# Multiple endpoints in survival analysis of individual careers

I analyze labour market activities. I measure JD: job duration (time between beginning and ending of employment) and PD: professional duration (the time spent in a specific vocation). My sample is episode based (not individual based), thats important for PD: I measure PD as two subsequent job episodes in the same vocation. PD therefore is greater than or equal to JD by definition. Furthermore I have more data points for JD (every single employment gives a data point) than for PD (for every employee two subsequent employments in the same vocation are merged to one data point).

I am interested in the difference between JD and PD and I want to compare this difference for multiple groups.

Testing JD and separately PD isn't desirable. Suppose group A has a short JD and a slightly longer PD. Group B could then have a long JD but a PD that's only slightly longer than B's JD. What test can be performed to check for a difference of the difference between JD and PD?

Does it makes sense to test for a difference in proportions of JD to PD in groups?

Non-sequitor: what does the rho do in R's survdiff-test and how should I choose rho?

My approach still seems unclear. Here's what I do exactly:

I use a database storing people's id (ID), begin data of an occupation (BEGIN), end date of an occupation (END) and type of occupation (TYPE).

• To gather JD I take BEGIN and END and build different groups using TYPE.
• To receive PD I do the following: For every ID if 2 subsequent employments (e1, e2) have the same TYPE, I merge them to one episode (with BEGIN(e1) and END(e2)). I repeat this step until no more merges are possible (e.g. if there are 3 subsequent employments (e1, e2, e3) of the same TYPE, I end up with one episode (with BEGIN(e1) and END(e3))

Finally, what I try to find out is, if the difference between JD and PD follows a similar pattern for different types or not.

If you want independent time-to-event models, you could calculate a "delta" ID = PD-JD or an interim duration (unemployment possibly, or time in subsequent jobs of similar function). Time-to-new-vocation is a meaningful outcome on its own. In such models, you could adjust for the JD by having it as a covariate/stratum variable in a Cox proportional hazards model. This would allow you to compare people of different job markets with the same duration of employment. So people in the medical field with 5 years experience versus people in the architecture field with 5 years experience would be compared in their rate of re-employment.
Looking at the fraction of JD to PD is possibly a meaningful analysis, though intuitively I don't believe there's any reason to assume that the shorter the time of employment, the shorter the time until finding another capacity.
• thank you for improving my question and for your answer. I think my poor wording lead to a misconception: due to the design of the data, I cannot calculate a ID = PD - JD (at least I cannot do that on an individual base), because my observations are "episode based" not "indivdual based". That means, apart from Surv(PD) >= Surv(JD) the two samples don't have much in common... – Marcel Feb 12 '13 at 19:18
• No, it's the same data source. Let's consider an individual that's an architect for one year, then is unemployed and then is an architect again. For JD that's 2 episodes (each 1 year long). For PD that's just 1 episode (length: 3 years). So I could link the episodes to individuals, still I cannot perform ID = PD - JD as the number of episodes is different. – Marcel Feb 12 '13 at 21:02