I am learning the random survival forest model which output is cumulative hazard function. In the paper[1], they used the interval of cumulative hazard function as risk score.
I simulated on Weibull distribution. Let X and Y are the random variable from different Weibull distribution.Since I know the distribution of random variables, I could caculated probability $Pr(X > Y)$. Ideally, if risk score of X is smaller than Y, $Pr(X > Y)$ should be bigger than 0.5. I use both cumulative hazard function and its interval as risk score. But I found those had poor performance when $Pr(X > Y)$ is close to 0.5, 0.4 for example.
So is there a better Risk Score derived from hazard function?
[1]Ishwaran H, Kogalur U B, Blackstone E H, et al. Random survival forests[J]. The Annals of Applied Statistics, 2008: 841-860.
