# Beta coefficient estimate at each time point Function that ouputs beta coefficient estimate of each covariate at each observation time point for a given tree, which can be used to plot the time-varying coefficients. ```r mat.tvbeta(indx, fulltree, subtrees = NULL, survtime, survstatus, x) ``` ## Arguments - `indx`: Index number of a subtree that needs to be analyzed - `fulltree`: output of `output.coxphout`. - `subtrees`: (Optional) output of `prune`. - `survtime`: survival time/ follow up time of subjects - `survstatus`: survival status of subjects. 0 for alive and 1 for dead - `x`: a data frame of covariates. In case of single covariate, use [,,drop =F] to keep the data frame structure ## Returns For each predictor, `mat.tvbeta` gives the coefficient values at each observation time for a given subtree. The function outputs a matrix that can be used to plot the time-varying coefficient estimates over time. The number of rows in the matrix is the # of observations and the number of columns is the product of the # of covariates and the # of specified subtrees. ## References Xu, R. and Adak, S. (2002), Survival Analysis with Time-Varying Regression Effects Using a Tree-Based Approach. Biometrics, 58: 305-315. ## Examples ```r #This function requires output from output.coxphout, prune, and the original data set. data('alcohol') require(survival) coxtree <- coxph.tree(alcohol[,'time'], alcohol[,'event'], x = alcohol[,'alc', drop = FALSE], D = 4) nodetree <- output.coxphout(coxtree) subtrees <- prune(nodetree) #creating matrix of beta coefficients at each event time point for all subtrees k <- nrow(subtrees) for (l in 1:k) { print(paste("Tree #",l)) coeftmp <- mat.tvbeta(l,nodetree,subtrees,alcohol[,'time'], alcohol[,'event'], x = data.frame(model.matrix(~alc, data=alcohol)[,-c(1), drop = FALSE])) if (l == 1) coef <- coeftmp if (l > 1) coef <- cbind(coef,coeftmp) } ##Creating plot of all subtrees for each predictor: p <- ncol(coef)/k #Number of variables x = data.frame(model.matrix(~alc, data=alcohol)[,-c(1), drop = FALSE]) xnames <- xname(x) xnames <- c('Alcohol 1', 'Alcohol 4') #Subsetting data coefnew <- data.frame(coef) survtime <- alcohol[,'time'] #Setting desired depth (All the subtrees) kk <- nrow(subtrees) for (j in 1:p) { matplot(survtime,coefnew[,seq(from=j,to=kk*p,by=p)],type="l",lty=1:kk,col= (1:kk)+1 ,xlab="Survival Time",ylab=" ") title(main=paste('all:', xnames[j])) legend('bottomleft', legend = paste('tree number', 1:kk), lty=1:kk,col= (1:kk)+1) } ##Creating a plot showing changes in coefficient of two predictors in full tree #creating matrix of beta coefficients at each event time point for full tree coeftmp <- mat.tvbeta(1,nodetree,subtrees,alcohol[,'time'], alcohol[,'event'], x = data.frame(model.matrix(~alc, data=alcohol)[,-c(1), drop = FALSE])) coefnew <- coeftmp matplot(survtime,coefnew,type="l",lty=1:2,col= (1:2)+1,xlab="Survival Time",ylab=" ") legend('bottomleft', legend = c("Alcohol 1", "Alcohol 4"), lty=1:2,col= (1:2)+1) ```

mat.tvbeta function