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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.

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  • $\begingroup$ Please provide some more details about why "the data for that variable is not collected at all." There's an example on this page for a situation where a loan amount is a predictor but not all cases involved loans. In that case, you use a dummy variable to deal with the loan/no-loan possibility and include 0 for the value of the loan in no-loan cases; no imputation. If your situation isn't so straightforward, please provide more information about your particular application in an edited version of this question. $\endgroup$
    – EdM
    May 14, 2016 at 15:09

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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.

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  • $\begingroup$ Ultimately I do not know why they are missing and only have guesses since I'm not the one collecting the data. Guess I just have to make some tough decisions on which approach I go with. Thanks for the response, it's just what I was looking for. $\endgroup$
    – ChuckP
    May 14, 2016 at 16:24
  • $\begingroup$ Some serious discussion with those collecting the data might help clarify what's going on, or at least might motivate them to annotate future data better. There are few things more frustrating in clinical data analysis than not knowing why data are missing when there was every opportunity for including notations about missingness during data collection. $\endgroup$
    – EdM
    May 14, 2016 at 16:33

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