Quantifying explanatory power


I have a continuous predictor and a time-to-event binary outcome in two population defined by their medical history.
My hypothesis is that the predictor is [a much stronger predictor/explains more variance/has more explanatory power] in one of the populations than in the other.
How should I go about quantifying this and testing a null hypothesis of “equal predictive power”?

The interpretation is critical. I need a strong enough message for a reader to be able to say “this predictor really says everything in population A, but is only part of the story in population B”.

Would be grateful for any advice.

Noam Barda

Try methods in Statistically Efficient Ways to Quantify Added Predictive Value of New Measurements | Statistical Thinking