How to handle missing data in my situation?

I have two variables that I intend to use for creating prediction models for which I'm unsure how to handle missing values. The reason is that both are separated into multiple columns.

All participants in my data have the same genetic disease, which can be caused by one of two distinct genetic mutations. So I have a binary variable asking if the participant was genotyped, a second column telling if the first genetic mutation is present/absent, and a third telling if the second mutation is present/absent. Since there is no possible overlap between both mutations, if missing values were not a concern, I would simply create a categorical variable that could take two values, either mutation 1 or mutation 2.

The second variable is IQ. I have a binary variable telling if an IQ test was passed and a second one dividing participants who passed an IQ test into three categories (Normal IQ, moderate disability, severe disability). In an ideal world, all my participants would have passed an IQ test, and I would simply use the results from the three categories.

Now, for my possible solutions:

1. Drop those two variables from my models --> Not ideal/possible since they are important predictors

2. Create my categorical variable for the mutation with what I have and use only complete cases for modelling --> Also not ideal as I am already dealing with a dataset that is not as big as I would have hoped.

3. Create an additional category for both, something like "Unknown/unmeasured" --> I'm not sure what the repercussions would be, but I'm guessing it would have a non-negligible impact on the coefficients for those variables on my models.

4. Perform multiple imputations on columns as they are right now --> It does not seem to make sense, some people would at the same time not be tested for IQ and have a value for IQ, same for mutation + some people would end up having both mutations, which is not possible.

5. Create the categories I need, then impute (One column for mutation, which can take values of either mutation 1 or 2, one column for IQ with the three categories) --> It doesn't seem right to modify data like this before imputation, especially to attribute an IQ result for someone when the preceding column said the participant didn't pass an IQ test.

Is there an adequate way to do multiple imputations in this case? If not, is one of the solutions preferable?

As far as I can see, both dichotomous variables (If IQ test was passed and if genotyping was done) are missing at random, while the following variables are directly dependent on the result of the first.

Let's examine the mechanisms of missingness.

In the genetic covariate example, missingness can come about in two ways. Either:

• The genetic marker is missing because the test was not done, or
• The genetic marker could be missing because the test was done and something else happened to prevent the data from being recorded. Maybe a test tube was dropped.

The second example is the ideal example. This is called "missing completely at random". The first example is going to be a real pain. Presumably, there is some reason why the test was not done. If information as to why the patient did not get the test is present elsewhere in your data, then the missingness is "missing at random". You can devise a model to use the information in the data to predict the missingness through a technique called "multiple imputation".

But suppose you don't have that data. Then you have something called "missing not at random". Without any data which could be used to predict the missingness, then we have no real way of imputing the missing information and are subject to bias if we do.

Say that patients did not get the test if they were really sick, and the mutation is associated with being very sick. Then you're going to systematically underestimate the prevalence of the mutation in your sample because only healthy people got the test.

Similar arguments can be made for the IQ variable. You're doing to have to think about why that data is missing, and only you can think about it because you're closest to the problem and the data collected. If you feel your data is missing completely at random or missing at random (terrible names for these phenomena, I know) then you can use a package like {mice} in R to do the imputation.

• Thank you for your answer! I read a lot about multiple imputations but still consider myself a beginner. As I understand, there is no clear way to assess if they are MAR or MNAR. So, while there is no problem with imputing those variables from a statistical point of view, there is still a need to think about the reason why they are missing and the impact of the missingness ? Sep 28, 2022 at 22:58
• @floubert Yes, you've got that right. You can mechanically impute them, no problem. the question is should you. Sep 29, 2022 at 4:03