survival analysis - concerns about duration times


I'm very much a beginner at survival analysis - i know the basics, but I still get a bit lost when it comes to details.

I am researching the survival of authoritarian regimes (so not countries) under different conditions (let's call them Y). My data includes information on all regimes between 1950 and 2012. Additionally, regimes that are older than 1950 have the original start date recorded. Because of that, I have two duration variables, one which counts years survived since 1950 (A), and one which counts years survived since inception of the regime (B).

My question is: which one do I use? I have no information on Y before 1950, so if I use B (a more accurate duration variable) will that not produce bias estimates? I cannot determine anything about Y at all and whether it contributed to the regime having survived up until 1950.

On the other hand, if I use A, I am clearly ignoring the fact that some regimes have been in place for tens (or even hundeds) of years prior to 1950. That produces biased estimates as well.

Any suggestions?

Thanks so much in advance!

Either way you do it, you will have some additional issues to deal with. If you use A then your data are left censored as well as right censored. If you use B then you (I presume) are missing data on countries that failed before 1950.

The problem of left censoring is probably easier to deal with - it's a well known one in survival analysis.