Package 'corrMCT'

ICC adjusted Bonferroni method

Description

corr.Bonferroni performs the ICC adjusted Bonferroni method proposed by Shi, Pavey, and Carter(2012). Power law approximation by r is tricky, suggested options was listed in the paper.

Usage

corr.Bonferroni(p, ICC, r = 0, alpha = 0.05)

Arguments

p	A numeric vector. A length $m$ P-value vector from multiple tests.
ICC	A number. Intraclass correlation correction factor, a real number between (0, 1).
r	A number. Tuning parameter for g** between (0, 1). Default r=0.
alpha	A real number. $1-\alpha$ is the confidence level, alpha must between (0, 1).

Value

A numeric vector of adjusted p-values.

References

Shi, Q., Pavey, E. S., & Carter, R. E. (2012). Bonferroni‐based correction factor for multiple, correlated endpoints. Pharmaceutical statistics, 11(4), 300-309.

Examples

m <- 10
corr.Bonferroni(
  p = runif(m),
  ICC = 0.3
)

---

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, a = 0.5, b = 0.6, penalty = 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.
a	A numeric number. $a \in (0,1)$ determines the greatest penalty on weight, Default a=0.5. Details see Huang et al (2024+).
b	A numeric number. $b \in (0,1)$ is the shape parameter of the penalty function. $b = 1$ produce a linear function.
penalty	A function. User can define their own penalty 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))
)

---

AR(1) correlation matrix

Description

An easy function to generate a AR(1) correlation matrix.

Usage

corrmat_AR1(m, rho)

Arguments

m	An integer. Dimension of the correlation matrix.
rho	A number. Correlation coefficient between $(0,1)$

Value

A correlation matrix

Examples

corrmat_AR1(
  m = 3,
  rho = 0.2
)

---

Block design correlation matrix

Description

An easy function to generate a block design correlation matrix. Each diagonal element $R_i$ is a compound symmetric matrix with dimension $d_i \times d_i$. Correlation coefficient in each block is $\rho_i$. All the off-diagonal elements are $0$.

Usage

corrmat_block(d, rho)

Arguments

d	An integer vector. Length $B$ of block dimensions. Element of d can be 1, it would not generate a sub-matrix with the corresponding element in rho, but just $1$.
rho	A numeric vector. A length $B$ vector of correlation coefficients, represent $B$ different block of correlation matrix.

Value

A correlation matrix

Examples

corrmat_block(
  d = c(2,3,4),
  rho = c(0.1, 0.3, 0.5)
)

---

Block AR(1) design correlation matrix

Description

An easy function to generate a block AR(1) design correlation matrix. Each diagonal element $R_i$ is an AR(1) correlation matrix with dimension $d_i \times d_i$. Correlation coefficient in each block is $\rho_i$. All the off-diagonal elements are $0$.

Usage

corrmat_blockAR1(d, rho)

Arguments

d	An integer vector. Length $B$ of block dimensions. Element of d can be 1, it would not generate a sub-matrix with the corresponding element in rho, but just $1$.
rho	A numeric vector. A length $B$ vector of correlation coefficients, represent $B$ different block of correlation matrix.

Value

A correlation matrix

Examples

corrmat_blockAR1(
  d = c(2,3,4),
  rho = c(0.1, 0.3, 0.5)
)

---

Compound symmetric correlation matrix

Description

An easy function to generate a compound symmetric correlation matrix

Usage

corrmat_CS(m, rho)

Arguments

m	An integer. Dimension of the correlation matrix.
rho	A number. Correlation coefficient between $(0,1)$

Value

A correlation matrix

Examples

corrmat_CS(
  m = 3,
  rho = 0.2
)

---

Weighted Hochberg method

Description

WHC performs the weighted Hochberg method proposed by Tamhane and Liu (2008).

Usage

WHC(p, w, 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.
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

Tamhane, A. C., & Liu, L. (2008). On weighted Hochberg procedures. Biometrika, 95(2), 279-294.

Examples

m <- 5
WHC(
  p = runif(m),
  w = runif(m)
)

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