How to interpret time-varying AUC for Survival Analysis?

Question

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!

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Edit for clarification:

The cumulative/dynamic AUC is defined by Lambert and Chevret as: \begin{equation} 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 \end{equation}

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 $t_r > t$.

Answer 1

The Weibull model is unique in that it satisfies both the accelerated failure time assumption (multiplicative survival curves) as well as the proportional hazards assumption (multiplicative hazard curves). This should explain why the difference in performance between these models is essentially indiscernible. Can you elaborate on the x-axis in each of your plots? Is this the number of subjects or events in the model? If so then it should not be surprising that a model based on more events fits better than a model based on fewer events. If this is not the correct interpretation of the x-axis let me know.