wwratio {WWR} | R Documentation |
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)
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 |
tl |
A vector of total numbers of losses in group 1 for each of the two outcomes. Note that |
xp |
The ratios between |
cwindex |
The win contribution index defined as the ratio between |
clindex |
The loss contribution index defined as the ratio between |
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.
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)