Methods for censored covariates 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. 
 A: You may be contended by creating a consistent set of features from all the datasets. 
That is, from initial merged dataset
  x_censored  x_full
0       None     0.0
1       None     1.0
2       None     2.0
3       None     3.0
4          0     NaN
5          0     NaN
6         >0     NaN
7         >0     NaN

you can get a new consistent dataset 
   x>0  x_full_obs  is_censored
0    0         0.0            0
1    1         1.0            0
2    1         2.0            0
3    1         3.0            0
4    0         0.0            1
5    0         0.0            1
6    1         0.0            1
7    1         0.0            1

This dataset will preserve all the available information and make them ready for fitting models:


*

*The first column keeps all the information from the bucketed observations and also from full observations, converted to the bucketed form.

*The second column keeps all the information from full observations, and zeros, if observations were bucketed. I could use any number instead of 0.

*The third column is a dummy variable telling whether 0 in the first column is a genuine zero or a substitute for no information.


I used the folliwing Python code for this example:
# making initial dataset
import pandas as pd
data_in = pd.DataFrame({'x_full': [0,1,2,3,None,None,None,None], 
                       'x_censored':[None,None,None,None,'0', '0', '>0', '>0']})
print(data_in)
# preprocessing it 
data_out = pd.DataFrame(index=data_in.index)
data_out['x>0'] = ((data_in['x_full'] > 0) | (data_in['x_censored']=='>0')).astype(int)
data_out['x_full_obs'] = data_in['x_full'].fillna(0)
data_out['is_censored'] = data_in['x_full'].isnull().astype(int)
print(data_out)

A: I can only recall anne whitehead's book on meta-analysis ie chapter 9, section 9.3 on 'different rating scales or methods of assessment across trials'. There is likely some sound, practical advice in there: anne whitehead's book
A: I feel the first thing is to determine the data type of your predictors or combine your predictor into one data type. If your predictors include censored one, you may refer to: Multiple Imputation for M-Regression With Censored Covariates (JASA, 2012). This paper purposes a semiparameter approach, I believe this is the most updated one in this line of literature. However, other prior methods mentioned in this paper might enough suit your purpose. 
Hope this helps.
