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

## Description

Calculate weighted win loss statistics and their corresponding variances under the global NULL hypothesis based on Luo et al. (2017) paper, which is a generalization of the win ratio of Pocock et al. (2012) and the win difference of Luo et al. (2015)

## Usage

 `1` ```wwratio(y1, y2, d1, d2, z, wty1 = 1, wty2 = 1) ```

## 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 vector of group indicators with 1 denoting the treatment group and 0 the control group. `wty1` a numeric vector of weight indicators for the non-terminal event with values 1 to 4 corresponding to weights used in Luo et al. (2017). `wty2` a numeric vector of weight indicators for the terminal event with values 1 to 2 corresponding to weights used in Luo et al. (2017).

## Details

weighted win statistics

## Value

 `n1` Number of subjects in group 1 `n0` Number of subjects in group 0 `n` Total number of subjects in both groups `wty1` Weight for non-terminal event `wty2` Weight for terminal event `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` weighted win ratio `vr` estimated variance of weighted win ratio `tr` standardized log(wr) `pr` 2-sided p-value of tr `wd` weighted win difference `vd` estimated variance of weighted win difference `td` standardized wd `pd` 2-sided p-value of td `wp` weighted win product `vp` estimated variance of weighted 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.

Luo X., Qiu J., Bai S. and Tian H. 2017. Weighted win loss approach for analyzing prioritized outcomes. Statistics in Medicine, doi: 10.1002/sim.7284.

`wlogr2`,`winratio`

## Examples

 ``` 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 29 30 31 32``` ```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) i<-1 ##i=1,2,3,4 j<-2 ##j=1,2 wtest<-wwratio(y1,y2,d1,d2,z,wty1=i,wty2=j) summary(wtest) ```

### Example output

```Total number of subjects:                            300
Number of subjects in group 1:                       150
Number of subjects in group 0:                       150

Win total in group 1:                                16723.96
Loss total in group 1:                               7822.68
Win total in group 1 from most to least important:   15125.96 1598
Loss total in group 1 from most to least important:  7025.68 797
Win contribution indexes in group 1:                 0.62 0.07
Loss contribution indexes in group 1:                0.29 0.03

The win difference statistic:         Test Stat   8901.2735
sd          0.3937
z           4.3516
p-value     0
95% CI      (8845.6548,8956.8922)

The win ratio statistic:              Test Stat   2.1379
sd          4.5291
z           2.9057
p-value     0.0037
95% CI      (1.6822,2.717)

The win product statistic:            Test Stat   4.3167
sd          10.4214
z           2.4307
p-value     0.0151
95% CI      (3.2848,5.6728)
```

WWR documentation built on May 2, 2019, 11:02 a.m.