So actually air density has much less of an effect on turbines than piston aircraft. Temperature is the most critical factor. At low altitude the gearbox is limiting (usually the MAUM) then temperature kicks in (starting ambient temperature plus air has to be compressed more so gets hotter still). Then finally at really high altitude, the dominant factor becomes the sheer lack of air and the compressor maximum speed becomes the limiting factor. You can see these step changes in a typical power available chart in a military flight manual - it's slightly less obvious in the civilian presentation. OEI you are generally always temperature limited when at altitude due to having insufficient ceiling to get to the altitudes where raw air density becomes a problem.
Thank you Mr Shawn Coyle for helping me in researching that nugget with your excellent text books, may you rest in peace sir.