# Survival Analysis/Frailty Model

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?

Thanks and regards,

• You could try reading-up on non-homogenous Poisson processes, which for example can be trained to model seasonality (e.g. tending to visit at weekends rather than weekdays). Hard to say much more without knowing how your model will be used. – Creosote Sep 5 '15 at 19:30

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).

• Any reference (preferably with example(s)) will be very helpful. – PTDS Sep 3 '15 at 3:09

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.