Survival Analysis/Frailty Model

Question

I am trying to build a probability model for the following situation:

I have a very large dataset, whose rows are users and columns are the features.

All the users visit a particular store X (once or more) over a period of 14 days. We have an indicator variable (column), which denotes the store visits for each user.

My goal is to compute the probability distribution of the inter-visit intervals for each user/group of users.

I initially thought of “Survival Analysis”, where “visiting store X” will be equivalent to a “death” event. However, then I realized that there might be several such “death” events for each user.

Hence my confusion: Should this be a “Survival Analysis” type of problem? Or, is this a “Frailty Model” problem? Or, something else?

Please advise.

Thanks and regards,

Answer 1

This seems like a recurrent events situation. Some possible modelling approaches include negative binomial regression. In that case the between visit waiting times follow an exponential distribution for each patient (and a gamma distribution across patients).

Answer 2

It depends on what you want to model. Survival analysis tools would be useful if:

1. You know the inter-event times (it is not clear if you have just the number of visits / 14 days or if you have the times of these visits). In other words, the structure of the data should be put into a (Tstart, Tstop, status) for Survival tools.

2. If the data is in the format I specified at (1), then you can use several models, including the Andersen-Gill or frailty models for recurrent events. This can be done in R with coxph function in the survival package.

Good literature for recurrent events data can be found in "The Statistical Analysis of Recurrent Events" by Cook & Lawless, where you can find what models to use for what situation.

If you do not have the exact times of the events, then a Poisson / Negative binomial generalized linear model might be appropriate, depending on your data.