# winratio: Win Loss Statistics In WWR: Weighted Win Loss Statistics and their Variances

## Description

Calculate the win loss statistics of Pocock et al. (2012) and the corresponding variances, which are based on a U-statistic method of Luo et al. (2015)

## Usage

 `1` ```winratio(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 denoting otherwise. `d2` a numeric vector of event indicators with 1 denoting the terminal event is observed and 0 denoting otherwise.Note that Luo et al. (2015) use a single indicator d so that d=1 if and only if `d1`=1 and `d2`=1; d=2 if and only if `d1`=0 and `d2`=1; d=3 if and only if `d1`=0 and `d2`=0; and d=4 if and only if `d1`=1 and `d2`=0. `z` a numeric vector of group indicators with 1 denoting the treatment group and 0 the control group.

## Details

win loss statistics

## Value

 `n1` Number of subjects in group 1 `n0` Number of subjects in group 0 `n` Total number of subjects in both groups `totalw` Total number of wins in group 1 `totall` Total number of losses in group 1 `tw` A vector of total numbers of wins in group 1 for each of the two outcomes. Note that `totalw`=sum(`tw`), and the first element is for the terminal event and the second element is for the non-terminal event. `tl` A vector of total numbers of losses in group 1 for each of the two outcomes. Note that `totall`=sum(`tl`), and the first element is for the terminal event and the second element is for the non-terminal event. `xp` The ratios between `tw` and `tl` `cwindex` The win contribution index defined as the ratio between `tw` and `totalw`+`totall` `clindex` The loss contribution index defined as the ratio between `tl` and `totalw`+`totall` `wr` win ratio `vr` estimated variance of win ratio `tr` standardized log(wr) `pr` 2-sided p-value of tr `wd` win difference `vd` estimated variance of win difference `td` standardized wd `pd` 2-sided p-value of td `wp` win product `vp` estimated variance of win product `tp` standardized log(wp) `pp` 2-sided p-value of tp

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.

`wlogr2`,`wwratio`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```n<-300 rho<-0.5 b2<-0.2 b1<-0.5 bc<-1.0 lambda10<-0.1;lambda20<-0.08;lambdac0<-0.09 lam1<-rep(0,n);lam2<-rep(0,n);lamc<-rep(0,n) z<-rep(0,n) z[1:(n/2)]<-1 lam1<-lambda10*exp(-b1*z) lam2<-lambda20*exp(-b2*z) lamc<-lambdac0*exp(-bc*z) 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) wtest<-winratio(y1,y2,d1,d2,z) summary(wtest) ```