Change Point Estimation for Clustered Signals

Description

A multiple testing procedure for clustered alternative hypotheses. It is assumed that the p-values under the null hypotheses follow U(0,1) and that the distributions of p-values from the alternative hypotheses are stochastically smaller than U(0,1). By aggregating information, this method is more sensitive to detecting signals of low magnitude than standard methods. Additionally, sporadic small p-values appearing within a null hypotheses sequence are avoided by averaging on the neighboring p-values.

Details

Author(s)

Hongyuan Cao, Wei Biao Wu, and Shannon T. Holloway Maintainer: Shannon T. Holloway <shannon.t.holloway@gmail.com>

References

Cao, H. and Wu, W. B. (2015) Changepoint estimation: Another look at multiple testing problems. Biometrika, 102, 974–980.

Change Point Estimation for Clustered Signals

Description

A multiple testing procedure for clustered alternative hypotheses. It is assumed that the p-values under the null hypotheses follow U(0,1) and that the distributions of p-values from the alternative hypotheses are stochastically smaller than U(0,1). By aggregating information, this method is more sensitive to detecting signals of low magnitude than standard methods. Additionally, sporadic small p-values appearing within a null hypotheses sequence are avoided by averaging on the neighboring p-values.

Usage

changePoint(pvalues, alpha, km, lm, compare = "BOTH", fdrlWindow = 3, 
fdrlNStep = 300, fdrlLambda = 0.1)

Arguments

Details

The comparison capability is included only for convenience and reproducibility of the original manuscript. The Benjamini-Hochberg and FDR_L methods cannot be accessed outside of the changePoint function.

The following methods retrieve individual results from a changePoint object, x:

BH(x): Retrieves a vector of integer values. An element is 1 if the null hypothesis is rejected by the Benjamini-Hochberg (1995) method.

blocks(x): Retrieves a list, each element of which is a vector of integer values. Each vector contains the indices of an alternative hypothesis block.

CW(x): Retrieves a vector of integer values. An element is 1 if the null hypothesis is rejected by the Cao-Wu change point (2015) method.

changePts(x): Retrieves a vector of integer values. The vector of change points identified by the Cao-Wu (2015) method. If no change points are identified, NULL is returned.

FDRL(x): Retrieves a vector of integer values. Elements are 1 if the null hypothesis is rejected by the FDR_L (Zhang et al. 2011) method.

critical(x): Retrieves the estimated critical value for testing used by the Cao-Wu (2015) method.

numAlt(x): Retrieves the estimated number of alternative hypotheses obtained by the Cao-Wu (2015) method.

piAlt(x): Retrieves the estimated proportion of alternative hypotheses obtained by the Cao-Wu (2015) method.

plot(x, y, logp, ...): Generates plots of -log(p) vs position or p-value vs position for each alternative hypothesis block obtained by the Cao-Wu (2015) method. logp is TRUE/FALSE indicating if -log(p)/p-values are plotted on the y-axis.

sigmaSq(x): Retrieves the estimated variance used to determine the critical value of the Cao-Wu (2015) method.

Value

Returns an object of class changePoint.

Author(s)

Hongyuan Cao, Wei Biao Wu, and Shannon T. Holloway Maintainer: Shannon T. Holloway <shannon.t.holloway@gmail.com>

References

Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57, 289–300.

Cao, H. and Wu, W. B. (2015) Changepoint estimation: Another look at multiple testing problems. Biometrika, 102, 974–980.

Zhang, C., Fan, J., and Yu, T. (2011). Multiple testing via FDRL for large-scale imaging data. Anals of Statistics, 39, 613–642.

Examples

m <- 5000

T <- c(rep(0.1,  75), rep( 0.8, 75), rep(1.8, 100), 
       rep(0.0,2250), rep(-1.5,250), rep(0.0,2250)) + 
     rnorm(m, mean=0.0, sd = 1.0)

pv <- 2.0*(1.0-pnorm(abs(T)))

res <- changePoint(pvalues = pv, 
                   alpha = 0.05, 
                   km = {log(m)}^2, 
                   lm = m^{1/4}, 
                   compare = "Both")

print(changePts(res))

print(head(cbind(BH(res),FDRL(res),CW(res))))

Class "changePoint"

Description

Value object returned by call to changePoint().

Objects from the Class

This object should not be created by users.

Slots

CW:

Object of class numeric or NULL. A vector of 1/0 values; 1 indicates that hypothesis was rejected by the Cao-Wu method.

chgPts:

Object of class numeric or NULL. The vector of change points identified by the Cao-Wu method. If no change points are identified, NULL.

pi_alt:

Object of class numeric. The estimated proportion of alternative hypotheses calculated using the Cao-Wu method.

num_alt:

Object of class numeric. The estimated number of alternative hypotheses calculated using the Cao-Wu method.

FDRL:

Object of class numeric or NULL. A vector of 1/0 values; 1 indicates that hypothesis was rejected by the FDR_L method.

BH:

Object of class numeric or NULL. A vector of 1/0 values; 1 indicates that hypothesis was rejected by the FDR_L method.

gammaStar:

Object of class numeric. The estimated critical value for testing used by the Cao-Wu method.

sigmaSq:

Object of class numeric. The estimated variance used to determine the critical value of the Cao-Wu method.

pVals:

Object of class numeric. The original p-values provided as input.

Methods

BH

signature(x = "changePoint"): Retrieves a vector of integer values. An elements is 1 if the null hypothesis is rejected by the Benjamini-Hochberg (1995) method.

blocks

signature(x = "changePoint"): Retrieves a list, each element of which is a vector of integer values. Each vector contains the indices of an alternative hypothesis block.

CW

signature(x = "changePoint"): Retrieves a vector of integer values. An element is 1 if the null hypothesis is rejected by the Cao-Wu change point (2015) method.

changePts

signature(x = "changePoint"): Retrieves a vector of integer values. The vector of change points identified by the Cao-Wu (2015) method. If no change points are identified, NULL is returned.

FDRL

signature(x = "changePoint"): Retrieves a vector of integer values. Elements are 1 if the null hypothesis is rejected by the FDR_L (Zhang et al. 2011) method.

critical

signature(x = "changePoint"): Retrieves the estimated critical value for testing used by the Cao-Wu (2015) method.

numAlt

signature(x = "changePoint"): Retrieves the estimated number of alternative hypotheses obtained by the Cao-Wu (2015) method.

piAlt

signature(x = "changePoint"): Retrieves the estimated proportion of alternative hypotheses obtained by the Cao-Wu (2015) method.

plot

signature(x = "changePoint", y = "missing", logp = FALSE, ...): Generates x-y plots of -log(p) vs position or p-value vs position for each alternative hypothesis block obtained by the Cao-Wu (2015) method. logp is TRUE/FALSE indicating if -log(p)/p-values are plotted on the y-axis.

sigmaSq

signature(x = "changePoint"): Retrieves the estimated variance used to determine the critical value of the Cao-Wu (2015) method.

Author(s)

Hongyuan Cao, Wei Biao Wu, and Shannon T. Holloway Maintainer: Shannon T. Holloway <shannon.t.holloway@gmail.com>

References

Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57, 289–300.

Cao, H. and Wu, W. B. (2015) Changepoint estimation: Another look at multiple testing problems. Biometrika, 102, 974–980.

Zhang, C., Fan, J., and Yu, T. (2011). Multiple testing via FDRL for large-scale imaging data. Anals of Statistics, 39, 613–642.

Examples

showClass("changePoint")