# Double Cox regression for win product Use two Cox regression models (one for the terminal event and the other for the non-trminal event) to model the win product adjusting for covariates ```r winreg(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 else. - `d2`: a numeric vector of event indicators with 1 denoting the terminal event is observed and 0 else. - `z`: a numeric matrix of covariates. ## Details This function uses two Cox regression models (one for the terminal event and the other for the non-trminal event) to model the win product adjusting for covariates. ## Returns - **beta1**: Estimated regression parameter based on the non-terminal event times `y1`, $\exp$(`beta1`) is the adjusted hazard ratio - **sigma1**: Estimated variance of `beta1` using the residual method instead of the inverse of Fisher information - **tb1**: Wald test statistics based on `beta1` and `sigma1` - **pb1**: Two-sided p-values of the Wald test statistics `tb1` - **beta2**: Estimated regression parameter based on the terminal event times `y2`, $\exp$(`beta2`) is the adjusted hazard ratio - **sigma2**: Estimated variance of `beta2` using the residual method instead of the inverse of Fisher information - **tb2**: Wald test statistics based on `beta2` and `sigma2` - **pb2**: Two-sided p-values of the Wald test statistics `tb2` - **beta**: `beta1`+`beta2`,$\exp$(-`beta`) is the adjusted win product - **sigma**: Estimated variance of `beta` using the residual method - **tb**: Wald test statistics based on `beta` and `sigma` - **pb**: Two-sided p-values of the Wald test statistics `tb` ## 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 `wrlogistic` ## 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) aa<-winreg(y1,y2,d1,d2,z) aa ```

winreg function