Calibration Constants for the Real-Data-Motivated Heterogeneous Setting

The fixed constants for the real-data-motivated heterogeneous mediation simulation of Yu and Kelley (in press), calibrated to the DNA-methylation case study of Guo et al. (2022): a \(p = 1008\)-mediator linear model with eleven active loci whose effects mix positive and negative signs. simulate_guo_mediation() generates data from these constants; the object is exported so the exact calibration is inspectable.

Usage

guo_calibration

Format

A list with components:

p, s, n

The mediator count (1008), confounder count (9, an intercept plus eight covariates), and case-study sample size (85).

locations

Indices of the eleven active mediators.

alpha_m

Outcome-mediator coefficients at the active loci (the designed simulation values).

Gamma_x

Exposure-mediator coefficients at the active loci.

alpha_z

Confounder-outcome coefficients (length 9).

Gamma_z

Confounder-mediator coefficients at the active loci (an 11 by 9 matrix).

beta_per_c1

The total indirect effect per unit c1, equal to sum(Gamma_x * alpha_m) \(\approx -1.597\) (the article reports -1.5977 from the unrounded coefficients).

alpha_m_estimated

The raw Guo et al. (2022) estimate of the outcome-mediator coefficients (for reference; the simulation uses the designed alpha_m).

alpha_m_variants

Two alternative outcome-mediator coefficient sets the article also studies, homogeneous_like and contrasting_like, which remain heterogeneous when paired with Gamma_x.

Source

Transcribed from the supplement of Yu and Kelley (in press) (its parameter-configuration section), which in turn calibrates to the simulation_allS.Rdata of Guo et al. (2022).

Details

Pairing the exposure-mediator coefficients Gamma_x with the outcome-mediator coefficients alpha_m gives a total indirect effect of beta_per_c1 \(\approx -1.597\) per unit of the signal scale \(c_1\). (The article reports \(-1.5977\), computed from the full-precision Guo coefficients; the values shipped here are those coefficients rounded to the three decimals printed in the supplement, which give \(-1.597\).)

References

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

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

See also

simulate_guo_mediation()

Other mediation simulation: mediation_ar1_cov(), pe_identification_study(), pe_power_curve(), pe_simulation_study(), plot.poemed_tbl(), simulate_guo_mediation(), simulate_mediation_data(), ss_power_pe_mediation()

Examples

str(guo_calibration, max.level = 1)
#> List of 11
#>  $ p                : int 1008
#>  $ s                : int 9
#>  $ n                : int 85
#>  $ locations        : int [1:11] 1 2 3 4 5 6 7 8 9 10 ...
#>  $ alpha_m          : num [1:11] 1 0.9 0.8 -0.9 -0.8 -0.7 0.6 0.5 0.4 0.3 ...
#>  $ Gamma_x          : num [1:11] -0.251 -0.221 -0.233 0.251 0.295 0.282 -0.332 -0.359 0.335 -0.345 ...
#>  $ alpha_z          : num [1:9] -0.336 -0.07 0.665 0.278 0.315 0.201 0.173 0.51 0.315
#>  $ Gamma_z          : num [1:11, 1:9] -0.045 -0.197 -0.076 -0.052 -0.033 -0.012 0.203 0.017 -0.364 -0.001 ...
#>  $ beta_per_c1      : num -1.6
#>  $ alpha_m_estimated: num [1:11] 0.166 0.243 0.248 -0.049 -0.294 -0.187 0.148 0.087 0.112 0.223 ...
#>  $ alpha_m_variants :List of 2
# The eleven individual indirect effects: nine negative and two positive
sign(guo_calibration$Gamma_x * guo_calibration$alpha_m)
#>  [1] -1 -1 -1 -1 -1 -1 -1 -1  1 -1  1
# Their sum is the total indirect effect per unit of c1
sum(guo_calibration$Gamma_x * guo_calibration$alpha_m)
#> [1] -1.597