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

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/wwratio.R

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)

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

`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).

weighted win statistics

`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

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

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)

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)