I see your point. My goal would actually use these features for confounder adjustment, and I am afraid that splitting the analysis into two (or more) models might lead to loss of power.

Dear marquisdecarabas, I will look into more detail in the Heckman-type corrections. I am adding also in the edited version of my question the specifics you required. Briefly, I have baseline data (time 1), stress test data (time 2 - but can be considered equivalent to time 1), and then events (time 3). Of course missingness is not at random, as patients without the stress test are those who are too frail or have specific ECG abnormalities. Finally, the stress test is very informative, if performed, with 4 or 5 quantitative variables generated, which would really be a pity to lose.