How to model discretised values of a continuous variable?

Question

I have some measurements--tissue swelling in response to an injury--with limited precision (mm). Thus, although the underlying phenomenon is continuous, my values are discrete. The values range between 0 and 20 mm. Many of these discretised values are zero (i.e. no measurable tissue swelling, although it might be present at a sub-mm scale).

Is it legitimate to treat the measurements as discrete and model them e.g. by the Poisson distribution, or should I stick to a continuous one? Which one makes sense for a zero-rich dataset? Maybe exponential?

Answer 1

One obvious solution is to treat this as interval censored data. I.e. when you record 1 mm, you might believe that this really means the true value lies between 0.5 and 1.5 mm (similarly, 0 means 0 to 0.5 mm). That's relatively straightforward. Whether that really makes any difference to the results of any analyses you might do, is hard to predict.

Additionally, you might want to add zero-inflation, if you think there's truly zeros in your data (because many methods for interval censoring would actually assume that you basically never have an exact zero). However, this may not make too much of a difference in your analyses and the model may have trouble figuring out whether patients are in (0, 0.5) vs. exact 0 / would struggle to estimate the related parameters, unless you have something that would give the model information about how to distinguish the cases/which cases are which.