I am dealing with survey data from firms to conduct survival analysis. I am going to estimate with Kaplan - Meier and a Cox Regression. I face rigth censored data as usual but I have to deal with the different starting operation year of each firm.
The survey covers 2006 - 2015.
Some firms start operations on 2006 and survive until end or close before they get censored. But then some others starts on 2007, 2008 or even 2014.
An easy way to deal with would be to just consider firms that started on 2006 and followed them until 2015. But then I would lose 80% of data.
The literature I says it shouldnt be a problem if I take in consideration the less exposed time to risk. As happens with medical survival analysis when you have patients information. I wonder if I should also control in my model the effect of the year they started operations. Or that wouldn´t be rigth at all.
Thanks in advance!