In stc04003/tranSurv: Transformation Model Based Estimation of Survival and Regression Under Dependent Truncation and Independent Censoring

knitr::opts_chunk$set(comment = NA, prompt = TRUE)

```{R session, echo = FALSE, message = FALSE} library(tranSurv)

This vignette provides a short tutorial on the usage of the package's main function, `trSurvfit`.

## Illustration
Example function in `?trSurvfit`
```{R trEx}
datgen <- function(n) {
    a <- -0.3
    X <- rweibull(n, 2, 4) ## failure times
    U <- rweibull(n, 2, 1) ## latent truncation time
    T <- (1 + a) * U - a * X ## apply transformation
    C <- 10 ## censoring
    dat <- data.frame(trun = T, obs = pmin(X, C), delta = 1 * (X <= C))
    return(subset(dat, trun <= obs))
}

Set a random seed and see data structure. ```{R data} set.seed(1) dat <- datgen(100) head(dat)

The `trun` is the truncation time, `obs` is the observed survival time, and `delta` is the censoring indicator.
Fitting this with `trSurvfit`:
```{R data-fit}
with(dat, trSurvfit(trun, obs, delta))

The function trSurvfit gives some important information. The conditional Kendall's tau for the observed data (before transformation) is 0.5312 with a $p$-value < 0.001. The restricted IPW Kendall's tau (Austin and Betensky, 2014) gives the same result. The transformation parameter, $a$, turns out to be $-0.3011$. The estimated survival curve (based on $a$) can be plotted with survfit: ```{R data-survfit} foo <- with(dat, trSurvfit(trun, obs, delta)) plot(foo)

## Simulation
Make a function to call the transformation parameter $\alpha$. 
```{R trEx-do}
do <- function(n){
  foo <- with(datgen(n), trSurvfit(trun, obs, delta))
  c(foo$byTau$par[1], foo$byP$par[1])
}

Try $n = 100$ with 100 replicates: ```{R trEx-run, cache = TRUE} set.seed(1) result <- replicate(100, do(100))

This returns a 2 by 100 matrix. 
The first row gives $\hat\alpha$ by maximizing the conditional Kendall's tau and the second row gives $\hat\alpha$ by minimizing the $p$-value from the conditional Kendall's tau test.
```{R trEx-res}
summary(t(result))

stc04003/tranSurv documentation built on July 21, 2021, 6:46 p.m.