Is Repurchase period in days a count variable?

Question

So I am doing a project where the response variable is the number of days in which a product is rebought. Explanatory variables are the weight of the product, serving size etc.

So basically I am predicting the number of days in which customers will likely rebuy, given the product weight, and serving size. All products are of the same type, so for example all products are from the bath bombs category.

I fitted all the regression models that I could've thought of, and Zero Inflated Negative Binomial fit the best (and a very good fit at that), because there was an excess of zero data points. So I came to the conclusion that the number of days is a count variable, so it makes sense.

I showed my work to a subject matter expert in statistics, and he stopped me midway to ask why did I fit a regression model. Why not survival analysis?

I thought the 'number of something' is a count variable, and the model was also a great fit. Is this a case of 'It does not make sense statistically, but if it works, it works' ?

Are there zero inflated survival analysis techniques?

Or are there cases where a number of days to an event act like count variables?

Answer 1

What do you do, if you are still waiting for some customers? You know it's a number larger than the current days you've waited, but not how much larger. "Censoring"/survival analysis gives you a way of dealing with that by using that information assuming some underlying distribution. The assumed underlying distribution can be many things including various continuous ones (you might treat day = interval censored time that falls within the day), discrete distributions like the one you used and even semi-parametric ones. There's extensions to things like zero inflation or "cure fractions" (= in this case people that never re-purchase). If you instead subset to only those where you've already observed a repurchase, you are severely biasing your estimates (and at the time you are making a prediction, you don't really know that the customer will repurchase).