Survival Analysis Applied when Individuals that "Died" can still Return I'm running an AB Test and using Survival Analysis to estimate the Return Rate to the website.
Each day (in a total of 7 days) I randomly assign 100 users to group A and 100 users to group B and after 7 days I stop the test.
Each day I also check the number of tracked users (only the ones participating in the experiment) who returned to the website.
At the end of the experiment, there will be:


*

*7 cohorts that passed through day 0

*6 cohorts through day 1

*5 cohorts through day 2

*...

*1 cohort through day 6
by Cohort I mean: on the first day of the experiment I assign 100 users to each group and that's my first cohort. On the second day of the experiment I assign another 100 users to each group, and these users are my second cohort, and so on.
As an example, the Return Rate of group A is simply the number of users of group A who returned to the website on day $i$ divided by the number of users that reached that day.
$$ RR_i = \frac{n_i}{N_i}$$


*

*$RR_i$ is the Return Rate on day $i$

*$N_i$ is the number of users that reached day $i$ (if $i = 2$, the number of cohorts that reached that day is 5, if each cohort has 100 users, then $N_2 = 500$)

*$n_i$ the number of users that returned on that day.


When using Survival Analysis, we assume that when an individual die, of course it never comes back. But in my analysis, an user that comes to the website on day 0, can return on day 1 and 2, or return on day 1, 3 and 6, or even return each of the following 7 days.
In that case, can I still use Survival Analysis?


*

*If so, what else do I need to consider in order to still make it valid?

*If not, what better approaches can I use?

 A: If you modeled this with Poisson regression, you would still be able to incorporate the time aspect and not violate the assumptions of the model since the outcome can accommodate multiple hits. You would be able to model event rates (number of events per persons at risk per unit time). Poisson regression is the "other proportional hazards model", the more widely known one be Cox regression. In R you will need to include a strata() term if you have multiple data lines with the same subject ID. (I'm sure other full-featured stats programs will have similar capabilities.)
The UCLA site has a series of worked examples at: https://stats.idre.ucla.edu/r/dae/poisson-regression/
Achim Zeileis,  Christian Kleiber, and  Simon Jackman have a nice tutorial at https://www.jstatsoft.org/article/view/v027i08
The source I learned it from was in Breslow and Day's second of two-volume monograph, "Statistical methods in cancer research. Volume II--The design and analysis of cohort studies". The IARC kindly makes it freely available at: https://publications.iarc.fr/_publications/media/download/3494/fb469ed43c52f0c738915cca6a0f31544b9ed7b6.pdf  The code is unfortunately not in a modern stats language, rather it's in GLIM. I found learning R rather easy after coming to the task from using GLIM. So if you are an R user perhaps the code in that source would still be useful. Certainly its discussion of validity concerns in cohort analysis would still be relevant.
