I am facing the situation that I have different data sources that in principle it makes sense to combine. The outcome (independent) variable is defined the same way, but the (likely) most important predictor was recorded in different ways. Sometimes as a numbee (0, 1, 2, ...), sometimes as 0 vs. >=1 and sometimes bucketed (e.g. 0, 1 to 2, 3 to 5 and >=5). I could simply create a 0/>=1 variable, but that would be throwing away information. 

It feels like someone must have thought about this one before... The only thing I managed to think of was a joint model for both outcomes, which would allow for a likelihood of the observed covariance to be right - or interval censored.

It feels like there must be quite a literature on this topic, but I failed to find a good review paper/obvious entry point to the literature. Perhaps "censored covariate" is not the best search term. Any recommendations or pointers to useful literature would be most welcome.