# Time to Event modeling, fixed but different durations

I am looking at probability of an event ($E$) for a number of customers. Each customer qualifies for the analysis through a qualifying Action ($A$), and has a finite Duration ($D$) to complete Event. There are a number of interim actions that should have an effect on reaching the Event. Unlike the time-to-event modeling I've done before, the Duration is known ahead of time, but is different for every customer. That is, customer 1 may have a duration of 3 months from their qualifying Action; whereas customer 2 may have a duration of 3 weeks. The duration is always known at the time of the qualifying Action.

Consider an advance car rental booking. Making the reservation is the qualifying Action. The Event of interest is whether the customer completes a full online profile. The Duration is the time period between contract & pickup. Interim actions might include receiving an email from the agency, calling into a help desk, starting the profile.

I think that incorporating duration is important because a customer booking 1 day in advance might (should) have a different propensity to complete an online profile than one who books 6 months in advance.

My instinct is to transform the duration to a proportion of the finite duration. Concretely, qualifying Action is time 0 and everyone has a duration of 100. But I've not seen that actually done in any of my literature review, and it feels like this may lose important information.

• It seems to me you'd only be losing important information if the probability of E varied with the duration and you were going to model it as a function of duration. Explaining why you even care about duration might help... – jbowman Oct 21 '13 at 0:10
• Thank you, jbowman. I have edited the question to include a fictitious use case, and an explanation why I think duration is important. – Amw 5G Oct 21 '13 at 13:07