), lists those cells and the ones that differ, and why.

Reading the Output

Every estimation and testing function returns a tidy data.frame with a term column and a numeric value column, carrying the poemed_tbl class so it prints with whole numbers shown without a decimal part, other quantities to a few significant figures, and p-values to four decimal places. The stored numbers keep full precision; only the display rounds. See poemed_tbl for the details.

How to Cite

If you use POEMED in published work, please cite Yu and Kelley (in press), the article that introduces its methods and the package. citation("POEMED") gives the full reference and a BibTeX entry.

References

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

Fan, J., Liao, Y., & Yao, J. (2015). Power enhancement in high-dimensional cross-sectional tests. Econometrica, 83(4), 1497–1541. doi:10.3982/ECTA12749

Guo, X., Li, R., Liu, J., & Zeng, M. (2022). High-dimensional mediation analysis for selecting DNA methylation loci mediating childhood trauma and cortisol stress reactivity. Journal of the American Statistical Association, 117(539), 1110–1121. doi:10.1080/01621459.2022.2053136

Guo, X., Li, R., Liu, J., & Zeng, M. (2023). Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic. Journal of Econometrics, 235(1), 166–179. doi:10.1016/j.jeconom.2022.03.001

Guo, X., Li, R., Liu, J., & Zeng, M. (2024). Estimations and tests for generalized mediation models with high-dimensional potential mediators. Journal of Business & Economic Statistics, 42(1), 243–256. doi:10.1080/07350015.2023.2174548

Author

Xiufan Yu and Ken Kelley