Package 'TFisher' reference manual

Title:	Optimal Thresholding Fisher's P-Value Combination Method
Description:	We provide the cumulative distribution function (CDF), quantile, and statistical power calculator for a collection of thresholding Fisher's p-value combination methods, including Fisher's p-value combination method, truncated product method and, in particular, soft-thresholding Fisher's p-value combination method which is proven to be optimal in some context of signal detection. The p-value calculator for the omnibus version of these tests are also included. For reference, please see Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.
Authors:	Hong Zhang and Zheyang Wu
Maintainer:	Hong Zhang <[email protected]>
License:	GPL-2
Version:	0.2.0
Built:	2024-10-31 16:33:06 UTC
Source:	https://github.com/cran/TFisher

CDF of soft-thresholding Fisher's p-value combination statistic under the null hypothesis.

Description

CDF of soft-thresholding Fisher's p-value combination statistic under the null hypothesis.

Usage

p.soft(q, n, tau1, M = NULL)
p.soft(q, n, tau1, M = NULL)

Arguments

`q`	- quantile, could be a vector.
`n`	- dimension parameter, i.e. the number of p-values to be combined.
`tau1`	- truncation parameter=normalization parameter. tau1 > 0.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Value

The left-tail probability of the null distribution of soft-thresholding Fisher's p-value combination statistic at the given quantile.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval <- runif(100)
softstat <- stat.soft(p=pval, tau1=0.05)
p.soft(q=softstat, n=100, tau1=0.05)
M = matrix(0.3,100,100) + diag(1-0.3,100)
p.soft(q=softstat, n=100, tau1=0.05, M=M)
pval <- runif(100)
softstat <- stat.soft(p=pval, tau1=0.05)
p.soft(q=softstat, n=100, tau1=0.05)
M = matrix(0.3,100,100) + diag(1-0.3,100)
p.soft(q=softstat, n=100, tau1=0.05, M=M)

CDF of omnibus soft-thresholding Fisher's p-value combination statistic under the null hypothesis.

Description

CDF of omnibus soft-thresholding Fisher's p-value combination statistic under the null hypothesis.

Usage

p.soft.omni(q, n, TAU1, M = NULL)
p.soft.omni(q, n, TAU1, M = NULL)

Arguments

`q`	- quantile, could be a vector.
`n`	- dimension parameter, i.e. the number of p-values to be combined.
`TAU1`	- a vector of truncation parameters (=normalization parameters). Must be in non-descending order.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Value

The left-tail probability of the null distribution of omnibus soft-thresholding Fisher's p-value combination statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

q = 0.01
n = 20
TAU1 = c(0.01, 0.05, 0.5, 1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.soft.omni(q=q, n=n, TAU1=TAU1, M=M)
q = 0.01
n = 20
TAU1 = c(0.01, 0.05, 0.5, 1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.soft.omni(q=q, n=n, TAU1=TAU1, M=M)

CDF of thresholding Fisher's p-value combination statistic under the null hypothesis.

Description

CDF of thresholding Fisher's p-value combination statistic under the null hypothesis.

Usage

p.tfisher(q, n, tau1, tau2, M = NULL, mu = NULL, sigma2 = NULL,
  p0 = NULL)
p.tfisher(q, n, tau1, tau2, M = NULL, mu = NULL, sigma2 = NULL,
  p0 = NULL)

Arguments

`q`	- quantile, could be a vector.
`n`	- dimension parameter, i.e. the number of p-values to be combined.
`tau1`	- truncation parameter. 0 < tau1 <= 1.
`tau2`	- normalization parameter. tau2 >= tau1.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.
`mu`	- the mean of TFisher statistics. Default = NULL.
`sigma2`	- the variance of TFisher statistics. Default = NULL.
`p0`	- the point masse of TFisher statistics. Default = NULL.

Value

The left-tail probability of the null distribution of thresholding Fisher's p-value combination statistic at the given quantile.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval <- runif(20)
tfstat <- stat.tfisher(p=pval, tau1=0.25, tau2=0.75)
p.tfisher(q=tfstat, n=20, tau1=0.25, tau2=0.75)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.tfisher(q=tfstat, n=20, tau1=0.25, tau2=0.75, M=M)
pval <- runif(20)
tfstat <- stat.tfisher(p=pval, tau1=0.25, tau2=0.75)
p.tfisher(q=tfstat, n=20, tau1=0.25, tau2=0.75)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.tfisher(q=tfstat, n=20, tau1=0.25, tau2=0.75, M=M)

CDF of omnibus thresholding Fisher's p-value combination statistic under the null hypothesis.

Description

CDF of omnibus thresholding Fisher's p-value combination statistic under the null hypothesis.

Usage

p.tfisher.omni(q, n, TAU1, TAU2, M = NULL, P0 = NULL)
p.tfisher.omni(q, n, TAU1, TAU2, M = NULL, P0 = NULL)

Arguments

`q`	- quantile, could be a vector.
`n`	- dimension parameter, i.e. the number of p-values to be combined.
`TAU1`	- a vector of truncation parameters. Must be in non-descending order.
`TAU2`	- a vector of normalization parameters. Must be in non-descending order.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.
`P0`	- a vector of point masses of TFisher statistics. Default = NULL.

Value

The left-tail probability of the null distribution of omnibus thresholding Fisher's p-value combination statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

q = 0.05
n = 20
TAU1 = c(0.01, 0.05, 0.5, 1)
TAU2 = c(0.1, 0.2, 0.5, 1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.tfisher.omni(q=q, n=n, TAU1=TAU1, TAU2=TAU2, M=M)
q = 0.05
n = 20
TAU1 = c(0.01, 0.05, 0.5, 1)
TAU2 = c(0.1, 0.2, 0.5, 1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.tfisher.omni(q=q, n=n, TAU1=TAU1, TAU2=TAU2, M=M)

CDF of truncated product method statistic under the null hypothesis.

Description

CDF of truncated product method statistic under the null hypothesis.

Usage

p.tpm(q, n, tau1, M = NULL)
p.tpm(q, n, tau1, M = NULL)

Arguments

`q`	- quantile, could be a vector.
`n`	- dimension parameter, i.e. the number of p-values to be combined.
`tau1`	- truncation parameter. 0 < tau1 <= 1.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Value

The left-tail probability of the null distribution of truncated product method statistic at the given quantile.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

2. Zaykin, D.V., Zhivotovsky, L. A., Westfall, P.H. and Weir, B.S. (2002), Truncated product method for combining P-values. Genet. Epidemiol., 22: 170–185. doi:10.1002/gepi.0042

Examples

pval <- runif(100)
tpmstat <- stat.tpm(p=pval, tau1=0.05)
p.tpm(q=tpmstat, n=100, tau1=0.05)
M = matrix(0.3,100,100) + diag(1-0.3,100)
p.tpm(q=tpmstat, n=100, tau1=0.05, M=M)
pval <- runif(100)
tpmstat <- stat.tpm(p=pval, tau1=0.05)
p.tpm(q=tpmstat, n=100, tau1=0.05)
M = matrix(0.3,100,100) + diag(1-0.3,100)
p.tpm(q=tpmstat, n=100, tau1=0.05, M=M)

CDF of omnibus truncated product method statistic under the null hypothesis.

Description

CDF of omnibus truncated product method statistic under the null hypothesis.

Usage

p.tpm.omni(q, n, TAU1, M = NULL)
p.tpm.omni(q, n, TAU1, M = NULL)

Arguments

`q`	- quantile, could be a vector.
`n`	- dimension parameter, i.e. the number of p-values to be combined.
`TAU1`	- a vector of truncation parameters. Must be in non-descending order.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence

Value

The left-tail probability of the null distribution of omnibus truncated product method statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

q = 0.05
n = 20
TAU1 = c(0.01, 0.05, 0.5, 1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.tpm.omni(q=q, n=n, TAU1=TAU1, M=M)
q = 0.05
n = 20
TAU1 = c(0.01, 0.05, 0.5, 1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
p.tpm.omni(q=q, n=n, TAU1=TAU1, M=M)

Statistical power of soft-thresholding Fisher's p-value combination test under Gaussian mixture model.

Description

Statistical power of soft-thresholding Fisher's p-value combination test under Gaussian mixture model.

Usage

power.soft(alpha, n, tau1, eps = 0, mu = 0)
power.soft(alpha, n, tau1, eps = 0, mu = 0)

Arguments

`alpha`	- type-I error rate.
`n`	- dimension parameter, i.e. the number of input p-values.
`tau1`	- truncation parameter=normalization parameter. tau1 > 0.
`eps`	- mixing parameter of the Gaussian mixture.
`mu`	- mean of non standard Gaussian model.

Details

We consider the following hypothesis test,

$H_0: X_i\sim F_0, H_a: X_i\sim (1-\epsilon)F_0+\epsilon F_1$

, where $\epsilon$ is the mixing parameter, $F_0$ is the standard normal CDF and $F = F_1$ is the CDF of normal distribution with $\mu$ defined by mu and $\sigma = 1$ .

Value

Power of the soft-thresholding Fisher's p-value combination test.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

alpha = 0.05
#If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:#
power.soft(alpha, 100, 0.05, eps = 0.1, mu = 1.2)
alpha = 0.05
#If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:#
power.soft(alpha, 100, 0.05, eps = 0.1, mu = 1.2)

Statistical power of thresholding Fisher's p-value combination test under Gaussian mixture model.

Description

Statistical power of thresholding Fisher's p-value combination test under Gaussian mixture model.

Usage

power.tfisher(alpha, n, tau1, tau2, eps = 0, mu = 0)
power.tfisher(alpha, n, tau1, tau2, eps = 0, mu = 0)

Arguments

`alpha`	- type-I error rate.
`n`	- dimension parameter, i.e. the number of input p-values.
`tau1`	- truncation parameter. 0 < tau1 <= 1.
`tau2`	- normalization parameter. tau2 >= tau1.
`eps`	- mixing parameter of the Gaussian mixture.
`mu`	- mean of non standard Gaussian model.

Details

We consider the following hypothesis test,

$H_0: X_i\sim F_0, H_a: X_i\sim (1-\epsilon)F_0+\epsilon F_1$

, where $\epsilon$ is the mixing parameter, $F_0$ is the standard normal CDF and $F = F_1$ is the CDF of normal distribution with $\mu$ defined by mu and $\sigma = 1$ .

Value

Power of the thresholding Fisher's p-value combination test.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

alpha = 0.05
#If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:#
power.tfisher(alpha, 100, 0.05, 0.25, eps = 0.1, mu = 1.2)
alpha = 0.05
#If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:#
power.tfisher(alpha, 100, 0.05, 0.25, eps = 0.1, mu = 1.2)

Statistical power of truncated product method test under Gaussian mixture model.

Description

Statistical power of truncated product method test under Gaussian mixture model.

Usage

power.tpm(alpha, n, tau1, eps = 0, mu = 0)
power.tpm(alpha, n, tau1, eps = 0, mu = 0)

Arguments

`alpha`	- type-I error rate.
`n`	- dimension parameter, i.e. the number of input p-values.
`tau1`	- truncation parameter. 0 < tau1 <= 1. tau1 > 0.
`eps`	- mixing parameter of the Gaussian mixture.
`mu`	- mean of non standard Gaussian model.

Details

We consider the following hypothesis test,

$H_0: X_i\sim F_0, H_a: X_i\sim (1-\epsilon)F_0+\epsilon F_1$

, where $\epsilon$ is the mixing parameter, $F_0$ is the standard normal CDF and $F = F_1$ is the CDF of normal distribution with $\mu$ defined by mu and $\sigma = 1$ .

Value

Power of the truncated product method test.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

alpha = 0.05
#If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:#
power.tpm(alpha, 100, 0.05, eps = 0.1, mu = 1.2)
alpha = 0.05
#If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:#
power.tpm(alpha, 100, 0.05, eps = 0.1, mu = 1.2)

Quantile of soft-thresholding Fisher's p-value combination statistic under the null hypothesis.

Description

Quantile of soft-thresholding Fisher's p-value combination statistic under the null hypothesis.

Usage

q.soft(p, n, tau1, M = NULL)
q.soft(p, n, tau1, M = NULL)

Arguments

`p`	- a scalar left probability that defines the quantile.
`n`	- dimension parameter, i.e. the number of input p-values.
`tau1`	- truncation parameter=normalization parameter. tau1 > 0.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Value

Quantile of soft-thresholding Fisher's p-value combination statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

## The 0.05 critical value of soft-thresholding statistic when n = 10:
q.soft(p=.99, n=20, tau1 = 0.05)
M = matrix(0.9,20,20) + diag(1-0.9,20)
q.soft(p=.99, n=20, tau1 = 0.05, M=M)
## The 0.05 critical value of soft-thresholding statistic when n = 10:
q.soft(p=.99, n=20, tau1 = 0.05)
M = matrix(0.9,20,20) + diag(1-0.9,20)
q.soft(p=.99, n=20, tau1 = 0.05, M=M)

Quantile of thresholding Fisher's p-value combination statistic under the null hypothesis.

Description

Quantile of thresholding Fisher's p-value combination statistic under the null hypothesis.

Usage

q.tfisher(p, n, tau1, tau2, M = NULL)
q.tfisher(p, n, tau1, tau2, M = NULL)

Arguments

`p`	- a scalar left probability that defines the quantile.
`n`	- dimension parameter, i.e. the number of input p-values.
`tau1`	- truncation parameter. 0 < tau1 <= 1.
`tau2`	- normalization parameter. tau2 >= tau1.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Value

Quantile of thresholding Fisher's p-value combination statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

## The 0.05 critical value of TFisher statistic when n = 10:
q.tfisher(p=.95, n=20, tau1=0.05, tau2=0.25)
## when corrrelated
M = matrix(0.3,20,20) + diag(1-0.3,20)
q.tfisher(p=.95, n=20, tau1=0.05, tau2=0.25, M=M)
## The 0.05 critical value of TFisher statistic when n = 10:
q.tfisher(p=.95, n=20, tau1=0.05, tau2=0.25)
## when corrrelated
M = matrix(0.3,20,20) + diag(1-0.3,20)
q.tfisher(p=.95, n=20, tau1=0.05, tau2=0.25, M=M)

Quantile of truncated product method statistic under the null hypothesis.

Description

Quantile of truncated product method statistic under the null hypothesis.

Usage

q.tpm(p, n, tau1, M = NULL)
q.tpm(p, n, tau1, M = NULL)

Arguments

`p`	- a scalar left probability that defines the quantile.
`n`	- dimension parameter, i.e. the number of input p-values.
`tau1`	- truncation parameter. 0 < tau1 <= 1.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Value

Quantile of truncated product method statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

2. Zaykin, D.V., Zhivotovsky, L. A., Westfall, P.H. and Weir, B.S. (2002), Truncated product method for combining P-values. Genet. Epidemiol., 22: 170–185. doi:10.1002/gepi.0042

Examples

## The 0.05 critical value of TPM statistic when n = 10:
q.tpm(p=.95, n=20, tau1 = 0.05)
M = matrix(0.3,20,20) + diag(1-0.3,20)
q.tpm(p=.95, n=20, tau1 = 0.05, M=M)
## The 0.05 critical value of TPM statistic when n = 10:
q.tpm(p=.95, n=20, tau1 = 0.05)
M = matrix(0.3,20,20) + diag(1-0.3,20)
q.tpm(p=.95, n=20, tau1 = 0.05, M=M)

Construct soft-thresholding Fisher's p-value combination statistic.

Description

Construct soft-thresholding Fisher's p-value combination statistic.

Usage

stat.soft(p, tau1)
stat.soft(p, tau1)

Arguments

`p`	- input p-values.
`tau1`	- truncation parameter=normalization parameter. tau1 > 0.

Details

Let $p_{i}$ , $i = 1,...,n$ be a sequence of p-values, the soft-thresholding statistic

$Soft = \sum_{i=1}^n -2\log(p_i/\tau_1)I(p_i\leq\tau_1)$

. Soft-thresholding is the special case of TFisher when tau1=tau2.

Value

Soft-thresholding Fisher's p-value combination statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval <- runif(100)
stat.soft(p=pval, tau1=0.05)
pval <- runif(100)
stat.soft(p=pval, tau1=0.05)

Construct omnibus soft-thresholding Fisher's p-value combination statistic.

Description

Construct omnibus soft-thresholding Fisher's p-value combination statistic.

Usage

stat.soft.omni(p, TAU1, M = NULL)
stat.soft.omni(p, TAU1, M = NULL)

Arguments

`p`	- input p-values.
`TAU1`	- a vector of truncation parameters (=normalization parameters). Must be in non-descending order.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Details

Let $x_{i}$ , $i = 1,...,n$ be a sequence of individual statistics with correlation matrix M, $p_{i}$ be the corresponding two-sided p-values, then the soft-thresholding statistics

$Soft_j = \sum_{i=1}^n -2\log(p_i/\tau_{1j})I(p_i\leq\tau_{1j})$

, $j = 1,...,d$ . The omnibus test statistic is the minimum p-value of these soft-thresholding tests,

$W_o = min_j G_j(Soft_j)$

, where $G_j$ is the survival function of $Soft_j$ .

Value

omni - omnibus soft-thresholding statistic.

pval - p-values of each soft-thresholding tests.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval = runif(20)
TAU1 = c(0.01, 0.05, 0.5, 1)
stat.soft.omni(p=pval, TAU1=TAU1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
stat.soft.omni(p=pval, TAU1=TAU1, M=M)
pval = runif(20)
TAU1 = c(0.01, 0.05, 0.5, 1)
stat.soft.omni(p=pval, TAU1=TAU1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
stat.soft.omni(p=pval, TAU1=TAU1, M=M)

Construct thresholding Fisher's p-value combination statistic.

Description

Construct thresholding Fisher's p-value combination statistic.

Usage

stat.tfisher(p, tau1, tau2)
stat.tfisher(p, tau1, tau2)

Arguments

`p`	- input p-values.
`tau1`	- truncation parameter. 0 < tau1 <= 1.
`tau2`	- normalization parameter. tau2 >= tau1.

Details

Let $p_{i}$ , $i = 1,...,n$ be a sequence of p-values, the thresholding Fisher's p-value combination statistic

$TFisher = \sum_{i=1}^n -2\log(p_i/\tau_2)I(p_i\leq\tau_2)$

Value

Thresholding Fisher's p-value combination statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval <- runif(100)
stat.tfisher(p=pval, tau1=0.05, tau2=0.25)
pval <- runif(100)
stat.tfisher(p=pval, tau1=0.05, tau2=0.25)

Construct omnibus thresholding Fisher's (TFisher) p-value combination statistic.

Description

Construct omnibus thresholding Fisher's (TFisher) p-value combination statistic.

Usage

stat.tfisher.omni(p, TAU1, TAU2, M = NULL, MU = NULL, SIGMA2 = NULL,
  P0 = NULL)
stat.tfisher.omni(p, TAU1, TAU2, M = NULL, MU = NULL, SIGMA2 = NULL,
  P0 = NULL)

Arguments

`p`	- input p-values from potentially correlated input sstatistics.
`TAU1`	- a vector of truncation parameters. Must be in non-descending order.
`TAU2`	- a vector of normalization parameters. Must be in non-descending order.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence
`MU`	- a vector of means of TFisher statistics. Default = NULL.
`SIGMA2`	- a vector of variances of TFisher statistics. Default = NULL.
`P0`	- a vector of point masses of TFisher statistics. Default = NULL.

Details

Let $x_{i}$ , $i = 1,...,n$ be a sequence of individual statistics with correlation matrix M, $p_{i}$ be the corresponding two-sided p-values, then the TFisher statistics

$TFisher_j = \sum_{i=1}^n -2\log(p_i/\tau_{2j})I(p_i\leq\tau_{1j})$

, $j = 1,...,d$ . The omnibus test statistic is the minimum p-value of these thresholding tests,

$W_o = min_j G_j(Soft_j)$

, where $G_j$ is the survival function of $Soft_j$ .

Value

omni - omnibus TFisher statistic.

pval - p-values of each TFisher tests.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval = runif(20)
TAU1 = c(0.01, 0.05, 0.5, 1)
TAU2 = c(0.1, 0.2, 0.5, 1)
stat.tfisher.omni(p=pval, TAU1=TAU1, TAU2=TAU2)
M = matrix(0.3,20,20) + diag(1-0.3,20)
stat.tfisher.omni(p=pval, TAU1=TAU1, TAU2=TAU2, M=M)
pval = runif(20)
TAU1 = c(0.01, 0.05, 0.5, 1)
TAU2 = c(0.1, 0.2, 0.5, 1)
stat.tfisher.omni(p=pval, TAU1=TAU1, TAU2=TAU2)
M = matrix(0.3,20,20) + diag(1-0.3,20)
stat.tfisher.omni(p=pval, TAU1=TAU1, TAU2=TAU2, M=M)

Construct truncated product method statistic.

Description

Construct truncated product method statistic.

Usage

stat.tpm(p, tau1)
stat.tpm(p, tau1)

Arguments

`p`	- input p-values.
`tau1`	- truncation parameter. 0 < tau1 <= 1.

Details

Let $p_{i}$ , $i = 1,...,n$ be a sequence of p-values, the TPM statistic

$TPM = \sum_{i=1}^n -2\log(p_i)I(p_i\leq\tau_2)$

. TPM is the special case of TFisher when tau2=1.

Value

Truncated product method statistic.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

2. Zaykin, D.V., Zhivotovsky, L. A., Westfall, P.H. and Weir, B.S. (2002), Truncated product method for combining P-values. Genet. Epidemiol., 22: 170–185. doi:10.1002/gepi.0042

Examples

pval <- runif(100)
stat.tpm(p=pval, tau1=0.05)
pval <- runif(100)
stat.tpm(p=pval, tau1=0.05)

Construct omnibus truncated product method statistic.

Description

Construct omnibus truncated product method statistic.

Usage

stat.tpm.omni(p, TAU1, M = NULL)
stat.tpm.omni(p, TAU1, M = NULL)

Arguments

`p`	- input p-values.
`TAU1`	- a vector of truncation parameters. Must be in non-descending order.
`M`	- correlation matrix of the input statistics. Default = NULL assumes independence.

Details

Let $x_{i}$ , $i = 1,...,n$ be a sequence of individual statistics with correlation matrix M, $p_{i}$ be the corresponding two-sided p-values, then the truncated product method statistics

$TPM_j = \sum_{i=1}^n -2\log(p_i)I(p_i\leq\tau_{1j})$

, $j = 1,...,d$ . The omnibus test statistic is the minimum p-value of these truncated product method tests,

$W_o = min_j G_j(TPM_j)$

, where $G_j$ is the survival function of $TPM_j$ .

Value

omni - omnibus truncated product method statistic.

pval - p-values of each truncated product method tests.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval = runif(20)
TAU1 = c(0.01, 0.05, 0.5, 1)
stat.tpm.omni(p=pval, TAU1=TAU1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
stat.tpm.omni(p=pval, TAU1=TAU1, M=M)
pval = runif(20)
TAU1 = c(0.01, 0.05, 0.5, 1)
stat.tpm.omni(p=pval, TAU1=TAU1)
M = matrix(0.3,20,20) + diag(1-0.3,20)
stat.tpm.omni(p=pval, TAU1=TAU1, M=M)

Package 'TFisher'

Help Index

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