When is it ok to MI Data with MNAR predictor without further instructions

Question

I have a data set with predictors that are mostly MAR(supposedly), however I do also have one that is likely to be MNAR in the sense that the missing of that predictor depends on an unobserved variable(the data for that variable is not collected at all). I'm wondering if there is a condition in which a straight forward imputation would make sense. eg. if none of the other predictors and response depends on that unobserved variable?

Edit: The MNAR predictor is a measurement of the concentration of certain chemicals in the peritoneal fluid. The missingness can be attributed to the absence of available fluid to examine(wether it's because of the failure to extract it or there just aren't enough of it to extract). I don't have the stats eg. the volume of said fluid.

Answer 1

One nice statement of missingness at random (MAR) is "given the observed data, [missingness] does not depend on the unobserved data." Let's apply that principle to this case.

From your question it seems that absent information on the concentration of a chemical in peritoneal fluid is typically due to lack of sufficient fluid to extract, which I will take to be due to biologic or clinical factors at least to start. That lack of sufficient fluid is itself an observation, which you could code as 0 = insufficient, 1 = sufficient. (It might even be that the availability of peritoneal fluid is itself a predictor, if it's related to the clinical situation you are studying.) With sufficiency of fluid included as observed data in the model, the missingness of concentration information no longer depends on unobserved data. You then would proceed to code concentration as 0 for the missing cases, and interpret the coefficients as on this page for a similar situation with loan amounts.

Note that this approach depends on your knowing that unavailability of fluid was the reason for missingness. If some missing data were due to technical measurement problems when fluid was available, those concentrations should be imputed.

If data are missing because someone decided not to collect the fluid or failed to perform the analysis despite having fluid, then it might still be reasonable to impute the availability of fluid (in the first case) and concentrations (in both cases) unless you have reason to suspect that some unobserved mechanism related to your study was responsible for such decisions.

The difficulty will be if you don't know whether it is biologic limitations on peritoneal fluid volume, a decision not to take any fluid or perform the assay, or technical errors that led to the missingess.