You can't really compare EK with Colgan because few if any EK Pilots are allowed to "commute" and you probably get paid 10 times more than a Colgan Pilot so can afford housing etc. Best bit of advice when sick is to call / email your Duty Pilot / Fleet Manager as a back up.
I've never worked in an airline which has a pilot sick record, most levels are low because of your professionalism /positive attitude etc. You will find however they are managing the few and as always the majority have to suffer