I have a dataset where the subjects are job contracts. It spans from the 80s to 2019. Each contract has a start of contract and end of contract date, unless they were still active in 2019 in which case their end of contract date is "2099". I want to use survival analysis for the duration of contracts during different time periods for the contracts: I want to take the duration of contracts during the time period 2004-2008 and then during the time period 2014-2018. Thus, the event would be end of contract.
Is this feasible? If it is a special case of survival analysis, are there any resources I can read on how to proceed, or is it considered just a regular survival analysis and should just follow standard procedure?
My concern is that some job contracts span the two time periods. Does that make any difference? Are data censored only if contracts last longer than 2018, or is there any way I should take into account data as censored for the first time period if they last longer than 2008 (for example, a contract that lasted from 2005 to 2010, as I would only observe its duration from 2005 to 2008)?
Thanks a lot for the help.