Package 'TFisher'

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: 2024-11-18 04:53:41 UTC
Source: https://github.com/cran/TFisher

Help Index


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)

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.

See Also

stat.soft for the definition of the statistic.

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)

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)

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.

See Also

stat.soft.omni for the definition of the statistic.

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)

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)

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.

See Also

stat.tfisher for the definition of the statistic.

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)

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)

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.

See Also

stat.tfisher.omni for the definition of the statistic.

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)

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)

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

See Also

stat.tpm for the definition of the statistic.

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)

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)

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.

See Also

stat.tpm.omni for the definition of the statistic.

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)

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)

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,

H0:XiF0,Ha:Xi(1ϵ)F0+ϵF1H_0: X_i\sim F_0, H_a: X_i\sim (1-\epsilon)F_0+\epsilon F_1

, where ϵ\epsilon is the mixing parameter, F0F_0 is the standard normal CDF and F=F1F = F_1 is the CDF of normal distribution with μ\mu defined by mu and σ=1\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.

See Also

stat.soft for the definition of the statistic.

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)

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)

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,

H0:XiF0,Ha:Xi(1ϵ)F0+ϵF1H_0: X_i\sim F_0, H_a: X_i\sim (1-\epsilon)F_0+\epsilon F_1

, where ϵ\epsilon is the mixing parameter, F0F_0 is the standard normal CDF and F=F1F = F_1 is the CDF of normal distribution with μ\mu defined by mu and σ=1\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.

See Also

stat.tfisher for the definition of the statistic.

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)

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)

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,

H0:XiF0,Ha:Xi(1ϵ)F0+ϵF1H_0: X_i\sim F_0, H_a: X_i\sim (1-\epsilon)F_0+\epsilon F_1

, where ϵ\epsilon is the mixing parameter, F0F_0 is the standard normal CDF and F=F1F = F_1 is the CDF of normal distribution with μ\mu defined by mu and σ=1\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.

See Also

stat.soft for the definition of the statistic.

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)

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)

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.

See Also

stat.soft for the definition of the statistic.

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)

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)

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.

See Also

stat.tfisher for the definition of the statistic.

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)

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)

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

See Also

stat.tpm for the definition of the statistic.

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)

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

Description

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

Usage

stat.soft(p, tau1)

Arguments

p

- input p-values.

tau1

- truncation parameter=normalization parameter. tau1 > 0.

Details

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

Soft=i=1n2log(pi/τ1)I(piτ1)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)

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)

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

Softj=i=1n2log(pi/τ1j)I(piτ1j)Soft_j = \sum_{i=1}^n -2\log(p_i/\tau_{1j})I(p_i\leq\tau_{1j})

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

Wo=minjGj(Softj)W_o = min_j G_j(Soft_j)

, where GjG_j is the survival function of SoftjSoft_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)

Construct thresholding Fisher's p-value combination statistic.

Description

Construct thresholding Fisher's p-value combination statistic.

Usage

stat.tfisher(p, tau1, tau2)

Arguments

p

- input p-values.

tau1

- truncation parameter. 0 < tau1 <= 1.

tau2

- normalization parameter. tau2 >= tau1.

Details

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

TFisher=i=1n2log(pi/τ2)I(piτ2)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)

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)

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 xix_{i}, i=1,...,ni = 1,...,n be a sequence of individual statistics with correlation matrix M, pip_{i} be the corresponding two-sided p-values, then the TFisher statistics

TFisherj=i=1n2log(pi/τ2j)I(piτ1j)TFisher_j = \sum_{i=1}^n -2\log(p_i/\tau_{2j})I(p_i\leq\tau_{1j})

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

Wo=minjGj(Softj)W_o = min_j G_j(Soft_j)

, where GjG_j is the survival function of SoftjSoft_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)

Construct truncated product method statistic.

Description

Construct truncated product method statistic.

Usage

stat.tpm(p, tau1)

Arguments

p

- input p-values.

tau1

- truncation parameter. 0 < tau1 <= 1.

Details

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

TPM=i=1n2log(pi)I(piτ2)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)

Construct omnibus truncated product method statistic.

Description

Construct omnibus truncated product method statistic.

Usage

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

TPMj=i=1n2log(pi)I(piτ1j)TPM_j = \sum_{i=1}^n -2\log(p_i)I(p_i\leq\tau_{1j})

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

Wo=minjGj(TPMj)W_o = min_j G_j(TPM_j)

, where GjG_j is the survival function of TPMjTPM_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)