Double Cox regression for win product

Description

Use two Cox regression models (one for the terminal event and the other for the non-trminal event) to model the win product adjusting for covariates

Usage

winreg(y1,y2,d1,d2,z)

Arguments

Details

This function uses two Cox regression models (one for the terminal event and the other for the non-trminal event) to model the win product adjusting for covariates.

Value

Author(s)

Xiaodong Luo

References

Pocock S.J., Ariti C.A., Collier T. J. and Wang D. 2012. The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. European Heart Journal, 33, 176-182.

Luo X., Tian H., Mohanty S. and Tsai W.-Y. 2015. An alternative approach to confidence interval estimation for the win ratio statistic. Biometrics, 71, 139-145.

Luo X., Qiu J., Bai S. and Tian H. 2017. Weighted win loss approach for analyzing prioritized outcomes. Statistics in Medicine, to appear.

See Also

wrlogistic

Examples

###Generate data
n<-300
rho<-0.5
b2<-c(1.0,-1.0)
b1<-c(0.5,-0.9)
bc<-c(1.0,0.5)
lambda10<-0.1;lambda20<-0.08;lambdac0<-0.09
lam1<-rep(0,n);lam2<-rep(0,n);lamc<-rep(0,n)
z1<-rep(0,n)
z1[1:(n/2)]<-1
z2<-rnorm(n)
z<-cbind(z1,z2)

lam1<-lam2<-lamc<-rep(0,n)
for (i in 1:n){
    lam1[i]<-lambda10*exp(-sum(z[i,]*b1))
    lam2[i]<-lambda20*exp(-sum(z[i,]*b2))
    lamc[i]<-lambdac0*exp(-sum(z[i,]*bc))
}
tem<-matrix(0,ncol=3,nrow=n)

y2y<-matrix(0,nrow=n,ncol=3)
y2y[,1]<-rnorm(n);y2y[,3]<-rnorm(n)
y2y[,2]<-rho*y2y[,1]+sqrt(1-rho^2)*y2y[,3]
tem[,1]<--log(1-pnorm(y2y[,1]))/lam1
tem[,2]<--log(1-pnorm(y2y[,2]))/lam2
tem[,3]<--log(1-runif(n))/lamc

y1<-apply(tem,1,min)
y2<-apply(tem[,2:3],1,min)
d1<-as.numeric(tem[,1]<=y1)
d2<-as.numeric(tem[,2]<=y2)

y<-cbind(y1,y2,d1,d2)
z<-as.matrix(z)
aa<-winreg(y1,y2,d1,d2,z)
aa

Logistic regression for win ratio

Description

Use a logistic regression model to model win ratio adjusting for covariates with the user-supplied comparison results

Usage

wrlogistic(aindex,z,b0=rep(0,ncol(z)),tol=1.0e-04,maxiter=20)

Arguments

Details

This function uses a logistic regression model to model win ratio adjusting for covaraites. This function uses the pairwise comparision result supplied by the user which hopefully will speed up the program.

Value

Author(s)

Xiaodong Luo

References

Pocock S.J., Ariti C.A., Collier T. J. and Wang D. 2012. The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. European Heart Journal, 33, 176-182.

Luo X., Tian H., Mohanty S. and Tsai W.-Y. 2015. An alternative approach to confidence interval estimation for the win ratio statistic. Biometrics, 71, 139-145.

Luo X., Qiu J., Bai S. and Tian H. 2017. Weighted win loss approach for analyzing prioritized outcomes. Statistics in Medicine, to appear.

See Also

winreg

Examples

###Generate data
n<-300
rho<-0.5
b2<-c(1.0,-1.0)
b1<-c(0.5,-0.9)
bc<-c(1.0,0.5)
lambda10<-0.1;lambda20<-0.08;lambdac0<-0.09
lam1<-rep(0,n);lam2<-rep(0,n);lamc<-rep(0,n)
z1<-rep(0,n)
z1[1:(n/2)]<-1
z2<-rnorm(n)
z<-cbind(z1,z2)

lam1<-lam2<-lamc<-rep(0,n)
for (i in 1:n){
    lam1[i]<-lambda10*exp(-sum(z[i,]*b1))
    lam2[i]<-lambda20*exp(-sum(z[i,]*b2))
    lamc[i]<-lambdac0*exp(-sum(z[i,]*bc))
}
tem<-matrix(0,ncol=3,nrow=n)

y2y<-matrix(0,nrow=n,ncol=3)
y2y[,1]<-rnorm(n);y2y[,3]<-rnorm(n)
y2y[,2]<-rho*y2y[,1]+sqrt(1-rho^2)*y2y[,3]
tem[,1]<--log(1-pnorm(y2y[,1]))/lam1
tem[,2]<--log(1-pnorm(y2y[,2]))/lam2
tem[,3]<--log(1-runif(n))/lamc

y1<-apply(tem,1,min)
y2<-apply(tem[,2:3],1,min)
d1<-as.numeric(tem[,1]<=y1)
d2<-as.numeric(tem[,2]<=y2)

y<-cbind(y1,y2,d1,d2)
z<-as.matrix(z)
###################

#####Define the comparison function
comp<-function(y,x){
  y1i<-y[1];y2i<-y[2];d1i<-y[3];d2i<-y[4]
  y1j<-x[1];y2j<-x[2];d1j<-x[3];d2j<-x[4] 
  w2<-0;w1<-0;l2<-0;l1<-0
  
  if (d2j==1 & y2i>=y2j) w2<-1
  else if (d2i==1 & y2j>=y2i) l2<-1
  
  if (w2==0 & l2==0 & d1j==1 & y1i>=y1j) w1<-1
  else if (w2==0 & l2==0 & d1i==1 & y1j>=y1i) l1<-1
  
  comp<-0
  if (w2==1) comp<-1 
  else if (l2==1) comp<-(-1)
  else if (w1==1) comp<-2
  else if (l1==1) comp<-(-2)
  
  comp
}
bin<-rep(0,n*(n-1)/2)
for (i in 2:n)for (j in 1:(i-1))bin[(i-1)*(i-2)/2+j]<-comp(y[i,],y[j,])
###Use the win loss indicator matrix to calculate the general win loss statistics
bb2<-wrlogistic(bin,z,b0=rep(0,ncol(z)),tol=1.0e-04,maxiter=20)
bb2


####Calculate the win, loss, tie result using Fortran loops to speed up the process
####Using the "inline" package to convert the code into Fortran

#install.packages("inline") #Install the package "inline''
library("inline") ###Load the package "inline"

########################################################
# The use of ``inline'' needs ``rtools'' and ``gcc''
# in the PATH environment of R.
# The following code will put these two into
# the PATH for the current R session ONLY.
########################################################

#rtools <- "C:\Rtools\bin"
#gcc <- "C:\Rtools\gcc-4.6.3\bin"
#path <- strsplit(Sys.getenv("PATH"), ";")[[1]]
#new_path <- c(rtools, gcc, path)
#new_path <- new_path[!duplicated(tolower(new_path))]
#Sys.setenv(PATH = paste(new_path, collapse = ";"))

codex4 <- "
integer::i,j,indexij,d1i,d2i,d1j,d2j,w2,w1,l2,l1
double precision::y1i,y2i,y1j,y2j
do i=2,n,1
   y1i=y(i,1);y2i=y(i,2);d1i=dnint(y(i,3));d2i=dnint(y(i,4))
   do j=1,(i-1),1
      y1j=y(j,1);y2j=y(j,2);d1j=dnint(y(j,3));d2j=dnint(y(j,4)) 
      indexij=(i-1)*(i-2)/2+j
      w2=0;w1=0;l2=0;l1=0
      if (d2j==1 .and. y2i>=y2j) then
         w2=1
      else if (d2i==1 .and. y2j>=y2i) then
         l2=1
      else if (d1j==1 .and. y1i>=y1j) then
         w1=1
      else if (d1i==1 .and. y1j>=y1i) then
         l1=1
      end if
      aindex(indexij)=0
      if (w2==1) then 
         aindex(indexij)=1
      else if (l2==1) then
         aindex(indexij)=-1
      else if (w2==0 .and. l2==0 .and. w1==1) then
         aindex(indexij)=2
      else if (w2==0 .and. l2==0 .and. l1==1) then
         aindex(indexij)=-2
      end if
   end do
end do
"
###Convert the above code into Fortran
cubefnx4<-cfunction(sig = signature(n="integer", p="integer", y="numeric", aindex="integer"), 
            implicit = "none",dim = c("", "", "(n,p)", "(n*(n-1)/2)"), codex4, language="F95")

###Use the converted code to calculate the win, loss and tie indicators
options(object.size=1.0E+10)
ain<-cubefnx4(length(y[,1]),length(y[1,]), y, rep(0,n*(n-1)/2))$aindex

####Perform the logistic regression
aa2<-wrlogistic(ain,z,b0=rep(0,ncol(z)),tol=1.0e-04,maxiter=20)
aa2

Inverse matrix

Description

This will calculate the inverse matrix by Gauss elimination method

Usage

zinv(y)

Arguments

Details

Inverse matrix

Value

Note

This provides the inverse matrix using Gauss elimination method, this program performs satisfactorily when the size of the matrix is less than 50

Author(s)

Xiaodong Luo

Examples

y<-matrix(c(1,2,0,1),ncol=2,nrow=2)
zinv(y)