I am analysizing data from a clinical trial.
I used multiple imputation to impute the (binary) outcome variable, which is the only variable with missing data.
All of the covariates are categorical and I am encountering the problem of complete separation, therefore I am using the %FL macro in SAS (which is based on Profile Penalised Likelihood - http://www.meduniwien.ac.at/user/georg.heinze/techreps/tr2_2004.pdf) to obtain estimates, confidence intervals and Likelihood Ratio Tests (as Wald test is not an option as stated here, for example: https://statisticalhorizons.com/wp-content/uploads/Allison.StatComp.pdf at 9.6.1).
Now, I would like to pool the LRT statistics (or their resulting p-values) to obtain a pooled p-value, given all of my imputed datasets.
Now, let's assume Stef van Buuren's @stefvanbuuren.nl notation for a while (https://stefvanbuuren.name/fimd/sec-multiparameter.html):
I assume D1 would not be an option, since I am not dealing with Wald tests but with (univariate) Profile Penalised Likelihood Ratio Tests
For the same reason, D2 would not be an option, and not even Eekhout's median p-value (https://scholar.google.com/citations?view_op=view_citation&hl=en&user=Xkpbc1AAAAAJ&cstart=20&pagesize=80&sortby=pubdate&citation_for_view=Xkpbc1AAAAAJ:aqlVkmm33-oC) nor Licht's transfromation of p-values (https://d-nb.info/101104966x/34) would be appropriate, as their solutions are based on Wald tests.
D3 would fit my case, however, since I am not sure if this would be good enough, since I am using Profile Penalized Likelihood and the fact that I am using a Macro to get the result make it difficult to calculate D3 constrained to the average parameter estimates.
Therefore, my question is the following: how can I combine Profile Penalised LRT Statistics in Multiple Imputation?
I would appreciate any kind of hint!
