# Logistic regression for win ratio Use a logistic regression model to model win ratio adjusting for covariates with the user-supplied comparison results ```r 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. ## Returns - **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 ## 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. ## Author(s) Xiaodong Luo ## See Also `winreg` ## Examples ```r ###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 ```

wrlogistic function