Multiple imputation of binary endpoint using underlying continuous variable

I have a response variable (Yes/No) by visit with some missing values. I am considering imputing the underlying continuous variable in SAS using proc MI. After this process, I will have, let's say, M imputed datasets. How should I combine them into one dataset?

In other words, how can I apply Rubin's rule if I need a simple summary at the end, such as the count of responders/non-responders at each visit for each treatment group? Or should Rubin's rule be used only when we need to compare treatments with, say, a relative risk/risk difference/odds ratio?

• (Note: imputation, imputed, and imputing are not typos... (in this context) - "5. (transitive, statistics) To replace missing data with substituted values.". See also Imputation (statistics).) Nov 11, 2023 at 2:39
• You ask: "I will have, let's say, M imputed datasets. How should I combine them into one dataset?" You do not combine the multiple datasets into one. You use Rubin's rules to combine the results of the same modeling approach on the multiple datasets. Stef van Buuren's Flexible Imputation of Missing Data is an excellent and freely available resource, starting from basic principles and working up from there.
– EdM
Nov 11, 2023 at 16:05
• @EdM thanks for the book! is my understanding that multiple imputation technique and Rubin's rule are for comparison of treatments only? What should I do when I have single-arm data with some missing data? Also what is still not clear for me which steps shall I follow, i.e. first algorithm: 1. impute underlying continuous endpoint; 2. dichotomize to have binary; 3. use Rubin's rule to combine the results; or second algorithm: 1. impute binary endpoint; 2. use Rubin's rule to combine the results
– Kate
Nov 13, 2023 at 12:37
• @Kate Please register &/or merge your accounts (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question.
– Sycorax
Nov 13, 2023 at 14:10
• You can use Rubin's rules for many types of comparisons. In principle, you can compare (imputed) binary outcomes as a function of treatment-group membership, modeled for example with logistic regression. In the log-odds scale of that model, Rubin's rules hold and you could compare log-odds/probabilities of the outcome among groups. I'm worried that your binary outcome, however, seems to come from dichotomizing a continuous variable. That's not usually wise. The discussion on this page applies to outcomes as well as to predictor variables.
– EdM
Nov 13, 2023 at 14:51

PROC FREQ provides an asymptotic standard error for proportions ($$\sqrt{\hat p(1-\hat p)/n}$$) which you can combine along with the proportion estimate using PROC MIANALYZE. This might be acceptable for larger samples with proportions that are not close to the boundaries (0 or 1).