# Sensitivity Analysis for Missing Not at Random (MNAR) data

I currently have a dataset which contains variables with different degrees of missingingness. One of the key variables for my analysis has about 12% of the values Missing Not at Random (MNAR).

From previous research I have done, I gather that most current MI methods assume a MAR mechanism, but could still be useful in MNAR scenarios. The worst possible solution to dealing with MNAR data is still a complete case analysis.

I've heard that you can deal with MNAR by using Pattern Mixture Models and Selection Models, but I do not have any experience with using these in R (which is the software I usually use for analysis). Alternatively, I have seen that the mice package has a method called mice.impute.ri which can be used with 'non-ignorable data'. I also saw that there is an older package, SensMice (from 2011), which performs sensitivity analysis after the mice imputation has already been done. However, it no longer seems to be compatible with my version of Rstudio and there doesn't seem to be much recent word on this package.

Does anyone have practical advice on how I can conduct my imputation for this variable? It is preferable for advice that relates to specific R packages that might be useful. Otherwise, theoretical advice or steps to take in the imputation process are also appreciated.

• Given that this question is not asking for R code & states, "Does anyone have practical advice on how I can conduct my imputation for this variable? ... theoretical advice or steps to take in the imputation process are also appreciated", I think this should be considered on topic here. Jun 29, 2016 at 17:52
• That is, indeed, correct. I do not require any R code. Pointers to specific packages and R code are a bonus for me, but theoretical advice is first and foremost what I need.
– RNB
Jun 30, 2016 at 8:47

I'm currently dealing with that same problem too. I have a data set with 70 kovariables and a lot of them have missing values. Most of them are definitely MNAR.

One great paper i found is this one. http://journals.lww.com/epidem/Fulltext/2011/03000/Sensitivity_Analysis_When_Data_Are_Missing.25.aspx

they also perform a sensitivy analalysis witn SensMice and have great examples.

Did you made any progress in your analysis yet? I am still struggling with the interpretation of a sensitivity analysis with mice.

I mean it's a lot of work to do a sensitivity analysis for one variable, and i have 70 variables....

Can i just ask one thing just for clarification? You do a sensitivity analysis because you want to see what happens if you slowly drift from the MAR assumption to MNAR right? So you change step by step the parameters from the assumpted distribution... But in the end you won't be able to find the "best" parameters, you just know at what value you must be careful when you interprate the parameters of your prediction model ( since you used MAR assumption). In the end you still use MICE under MAR assumption....

I'm struggling with this topic for a while now, and I'm really not sure if i understood it right....Maybe you can help me out?

• Thanks for the reference. I'm right with you...I'm not entirely sure how to go about this, but I think your interpretation about the purpose of sensitivity analysis seems correct. The way I look at it is, "we found these results, and even though our data are biased (MNAR), our sensitivity analysis— which biases the results the way we think they are biased in real life—shows that our results don't change". For now, i've taken a step back from this and i'm currently focusing on getting the rest of the analysis correct. But when I find some more insight, i'll be back to let you know.
– RNB
Jul 6, 2016 at 11:28