I have a large water chemistry dataset where my response variable (radium-226 concentration) has two types of missing data. Sometimes it is left censored, sometimes the value is reported, but most often (>99% of the time) the response is missing apparently at random (MAR). I have a reasonable estimate of the value below which the response variable is left censored. Also there is a high rate of predictor variables missing at random.

I am wondering how to proceed. There are R packages that do Tobit censored regression, like censReg and NADA. There are also R packages like mice and Hmisc / rms that can do MI on MAR data. If I ignore the data where the response variable is MAR, then I loose 99% of the observations, but I could then treat the remaining observations in a survival model. A package like Hmisc & rms can do imputation on my MAR predictor variables.

Are there R packages that can deal with both censoring and MAR?

Resppected authors such as Frank Harrell suggest dropping variables that have more than about 20% MAR prior to MI, so I wonder is it just silly to try to do MI on a response variable when more than 99% of the time it is MAR?

Any thoughts you have would be greatly appreciated. I am a statistics student and newbie at dealing with missing data.

  • $\begingroup$ Can you clarify whether the 99% includes both missing and censored, or whether you have 99% missing and some of that remaining 1% is censored? $\endgroup$ Jun 18, 2021 at 14:31
  • $\begingroup$ Thanks for the response. Out of about 85,000 records in the USGS database of produced water analyses from oil and gas wells, about 250 have reported radium-226 concentrations, 250 are left censored and reported as zero, and the remainder are missing apparently at random. $\endgroup$
    – Rick H
    Jun 18, 2021 at 17:42
  • $\begingroup$ When you saying MAR, do you mean missing completely at random (MCAR)? If not, how do you know it’s MAR? $\endgroup$
    – astel
    Jun 19, 2021 at 8:26

1 Answer 1


I think that's unfortunately too much missingness to adjust for. I'd recommend doing a complete case analysis on the observed and censored values. Even if MAR is plausible, which is impossible to tell with that much missing, the analysis would rely far too much on imputed values instead of real ones.

If you have other predictors that are nearly fully observed, say location or date, you could perform hypothesis tests to see how different the complete cases are from the overall dataset. But even if they are similar you'll still have trouble generalizing from the complete cases to the overall population.


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