  Multiple imputation is a widely used technique to handle missing data in
large observational studies. For variable selection on multiply-imputed
datasets, however, if we conduct selection on each imputed dataset separately,
different sets of important variables may be obtained. MI-LASSO, one of the
most popular solutions to this problem, regards the same variable across all
separate imputed datasets as a group of variables and exploits Group-LASSO to
yield a consistent variable selection across all the multiply-imputed datasets.
In this paper, we extend the MI-LASSO model into Bayesian framework and utilize
five different Bayesian MI-LASSO models to perform variable selection on
multiply-imputed data. These five models consist of three shrinkage priors
based and two discrete mixture prior based approaches. We conduct a simulation
study investigating the practical characteristics of each model across various
settings. We further demonstrate these methods via a case study using the
multiply-imputed data from the University of Michigan Dioxin Exposure Study.
The Python package BMIselect is hosted on Github under an Apache-2.0 license:
https://github.com/zjg540066169/Bmiselect.
