# How to interpret time-varying AUC for Survival Analysis?

I have trained some models for survival forecast (only interested in ranking of observations). I obtained C-index values as well as dynamic AUC values for the three trained models (CPH, AFT -weibull- and a Random Survival Forest) implemented in scikit-survival. I then calculated out-of-sample (test set) AUC for all three models. This is the output plot:

COX PH.

AFT.

RSF.

So the two questions are:

1. How should I interpret this upward trend in the model's predictive performance?

2. The AUC for the CPH and AFT looks almost the same. What situation could potentially explain this matching predictive performance for the two models?.

Thanks!

Edit for clarification:

The cumulative/dynamic AUC is defined by Lambert and Chevret as: $$$$AUC^{CD} (t) = \dfrac{\sum_{i=1}^{n} \sum_{j=1}^{n} I(X_j > t) \, I(X_i \leq t) \, I(\hat{\lambda}_j \leq \hat{\lambda}_i) \, w_{i}}{(\sum_{i=1}^{n} I(X_i > t)) (\sum_{i=1}^{n} I(X_i \leq t) \, w_{i})} \nonumber$$$$

It is a measure of how well a model can distinguish subjects who fail by a given time $$t_r \leq t$$ from those that fail in $$t_r > t$$.

• For those of us not familiar with "Ishwaran's formulation" could you please explain what is plotted along the horizontal axis of these plots?
– EdM
Dec 1, 2021 at 18:53
• Hi, EdM. The phrase was wrongly formulated, thanks for pointing that out. My reference was to Ishwaran´s work on RSF (which is the bases for the models implemented in python's Scikit Surv an R's randomforestSRC libraries. The X axis is the time. Dec 1, 2021 at 19:48