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#' Simulates Gaussian data with a given correlation matrix and applies a FWER controlling procedure on the correlations.
#'
#' @useDynLib TestCor
#' @importFrom Rcpp sourceCpp
#'
#' @param corr_theo the correlation matrix of Gaussien data simulated
#' @param n sample size
#' @param Nsimu number of simulations
#' @param alpha level of multiple testing
#' @param stat_test
#' \describe{
#' \item{'empirical'}{\eqn{\sqrt{n}*abs(corr)}}
#' \item{'fisher'}{\eqn{\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )}}
#' \item{'student'}{\eqn{\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)}}
#' \item{'gaussian'}{\eqn{\sqrt{n}*mean(Y)/sd(Y)} with \eqn{Y=(X_i-mean(X_i))(X_j-mean(X_j))}}
#' }
#' @param method choice between 'Bonferroni', 'Sidak', 'BootRW', 'MaxTinfty'
#' @param Nboot number of iterations for Monte-Carlo of bootstrap quantile evaluation
#' @param stepdown logical, if TRUE a stepdown procedure is applied
#' @param seed seed for the Gaussian simulations
#'
#' @return Returns a line vector containing estimated values for fwer, fdr, sensitivity, specificity and accuracy.
#'
#' @importFrom MASS mvrnorm
#' @export
#'
#' @references Bonferroni, C. E. (1935). Il calcolo delle assicurazioni su gruppi di teste. Studi in onore del professore salvatore ortu carboni, 13-60.
#' @references Drton, M., & Perlman, M. D. (2007). Multiple testing and error control in Gaussian graphical model selection. Statistical Science, 22(3), 430-449.
#' @references Romano, J. P., & Wolf, M. (2005). Exact and approximate stepdown methods for multiple hypothesis testing. Journal of the American Statistical Association, 100(469), 94-108.
#' @references Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Université Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.
#' @references Westfall, P.H. & Young, S. (1993) Resampling-based multiple testing: Examples and methods for p-value adjustment, John Wiley & Sons, vol. 279.
#' @seealso ApplyFwerCor, SimuFwer_oracle, SimuFdr
#'
#' @examples
#' Nsimu <- 1000
#' n <- 100
#' p <- 10
#' corr_theo <- diag(1,p)
#' corr_theo[1,3] <- 0.5
#' corr_theo[3,1] <- 0.5
#' alpha <- 0.05
#' SimuFwer(corr_theo,n,Nsimu,alpha,stat_test='empirical',method='Bonferroni',stepdown=FALSE)
SimuFwer <- function(corr_theo,n=100,Nsimu=1,alpha=0.05,stat_test='empirical',method='Sidak',Nboot=1000,stepdown=TRUE,seed=NULL){
if(sum(stat_test==c('empirical','fisher','student','2nd.order'))==0){ stop('Wrong value for stat_test.')}
if(sum(method==c('Bonferroni','Sidak','BootRW','MaxTinfty'))==0){ stop('Wrong value for method.')}
if(!is.null(seed)){ set.seed(seed) }
p <- nrow(corr_theo)
m <- p*(p-1)/2
corr_theo_vect <- vectorize(corr_theo)
H1 <- (corr_theo_vect!=0)
# we simulate all data outside the loop to improve time
data_all <- mvrnorm(n*Nsimu,rep(0,p),corr_theo)
false_positive <- array(0,dim=c(Nsimu))
true_positive <- array(0,dim=c(Nsimu))
nb_rejet <- array(0,dim=c(Nsimu))
for(nsimu in 1:Nsimu){
data <- data_all[(1:n)+n*(nsimu-1), ]
rejet <- ApplyFwerCor(data,alpha,stat_test,method,Nboot,stepdown,vect=TRUE,logical=TRUE)
true_positive[nsimu] <- sum(H1[rejet])
nb_rejet[nsimu] <- sum(rejet)
}
false_positive <- nb_rejet-true_positive
true_negative <- m-sum(H1)-false_positive
m1 <- rep(sum(H1),Nsimu)
# return fwer, fdr, sensitivity, specificity, accuracy
res <- c(mean(false_positive>0),mean(ifelse(nb_rejet==0,0,false_positive/nb_rejet)),mean(ifelse(m1==0,0,true_positive/sum(H1))),mean(ifelse(m1==m,0,true_negative/(m-sum(H1)))),mean((true_positive+true_negative)/m))
names(res) <- c('fwer','fdr','sensitivity','specificity','accuracy')
return(res)
}
#' Simulates Gaussian data with a given correlation matrix and applies oracle MaxTinfty on the correlations.
#' @description Simulates Gaussian data with a given correlation matrix and applies oracle MaxTinfty (i.e. Drton & Perlman (2007)'s procedure with the true correlation matrix) on the correlations.
#'
#' @param corr_theo the correlation matrix of Gaussien data simulated
#' @param n sample size
#' @param Nsimu number of simulations
#' @param alpha level of multiple testing
#' @param stat_test
#' \describe{
#' \item{'empirical'}{\eqn{\sqrt{n}*abs(corr)}}
#' \item{'fisher'}{\eqn{\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )}}
#' \item{'student'}{\eqn{\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)}}
#' \item{'gaussian'}{\eqn{\sqrt{n}*mean(Y)/sd(Y)} with \eqn{Y=(X_i-mean(X_i))(X_j-mean(X_j))}}
#' }
#' @param method only 'MaxTinfty' available
#' @param Nboot number of iterations for Monte-Carlo of bootstrap quantile evaluation
#' @param stepdown logical, if TRUE a stepdown procedure is applied
#' @param seed seed for the Gaussian simulations
#'
#' @return Returns a line vector containing estimated values for fwer, fdr, sensitivity, specificity and accuracy.
#'
#' @references Drton, M., & Perlman, M. D. (2007). Multiple testing and error control in Gaussian graphical model selection. Statistical Science, 22(3), 430-449.
#' @references Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Université Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.
#' @export
#' @seealso ApplyFwerCor_Oracle, SimuFwer
#'
#' @examples
#' Nsimu <- 1000
#' n <- 50
#' p <- 10
#' corr_theo <- diag(1,p)
#' corr_theo[1,3] <- 0.5
#' corr_theo[3,1] <- 0.5
#' alpha <- 0.05
#' SimuFwer_oracle(corr_theo,n,Nsimu,alpha,stat_test='empirical',stepdown=FALSE,Nboot=100)
SimuFwer_oracle <- function(corr_theo,n=100,Nsimu=1,alpha=0.05,stat_test='empirical',method='MaxTinfty',Nboot=1000,stepdown=TRUE,seed=NULL){
if(sum(stat_test==c('empirical','fisher','student','2nd.order'))==0){ stop('Wrong value for stat_test.')}
if(method!='MaxTinfty'){
stop('The only oracle procedure available is MaxTinfty.\n')
}
if(!is.null(seed)){ set.seed(seed) }
p <- nrow(corr_theo)
m <- p*(p-1)/2
corr_theo_vect <- vectorize(corr_theo)
H1 <- (corr_theo_vect!=0)
# we simulate all data outside the loop to improve time
data_all <- mvrnorm(n*Nsimu,rep(0,p),corr_theo)
false_positive <- array(0,dim=c(Nsimu))
true_positive <- array(0,dim=c(Nsimu))
nb_rejet <- array(0,dim=c(Nsimu))
for(nsimu in 1:Nsimu){
data <- data_all[(1:n)+n*(nsimu-1), ]
rejet <- ApplyFwerCor(data,alpha,stat_test,method,Nboot,stepdown,vect=TRUE,logical=TRUE)
true_positive[nsimu] <- sum(H1[rejet])
nb_rejet[nsimu] <- sum(rejet)
}
false_positive <- nb_rejet-true_positive
true_negative <- m-sum(H1)-false_positive
m1 <- rep(sum(H1),Nsimu)
# return fwer, fdr, sensitivity, specificity, accuracy
res <- c(mean(false_positive>0),mean(ifelse(nb_rejet==0,0,false_positive/nb_rejet)),mean(ifelse(m1==0,0,true_positive/sum(H1))),mean(ifelse(m1==m,0,true_negative/(m-sum(H1)))),mean((true_positive+true_negative)/m))
names(res) <- c('fwer','fdr','sensitivity','specificity','accuracy')
return(res)
}
#' Simulates Gaussian data with a given correlation matrix and applies a FDR controlling procedure on the correlations.
#'
#' @param corr_theo the correlation matrix of Gaussien data simulated
#' @param n sample size
#' @param Nsimu number of simulations
#' @param alpha level of multiple testing
#' @param stat_test
#' \describe{
#' \item{'empirical'}{\eqn{\sqrt{n}*abs(corr)}}
#' \item{'fisher'}{\eqn{\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )}}
#' \item{'student'}{\eqn{\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)}}
#' \item{'gaussian'}{\eqn{\sqrt{n}*mean(Y)/sd(Y)} with \eqn{Y=(X_i-mean(X_i))(X_j-mean(X_j))}}
#' }
#' @param method choice between 'LCTnorm' and 'LCTboot', developped by Cai & Liu (2016),
#' 'BH', traditional Benjamini-Hochberg (1995)'s procedure,
#' and 'BHboot', Benjamini-Hochberg (1995)'s procedure with bootstrap evaluation of pvalues
#' @param Nboot number of iterations for Monte-Carlo of bootstrap quantile evaluation
#' @param seed seed for the Gaussian simulations
#'
#' @return Returns a line vector containing estimated values for fwer, fdr, sensitivity, specificity and accuracy.
#'
#' @importFrom MASS mvrnorm
#' @export
#'
#' @references Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the royal statistical society. Series B (Methodological), 289-300.
#' @references Cai, T. T., & Liu, W. (2016). Large-scale multiple testing of correlations. Journal of the American Statistical Association, 111(513), 229-240.
#' @references Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Université Grenoble Alpes, France, \url{https://tel.archives-ouvertes.fr/tel-01971574v1}.
#' @seealso ApplyFdrCor, SimuFwer
#'
#' @examples
#' Nsimu <- 1000
#' n <- 100
#' p <- 10
#' corr_theo <- diag(1,p)
#' corr_theo[1,3] <- 0.5
#' corr_theo[3,1] <- 0.5
#' alpha <- 0.05
#' SimuFdr(corr_theo,n,Nsimu,alpha,stat_test='empirical',method='LCTnorm')
SimuFdr <- function(corr_theo,n=100,Nsimu=1,alpha=0.05,stat_test='empirical',method='LCTnorm',Nboot=1000,seed=NULL){
if(sum(stat_test==c('empirical','fisher','student','2nd.order'))==0){ stop('Wrong value for stat_test.')}
if(sum(method==c('LCTnorm','LCTboot','BH','BHboot'))==0){ stop('Wrong value for method.')}
if(!is.null(seed)){ set.seed(seed) }
p <- nrow(corr_theo)
m <- p*(p-1)/2
corr_theo_vect <- vectorize(corr_theo)
H1 <- (corr_theo_vect!=0)
# we simulate all data outside the loop to improve time
data_all <- mvrnorm(n*Nsimu,rep(0,p),corr_theo)
true_positive <- array(0,dim=c(Nsimu))
nb_rejet <- array(0,dim=c(Nsimu))
for(nsimu in 1:Nsimu){
data <- data_all[(1:n)+n*(nsimu-1), ]
rejet <- ApplyFdrCor(data,alpha,stat_test,method,Nboot,vect=TRUE)
true_positive[nsimu] <- sum(H1[rejet])
nb_rejet[nsimu] <- sum(rejet)
}
false_positive <- nb_rejet-true_positive
true_negative <- m-sum(H1)-false_positive
m1 <- rep(sum(H1),Nsimu)
# return fwer, fdr, sensitivity, specificity, accuracy
res <- c(mean(false_positive>0),mean(ifelse(nb_rejet==0,0,false_positive/nb_rejet)),mean(ifelse(m1==0,0,true_positive/sum(H1))),mean(ifelse(m1==m,0,true_negative/(m-sum(H1)))),mean((true_positive+true_negative)/m))
names(res) <- c('fwer','fdr','sensitivity','specificity','accuracy')
return(res)
}
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