  Multiple imputation (MI) is an established technique to handle missing data
in observational studies. Joint modeling (JM) and fully conditional
specification (FCS) are commonly used methods for imputing multilevel clustered
data. However, MI approaches for ordinal clustered outcome variables have not
been well studied, especially when there is informative cluster size (ICS). The
purpose of this study is to describe different imputation and analysis
strategies for the multilevel ordinal outcome when ICS exists. We conducted
comprehensive Monte Carlo simulation studies to compare five different methods:
complete case analysis (CCA), FCS, FCS+CS (include cluster size (CS) when
performing the imputation), JM, and JM+CS under different scenarios. We
evaluated their performances using an proportional odds logistic regression
model estimated with cluster weighted generalized estimating equations (CWGEE).
The simulation results show that including cluster size in imputation can
significantly improve imputation accuracy when ICS exists. FCS provides more
accurate and robust estimation than JM, followed by CCA for multilevel ordinal
outcomes. We further applied those methods to a real dental study.
