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I'm using logistic regression to evaluate a potential association between exercise levels and whether or not a person develops dementia. I'm using multiple imputation to help fill in (MAR) missing values (specifically, stata's mi impute).

My outcome (dementia: yes/no) is dichotomous, but is constructed using scores from different cognitive tests. For example, someone with an 8/20 or lower is considered to have dementia, while someone with 9/20 or higher is not. The person with 8/20 receives a "1" and the person with 9/20 receives "0" for the dementia outcome variable.

It's a bit more complicated than this, (as there are actually several different scores that are summed to get the total "20", and some people have different dementia score cut-offs due to age/other risk factors) but this is the general idea.

My question is this: should I impute all of the individual test scores that are then summed to get the total out of twenty and then construct the dichotomous dementia outcome after the multiple imputation? Or should I just impute the dichotomous dementia outcome variable?

I've read the other answers about imputing outcomes and it seems that imputing categorical outcome variables can be done/is done. My only concern is that I was told by an instructor that it is not wise to impute a dichotomous variable when it is being constructed from other items that themselves may or may not be missing.

I've tried it both ways and have found the results somewhat differ, so would like to choose the more appropriate method.

Many thanks.

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Imputing the individual test scores first and applying the threshold to make your dichotomous variable after would be the best course because it offers better precision.

The key reason is that most multiple imputation methods will use all the available data in a multivariate dataset to compute each missing value. If you impute on only a single data vector - like your dichotomous variable - then you give up the precision you get from any additional information.

For more detailed discussion about multiple imputation do's and don'ts, see Flexible Imputation of Missing Data by Stef Van Buuren

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  • $\begingroup$ You can of course never know for sure that a MAR assumption holds, but the more data you use, the more plausible it might be that the MAR assumption might hold. I would certainly never believe that it holds when you just have one yes/no at different times. Using the underlying scores also makes it more feasible that the correlations between subscales (and how these might influence missingness) can be taken into account. $\endgroup$
    – Björn
    Dec 22, 2015 at 10:45

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