R/SimCiRatHet.R

In SimComp: Simultaneous Comparisons for Multiple Endpoints

SimCiRatHet <-
function(trlist, grp, ntr, nep, ssmat, Num.Contrast, Den.Contrast, ncomp, alternative, 
                        conf.level, meanmat, CorrMatDat) {


varmat  <- do.call(rbind, lapply(trlist, function(x) apply(x, 2, var)))
if (any(meanmat<0)) {
  warning("At least one sample mean is negative; check whether the test direction", "\n",
      "is still correct", "\n")
}
estimate <- Num.Contrast%*%meanmat/(Den.Contrast%*%meanmat)

defrmat <- matrix(nrow=ncomp, ncol=nep)
for (j in 1:nep) {
  defrmat[,j] <- DfSattRat(n=ssmat[,1],sd=sqrt(varmat[,j]),Num.Contrast=Num.Contrast,
                           Den.Contrast=Den.Contrast,Margin=estimate[,j])
}
defrmat[defrmat<2] <- 2                                             # to be well-defined
defr <- matrix(apply(defrmat,1,min), nrow=ncomp, ncol=nep)          # matrix of dfs, minimum per row/contrast

CovMatDat  <- lapply(trlist, cov)                                   # list of covariance matrices of the data
if (is.null(CorrMatDat)) {
  CorrMatDat <- lapply(CovMatDat,cov2cor)                           # list of correlation matrices of the data
} else {
  sdmat <- lapply(CovMatDat, function(x) sqrt( diag( diag(x),nrow=nep ) )) # sds on the diagonal
  CovMatDat <- lapply(sdmat, function(x) x%*%CorrMatDat%*%x)        # final list of covariance matrices
}

M <- diag(1/ssmat[,1])
R <- NULL
for (z in 1:ncomp) {
  Rrow <- NULL
  for (w in 1:ncomp) {
    Rpart <- matrix(nrow=nep,ncol=nep)
    for (i in 1:nep) {
      for (h in 1:nep) {
        Rpart[i,h] <- ( t(Num.Contrast[z,]-estimate[z,i]*Den.Contrast[z,])%*%
                        diag( sapply(CovMatDat, function(x) x[i,h]) )%*%M%*%
                         (Num.Contrast[w,]-estimate[w,h]*Den.Contrast[w,]) ) /
                      sqrt( ( t(Num.Contrast[z,]-estimate[z,i]*Den.Contrast[z,])%*%diag(varmat[,i])%*%M%*%
                               (Num.Contrast[z,]-estimate[z,i]*Den.Contrast[z,]) ) *
                            ( t(Num.Contrast[w,]-estimate[w,h]*Den.Contrast[w,])%*%diag(varmat[,h])%*%M%*%
                               (Num.Contrast[w,]-estimate[w,h]*Den.Contrast[w,]) ) )
      }
    }
    Rrow <- cbind(Rrow,Rpart)
  }
  R <- rbind(R, Rrow)                                               # correlation matrix for multi-t
}
diag(R) <- 1

Azi     <- Bzi     <- Czi     <- Discrimi     <- lower     <- upper     <- matrix(nrow=ncomp,ncol=nep)
Azi.raw <- Bzi.raw <- Czi.raw <- Discrimi.raw <- lower.raw <- upper.raw <- matrix(nrow=ncomp,ncol=nep)
NSD <- 0

if (alternative=="greater") {
  for (z in 1:ncomp) {
    for (i in 1:nep) {
      lo1malqu <- qmvt(conf.level,tail="lower.tail",df=as.integer(defr[z,i]),corr=R)$quantile
      univarqu <- qt(p=conf.level, df=defrmat[z,i])
      Azi[z,i] <- ( t(Den.Contrast[z,])%*%meanmat[,i] )^2 - 
                         lo1malqu^2 * ( t(Den.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] )
      Bzi[z,i] <- -2 * ( (t(Num.Contrast[z,])%*%meanmat[,i]) * (t(Den.Contrast[z,])%*%meanmat[,i]) - 
                         lo1malqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] ) )
      Czi[z,i] <- ( t(Num.Contrast[z,])%*%meanmat[,i] )^2 - 
                         lo1malqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Num.Contrast[z,] )
      Discrimi[z,i] <- Bzi[z,i]^2 - 4*Azi[z,i]*Czi[z,i]
      if ( (Azi[z,i]>0) & (Discrimi[z,i]>=0) ) {
        upper[z,i] <- Inf
        lower[z,i] <- (-Bzi[z,i]-sqrt(Discrimi[z,i])) / (2*Azi[z,i])
      } else {
        upper[z,i] <- Inf; lower[z,i] <- -Inf; NSD <- NSD+1
      }
      Azi.raw[z,i] <- ( t(Den.Contrast[z,])%*%meanmat[,i] )^2 - 
                             univarqu^2 * ( t(Den.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] )
      Bzi.raw[z,i] <- -2 * ( (t(Num.Contrast[z,])%*%meanmat[,i]) * (t(Den.Contrast[z,])%*%meanmat[,i]) - 
                             univarqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] ) )
      Czi.raw[z,i] <- ( t(Num.Contrast[z,])%*%meanmat[,i] )^2 - 
                             univarqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Num.Contrast[z,] )
      Discrimi.raw[z,i] <- Bzi.raw[z,i]^2 - 4*Azi.raw[z,i]*Czi.raw[z,i]
      if ( (Azi.raw[z,i]>0) & (Discrimi.raw[z,i]>=0) ) {
        upper.raw[z,i] <- Inf
        lower.raw[z,i] <- (-Bzi.raw[z,i]-sqrt(Discrimi.raw[z,i])) / (2*Azi.raw[z,i])
      } else {
        upper.raw[z,i] <- Inf; lower.raw[z,i] <- -Inf
      }
    }
  }
}
if (alternative=="less") {
  for (z in 1:ncomp) {
    for (i in 1:nep) {
      up1malqu <- qmvt(conf.level,tail="upper.tail",df=as.integer(defr[z,i]),corr=R)$quantile
      univarqu <- qt(p=1-conf.level, df=defrmat[z,i])
      Azi[z,i] <- ( t(Den.Contrast[z,])%*%meanmat[,i] )^2 - 
                         up1malqu^2 * ( t(Den.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] )
      Bzi[z,i] <- -2 * ( (t(Num.Contrast[z,])%*%meanmat[,i]) * (t(Den.Contrast[z,])%*%meanmat[,i]) - 
                         up1malqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] ) )
      Czi[z,i] <- ( t(Num.Contrast[z,])%*%meanmat[,i] )^2 - 
                         up1malqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Num.Contrast[z,] )
      Discrimi[z,i] <- Bzi[z,i]^2 - 4*Azi[z,i]*Czi[z,i]
      if ( (Azi[z,i]>0) & (Discrimi[z,i]>=0) ) {
        upper[z,i] <- (-Bzi[z,i]+sqrt(Discrimi[z,i])) / (2*Azi[z,i])
        lower[z,i] <- -Inf
      } else {
        upper[z,i] <- Inf; lower[z,i] <- -Inf; NSD <- NSD+1
      }
      Azi.raw[z,i] <- ( t(Den.Contrast[z,])%*%meanmat[,i] )^2 - 
                             univarqu^2 * ( t(Den.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] )
      Bzi.raw[z,i] <- -2 * ( (t(Num.Contrast[z,])%*%meanmat[,i]) * (t(Den.Contrast[z,])%*%meanmat[,i]) - 
                             univarqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] ) )
      Czi.raw[z,i] <- ( t(Num.Contrast[z,])%*%meanmat[,i] )^2 - 
                             univarqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Num.Contrast[z,] )
      Discrimi.raw[z,i] <- Bzi.raw[z,i]^2 - 4*Azi.raw[z,i]*Czi.raw[z,i]
      if ( (Azi.raw[z,i]>0) & (Discrimi.raw[z,i]>=0) ) {
        upper.raw[z,i] <- (-Bzi.raw[z,i]+sqrt(Discrimi.raw[z,i])) / (2*Azi.raw[z,i])
        lower.raw[z,i] <- -Inf
      } else {
        upper.raw[z,i] <- Inf; lower.raw[z,i] <- -Inf
      }
    }
  }
}
if (alternative=="two.sided") {
  for (z in 1:ncomp) {
    for (i in 1:nep) {
      ts1malqu <- qmvt(conf.level,tail="both.tails",df=as.integer(defr[z,i]),corr=R)$quantile
      univarqu <- qt(p=1-(1-conf.level)/2, df=defrmat[z,i])
      Azi[z,i] <- ( t(Den.Contrast[z,])%*%meanmat[,i] )^2 - 
                         ts1malqu^2 * ( t(Den.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] )
      Bzi[z,i] <- -2 * ( (t(Num.Contrast[z,])%*%meanmat[,i]) * (t(Den.Contrast[z,])%*%meanmat[,i]) - 
                         ts1malqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] ) )
      Czi[z,i] <- ( t(Num.Contrast[z,])%*%meanmat[,i] )^2 - 
                         ts1malqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Num.Contrast[z,] )
      Discrimi[z,i] <- Bzi[z,i]^2 - 4*Azi[z,i]*Czi[z,i]
      if ( (Azi[z,i]>0) & (Discrimi[z,i]>=0) ) {
        upper[z,i] <- (-Bzi[z,i]+sqrt(Discrimi[z,i])) / (2*Azi[z,i])
        lower[z,i] <- (-Bzi[z,i]-sqrt(Discrimi[z,i])) / (2*Azi[z,i])
      } else {
        upper[z,i] <- Inf; lower[z,i] <- -Inf; NSD <- NSD+1
      }
      Azi.raw[z,i] <- ( t(Den.Contrast[z,])%*%meanmat[,i] )^2 - 
                             univarqu^2 * ( t(Den.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] )
      Bzi.raw[z,i] <- -2 * ( (t(Num.Contrast[z,])%*%meanmat[,i]) * (t(Den.Contrast[z,])%*%meanmat[,i]) - 
                             univarqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Den.Contrast[z,] ) )
      Czi.raw[z,i] <- ( t(Num.Contrast[z,])%*%meanmat[,i] )^2 - 
                             univarqu^2 * ( t(Num.Contrast[z,])%*%diag(varmat[,i])%*%M%*%Num.Contrast[z,] )
      Discrimi.raw[z,i] <- Bzi.raw[z,i]^2 - 4*Azi.raw[z,i]*Czi.raw[z,i]
      if ( (Azi.raw[z,i]>0) & (Discrimi.raw[z,i]>=0) ) {
        upper.raw[z,i] <- (-Bzi.raw[z,i]+sqrt(Discrimi.raw[z,i])) / (2*Azi.raw[z,i])
        lower.raw[z,i] <- (-Bzi.raw[z,i]-sqrt(Discrimi.raw[z,i])) / (2*Azi.raw[z,i])
      } else {
        upper.raw[z,i] <- Inf; lower.raw[z,i] <- -Inf
      }
    }
  }
}

list(estimate=estimate, NSD=NSD, lower.raw=lower.raw, upper.raw=upper.raw, 
     lower=lower, upper=upper, CovMatDat=CovMatDat, CorrMatDat=CorrMatDat, CorrMatComp=R, 
     degr.fr=defr, Num.Contrast=Num.Contrast, Den.Contrast=Den.Contrast, 
     alternative=alternative, conf.level=conf.level)


}