Package 'WLreg' reference manual

Title:	Regression Analysis Based on Win Loss Endpoints
Description:	Use various regression models for the analysis of win loss endpoints adjusting for non-binary and multivariate covariates.
Authors:	Xiaodong Luo [aut, cre], Sanofi [cph]
Maintainer:	Xiaodong Luo <[email protected]>
License:	GPL (>= 2)
Version:	1.0.0.1
Built:	2024-11-02 06:31:56 UTC
Source:	CRAN

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

Arguments

`y1`	a numeric vector of event times denoting the minimum of event times $T_1$ , $T_2$ and censoring time $C$ , where the endpoint $T_2$ , corresponding to the terminal event, is considered of higher clinical importance than the endpoint $T_1$ , corresponding to the non-terminal event. Note that the terminal event may censor the non-terminal event, resulting in informative censoring.
`y2`	a numeric vector of event times denoting the minimum of event time $T_2$ and censoring time $C$ . Clearly, y2 is not smaller than y1.
`d1`	a numeric vector of event indicators with 1 denoting the non-terminal event is observed and 0 else.
`d2`	a numeric vector of event indicators with 1 denoting the terminal event is observed and 0 else.
`z`	a numeric matrix of covariates.

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

`beta1`	Estimated regression parameter based on the non-terminal event times `y1`, $\exp$ (`beta1`) is the adjusted hazard ratio
`sigma1`	Estimated variance of `beta1` using the residual method instead of the inverse of Fisher information
`tb1`	Wald test statistics based on `beta1` and `sigma1`
`pb1`	Two-sided p-values of the Wald test statistics `tb1`
`beta2`	Estimated regression parameter based on the terminal event times `y2`, $\exp$ (`beta2`) is the adjusted hazard ratio
`sigma2`	Estimated variance of `beta2` using the residual method instead of the inverse of Fisher information
`tb2`	Wald test statistics based on `beta2` and `sigma2`
`pb2`	Two-sided p-values of the Wald test statistics `tb2`
`beta`	`beta1`+`beta2`, $\exp$ (-`beta`) is the adjusted win product
`sigma`	Estimated variance of `beta` using the residual method
`tb`	Wald test statistics based on `beta` and `sigma`
`pb`	Two-sided p-values of the Wald test statistics `tb`

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.

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
###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)
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 $\sqrt{n}\times$ `b`
`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

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.

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

###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)
zinv(y)

Arguments

`y`	a sqaure matrix

Details

Inverse matrix

Value

`yi`	the inverse of `y`

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

Package 'WLreg'

Help Index

Double Cox regression for win product

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Logistic regression for win ratio

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Inverse matrix

Description

Usage

Arguments

Details

Value

Note

Author(s)

Examples