I have a dataset in which I have predicted risk probabilities from a survival model. The probability predictions were made at two different times for each observation - similar to a repeated measures outcome. I want to do a test of the mean to see if the predicted values change between timepoints.
Typically, I would used a paired t-test, but in this case the mean and the variance of the measurement are not independent due to being predicted risk probabilities from a survival analysis. The variance at the extreme ends of probability predictions is smaller than risk probabilities in the center - essentially a non-constant variance dependent upon where on the probability scale the measurement is located, which violates the t-test assumption that the mean and variance are independent.
What would be a good alternative to the paired t-test in this situation? One thought I had (after making this post originally) was to use a Wilcoxon Rank Sum on the differences. Being rank based, it is distribution free but certainly less efficient.