Engine failures occur for vastly different reasons and operating conditions.
A whole bunch of tired turbine parts tend to happen at high power.
A bunch of compressor blade failures happen in early climb
Most of your what-was-that loud explosions happen at high power (takeoff/ early climb) due to part failures.
In the early days of jets (pre 1980s designs) there were many engine stall/surge event noises, without part failures, at power change excursions (Bodies etc.)
Even today if you have a very tired engine compressor (open clearances erroded blades) you will excacerbate the loss in stability just by accel or decel lag between the rotors.
But no I never noticed an overall major standout in flight regime statistics for run-of-the-mill SDR reports for engines.