ERP (version 2.2)

erpfatest: Adaptive Factor-Adjustement for multiple testing of ERP data

Description

Adaptive factor-adjusted FDR- and FWER-controlling multiple testing procedures for ERP data. The procedure is described in detail in Sheu, Perthame, Lee, and Causeur (2016).

Usage

erpfatest(dta, design, design0 = NULL, 
method = c("BH","holm","hochberg","hommel","bonferroni","BY","fdr","none"),nbf = NULL,
nsamples = 200, significance = c("Satterthwaite", "none"),
nbfmax = min(c(nsamples, nrow(design))) - ncol(design) - 1, alpha = 0.05, pi0 = 1,
wantplot = ifelse(is.null(nbf), TRUE, FALSE), s0 = NULL, min.err = 0.01, maxiter = 5, 
verbose = FALSE, svd.method = c("fast.svd", "irlba"))

Arguments

dta

Data frame containing the ERP measurements: each column corresponds to a time frame and each row to a curve.

design

Design matrix of the nonnull model for the relationship between the ERP and the experimental variables. Typically the output of the function model.matrix

design0

Design matrix of the null model. Typically a submodel of the nonnull model, obtained by removing columns from design. Default is NULL, corresponding to the model with no covariates.

method

FDR- or FWER- controlling multiple testing procedures as available in the function p.adjust. Default is "BH", for the Benjamini-Hochberg procedure (see Benjamini and Hochberg, 1995).

nbf

Number of factors in the residual covariance model. Default is NULL: the number of factors is determined by minimization of the variance inflation criterion as suggested in Friguet et al. (2009).

nsamples

Number of Monte-Carlo samples for the estimation of the null distribution. Default is nsamples=200, recommended when the Satterthwaite approximation is used.

significance

If "Satterthwaite", then the Monte-Carlo p-value is calculated with a Satterthwaite approximation of the null distribution. The other possible value is "none", for no calculation of the p-value.

nbfmax

Only required if nbf=NULL. The largest possible number of factors.

alpha

The FDR or FWER control level. Default is 0.05

pi0

An estimate of the proportion of true null hypotheses, which can be plugged into an FDR controlling multiple testing procedure to improve its efficiency. Default is 1, corresponding to the classical FDR controlling procedures. If NULL, the proportion is estimated using the function pval.estimate.eta0 of package fdrtool, with the method proposed by Storey and Tibshirani (2003).

wantplot

If TRUE, a diagnostic plot is produced to help choosing the number of factors. Only active if nbf=NULL.

s0

Prior knowledge of the time frames for which no signal is expected. For example, s0=c(1:50, 226:251) specifies that the first 50 time frames and time frames between 226 and 251 are known not to contain ERP signal. s0 can also be specified by giving the lower and upper fraction of the entire time interval in which the signal is to be searched for. For example: s0=c(0.2, 0.9) means that ERP signals are not expected for for the first 20 percent and last 10 percent of the time frames measured. Defaul is NULL and it initiates a data-driven determination of s0.

min.err

Control parameter for convergence of the iterative algorithm. Default is 1e-03.

maxiter

Maximum number of iterations in algorithms. Default is 5.

verbose

If TRUE, details are printed along the iterations of the algorithm. Default is FALSE.

svd.method

the EM algorithm starts from an SVD estimation of the factor model parameters. The default option to implement this SVD is fast.svd. An alternative option is an approximate but faster SVD by function irlba.

Value

pval

p-values of the Adaptive Factor-Adjusted tests.

correctedpval

Corrected p-values, for the multiplicity of tests. Depends on the multiple testing method (see function p.adjust).

significant

Indices of the time points for which the test is positive.

pi0

Value for pi0: if the input argument pi0 is NULL, the output is the estimated proportion of true null hypotheses using the method by Storey and Tibshirani (2003).

test

Pointwise factor-adjusted F-statistics if p>1, where p is the difference between the numbers of parameters in the nonnull and null models. Otherwise, if p=1, the function returns pointwise factor adjusted t-statistics (signed square-roots of F-statistics).

df1

Residual degrees of freedom for the nonnull model.

df0

Residual degrees of freedom for the null model.

nbf

Number of factors for the residual covariance model.

signal

Estimated signal: a pxT matrix, where p is the difference between the numbers of parameters in the nonnull and null models and T the number of frames.

r2

R-squared values for each of the T linear models.

Details

The method is described in Sheu et al. (2016). It combines a decorrelation step based on a regression factor model as in Leek and Storey (2008), Friguet et al. (2009) or Sun et al. (2012) with an adaptive estimation of the ERP signal. The multiple testing corrections of the p-values are described in the help documentation of the function p.adjust.

References

Causeur, D., Chu, M.-C., Hsieh, S., Sheu, C.-F. 2012. A factor-adjusted multiple testing procedure for ERP data analysis. Behavior Research Methods, 44, 635-643.

Friguet, C., Kloareg, M., Causeur, D. 2009. A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104, 1406-1415.

Leek, J.T., Storey, J.D. 2008. A general framework for multiple testing dependence. Proceedings of the National Academy of Sciences of the United States of America, 105, 18718-18723.

Sheu, C.-F., Perthame, E., Lee Y.-S. and Causeur, D. 2016. Accounting for time dependence in large-scale multiple testing of event-related potential data. Annals of Applied Statistics. 10(1), 219-245.

Storey, J. D., Tibshirani, R. 2003. Statistical significance for genome-wide experiments. Proceedings of the National Academy of Sciences of the United States of America, 100, 9440-9445.

Sun, Y., Zhang, N.R., Owen, A.B. 2012. Multiple hypothesis testing adjusted for latent variables, with an application to the AGEMAP gene expression data. The Annals of Applied Statistics, 6, no. 4, 1664-1688.

See Also

erpavetest, erptest, gbtest, p.adjust, pval.estimate.eta0

Examples

# NOT RUN {
# }
# NOT RUN {
data(impulsivity)

# Paired t-tests for the comparison of the ERP curves in the two conditions, 
# within experimental group High, at channel CPZ

erpdta.highCPZ = impulsivity[(impulsivity$Group=="High")&(impulsivity$Channel=="CPZ"),5:505] 
   # ERP curves for subjects in group 'High', at channel CPZ
covariates.highCPZ = impulsivity[(impulsivity$Group=="High")&(impulsivity$Channel=="CPZ"),1:4]
covariates.highCPZ = droplevels(covariates.highCPZ)
   # Experimental covariates for subjects in group 'High', at channel CPZ

design = model.matrix(~C(Subject,sum)+Condition,data=covariates.highCPZ)
   # Design matrix to compare ERP curves in the two conditions
design0 = model.matrix(~C(Subject,sum),data=covariates.highCPZ)
   # Design matrix for the null model (no condition effect)

tests = erpfatest(erpdta.highCPZ,design,design0,nbf=NULL,wantplot=TRUE,significance="none")
   # with nbf=NULL and significance="none", just to choose a number of factors
Ftest = erpFtest(erpdta.highCPZ,design,design0,nbf=6)
   # with nbf=6 (approximate conservative recommendation based on the variance inflation plot)
   # Signal detection: test for an eventual condition effect.
Ftest$pval

tests = erpfatest(erpdta.highCPZ,design,design0,nbf=6)
   # Signal identification: which are the significant intervals?

time_pt = seq(0,1000,2)     # sequence of time points (1 time point every 2ms in [0,1000])
nbs = 20                    # Number of B-splines for the plot of the effect curve
effect=which(colnames(design)=="ConditionSuccess")
erpplot(erpdta.highCPZ,design=design,frames=time_pt,effect=effect,xlab="Time (ms)",
        ylab=expression(Effect~curve~(mu~V)),bty="l",ylim=c(-3,3),nbs=nbs,
        cex.axis=1.25,cex.lab=1.25,interval="simultaneous")
   # with interval="simultaneous", both the pointwise and the simultaneous confidence bands
   # are plotted
points(time_pt[tests$significant],rep(0,length(tests$significant)),pch=16,col="blue")
   # Identifies significant time points by blue dots
title("Success-Failure effect curve with 95 percent C.I.",cex.main=1.25)
mtext(paste("12 subjects - Group 'High' - ",nbs," B-splines",sep=""),cex=1.25)

# }
# NOT RUN {
 
# }