corr.WHC {corrMCT}

Correlation adjusted weighted Hochberg method

Description

A new method implement correlation correction based on weighted Hochberg. An ACF is applied for weight reduction to conserve alpha. Details see Huang et al. (2024+). A correlation structure with too many zero leads the method reduce to weighted Hochberg.

Usage

corr.WHC(p, w, corr.mat, theta = 0.2, gamma = 0.3, ACF = NULL, alpha = 0.05)

Arguments

p

A numeric vector. A length m P-value vector from multiple tests.

w

A numeric vector. Any non-negative real numbers to denote the importance of the endpoints. Length must be equal to m. A single value, e.g. w = 1, represents equal weight. WHC can scale the weight vector as if the sum of weight is not 1.

corr.mat

A matrix. The dimension must be m \times m. Positive correlation is the theoretical assumption, however, it is robust to run with some negative elements in the correlation matrix.

theta

A numeric number. \theta \in (0,1) is the shape parameter of alpha conserving function. \theta = 0 is a straight line f(\rho) = 1-\gamma\rho. For \theta > 0, greater the value, more aggressive decreasing it allows. Default theta=0.10 is a relative conservative suggestion. Details see Huang et al (2024+).

gamma

A numeric number. \gamma \in (0,1) is the scale parameter of alpha conserving function. \gamma = 1 makes the function approach 1 when \rho = 1. \gamma < 1 sets a bound to prevent too much penalty on weight. Default theta=0.50 is a moderate suggestion. Details see Huang et al (2024+).

ACF

A function. User can define their own alpha conserving function. The basic rule is the function must be monotone decreasing from 0 to 1, and range from 1 to a where a \in (0,1). A convex function is recommended. Concave function can produce result, but have no meaning on alpha conserving.

alpha

A real number. 1-\alpha is the confidence level, alpha must between (0, 1).

Value

A table contains p-values, weights, adjusted critical values, significance

References

Huang, X. -W., Hua, J., Banerjee, B., Wang, X., Li, Q. (2024+). Correlated weighted Hochberg procedure. In-preparation.

Examples

m <- 5
corr.WHC(
  p = runif(m),
  w = runif(m),
  corr.mat = cor(matrix(runif(10*m), ncol = m))
)