Composite null hypothesis test p-value — composite_p

Computes the Huang (2019) JT-comp composite p-value for testing H0: alpha * beta = 0 against H1: alpha * beta != 0.

Usage

composite_p_value(a, b, var_a = 1, var_b = 1)

Arguments

a: Standardized z-statistic for alpha (alpha_hat / SE).
b: Standardized z-statistic for beta (beta_hat / SE).
var_a: Variance of the z-statistic for alpha across the collection of tests. Under the point null this is ~1; under H0(2)/H0(3) it is >1. Default 1 (conservative).
var_b: Variance of the z-statistic for beta across the collection of tests. Default 1.

Value

Numeric scalar in \([0, 1]\).

Details

The composite null decomposes into three cases (alpha=beta=0, alpha!=0/beta=0, alpha=0/beta!=0). The Wald/Sobel test is conservative under the first case because the product of two independent normals follows a normal product distribution, not a normal. This function computes a closed-form p-value that accounts for all three cases without estimating their proportions.

References

Huang, Y.-T. (2019). Genome-wide analyses of sparse mediation effects under composite null hypotheses. Annals of Applied Statistics, 13(1), 60-84.

Examples

composite_p_value(0, 0) # null: p = 1
#> [1] 1
composite_p_value(2, 2) # strong signal: small p
#> [1] 0.006459626
composite_p_value(2, 0) # H0(2): p = 1 (no mediation)
#> [1] 1