wrlogistic {WLreg}

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

aindex

a vector that collects the pairwise comparison results. Suppose there are a total of n subjects in the study, there are n(n-1)/2 elements in aindex. The (i-1)*(i-2)/2+j-th element, denoted by C_{ij}, is the comparison result between subject i and subject j, where i=2,\ldots,n and j=1,\ldots,i-1. The element C_{ij} is equal to 1 if subject i wins over subject j on the most important outcome, C_{ij} is equal to -1 if subject i loses against subject j on the most important outcome; C_{ij} is equal to 2 if subject i wins over subject j on the second most important outcome after tie on the most important outcome, C_{ij} is equal to -2 if subject i loses against subject j on the second most important outcome after tie on the most important outcome; and so forth until all the outcomes have been used for comparison; then C_{ij} is equal to 0 if an ultimate tie is resulted.

z

a matrix of covariates

b0

the initial value of the regression parameter

tol

error tolerence

maxiter

maximum number of iterations

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

b

Estimated regression parameter, \exp(b) is the adjusted win ratio

Ubeta

The score function

Vbeta

The estimated varaince of \sqrt{n}\timesb

Wald

Wald test statistics for the estimated parameter b

pvalue

Two-sided p-values of the Wald statistics

Imatrix

The information matrix

Wtotal

Total wins

Ltotal

Total losses

err

err at convergence

iter

number of iterations performed before covergence

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