Is it ever okay to drop missing observations? I have a dataset that looks at immigration applications and visa acceptances (granting of visas).  The rates are calculated for "accepted" and "rejected" of visa applications. 
However, the dataset also has values for cases that were closed. Normally this is when the immigrant either stopped showing up to appointments, migrated elsewhere, or died.  Because these numbers are not used when the rates are calculated, the rates often show up as missing (because the cases were neither accepted nor rejected).
That being said, if the only cases for that year were "otherwise closed," will it ever be okay to drop these observations? Part of the problem that I'm having is that random years in the dataset will be dropped, because the only decisions for that year were closed.
The otherwise closed cases are very arbitrary, and as I mentioned, are most probably cases where the immigrant migrated somewhere else, and probably just used the first country as a temporary place of transit.  The data does not specifically say why the immigrants left, why they were closed, etc. I'm not really sure how to deal with these missing values. I do not believe that standard imputation methods would work here, due to the rate calculations (but I could be wrong).
 A: The important distinction is in your case not the distinction between MCAR, MAR, and NMAR, but between real missing values and mechanical missing values. Real missing values are values that exist, but for some reason weren't recorded. Mechanical missing values don't exist, but the rectangular structure of a dataset forces us to give it a value, e.g. pregnancy status if your dataset also includes males. Imputation techniques are designed for real missing values. Your example is a case of mechanical missing values; the decision has not been made, so its value does not exist. If a substantial portion of migrants move on then that is an important feature of the migration process, and imputing those values hides that feature. 
A: It is clear a mix of at least 2 different missingness processes.


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*People that die from procedure unrelated causes/abandon/etc. due to reasons other than the likely outcome of the procedure. Here some imputation under MAR makes sense (if you can clearly identify the cases).

*People that give up/withdraw/drop-out due to not fulfilling some rules and/or thinking they are unlikely to be successful or that it is too much hassle.  Here it depends on whether you can from the data you have assess their chances if they had continued. If you can a MAR assumption is fine, otherwise you have a difficult MNAR situation. 


What to do about MNAR is difficult. Assuming such cases had no success may be a bit extreme (or very appropriate,  after all they did not succeed). Or impute under MAR and look at making these cases less successful until you hit 0% and contemplate that range of values.
