Can you use Cox proportional hazards model when there is no baseline group?

Question

I have a the following scenario.

A group of people will be given a coupon. Create a model to estimate how long it will take them (in days i.e. discrete count not continuous) to use the coupon based on a variety of personal characteristics.

I was thinking I could use Poisson regression, because we have the count of how many days from receiving the coupon to using it, but there is censoring because some people do not ever use the coupon.

I have thought perhaps I could use the Cox proportional hazards model, but from what I am reading you need a baseline group and treatment groups. Is that correct?

In my scenario there is no baseline group to compare to. We are not comparing people who didn't receive the coupon to people who did. We are only looking at people who did receive the coupon.

Can I still use the Cox proportional hazard model if there is no baseline group, if not can someone make a recommendation please. Thank you for your help!

Answer 1

As you have covariates to evaluate, a Cox model is certainly OK here. The software will choose some combination of covariate values to use as a baseline reference, and then evaluate the "hazards" of having the event for other values of the covariates, relative to that reference set.

If you only have a handful of possible event times, you might be better off using a discrete-time survival model. Cox models assume continuous time, and need to make some adjustments with lots of tied event times. A discrete-time survival model is a binomial regression on a carefully constructed data set, with one row for each individual at risk at each possible event time. This page outlines the idea and provides some links for further reference.