# Incident/Dynamic (I/D) ROC curve, AUC and integrated AUC (iAUC) estimation of censored survival data This function estimates the time-varying parameter estimate $\beta(t)$ of non-proportional hazard model using local-linear Cox regression as discussed in Heagerty and Zheng, 2005. ```r llCoxReg(Stime, entry=NULL, status, marker, span=0.40, p=1, window="asymmetric") ``` ## Arguments - `Stime`: For right censored data, this is the follow up time. For left truncated data, this is the ending time for the interval. - `entry`: For left truncated data, this is the entry time of the interval. The default is set to NULL for right censored data. - `status`: Survival status. - `marker`: Marker value. - `span`: bandwidth parameter that controls the size of a local neighborhood. - `p`: 1 if only the time-varying coefficient is of interest and 2 if the derivative of time-varying coefficient is also of interest, default is 1 - `window`: Either of "asymmetric" or "symmetric", default is asymmetric. ## Details This function calculates the parameter estimate $\beta(t)$ of non-proportional hazard model using local-linear Cox regression as discussed in Heagerty and Zheng, 2005. This estimation is based on a time-dependent Cox model (Cai and Sun, 2003). For **p=1**, the return item **beta** has two columns, the first column is the time-varying parameter estimate, while the second column is the derivative. However, if the derivative of the time-varying parameter is of interest, then we suggest to use **p=2**. In this case, **beta** has four columns, the first two columns are the same when **p=1**, while the last two columns estimates the coefficients of squared marker value and its derivative. ## Returns Returns a list of following items: - **time**: unique failure times - **beta**: estimate of time-varying parameter $\beta(t)$ at each unique failure time. ## References Heagerty, P.J., Zheng Y. (2005) Survival Model Predictive Accuracy and ROC curves **Biometrics**, 61 , 92 -- 105 ## Author(s) Patrick J. Heagerty ## Examples ```r data(pbc) ## considering only randomized patients pbc1 <- pbc[1:312,] ## create new censoring variable combine 0,1 as 0, 2 as 1 survival.status <- ifelse( pbc1$status==2, 1, 0) survival.time <- pbc1$fudays pbc1$status1 <- survival.status fit <- coxph( Surv(fudays,status1) ~ log(bili) + log(protime) + edema + albumin + age, data=pbc1 ) eta5 <- fit$linear.predictors x <- eta5 nobs <- length(survival.time[survival.status==1]) span <- 1.0*(nobs^(-0.2)) ## Not run: bfnx1 <- llCoxReg(Stime=survival.time, status=survival.status, marker=x, span=span, p=1) plot(bfnx1$time, bfnx1$beta[,1], type="l", xlab="Time", ylab="beta(t)") ## End(Not run) ```

llCoxReg function