Multiple imputation methods for missing multilevel ordinal outcomes

Multiple imputation (MI) is an established technique for handling missing data in observational studies. Joint modelling (JM) and fully conditional specification (FCS) are commonly used methods for imputing multilevel data. However, MI methods for multilevel ordinal outcome variables have not been well studied, especially when cluster size is informative on the outcome. The purpose of this study is to describe and compare different MI strategies for dealing with multilevel ordinal outcomes when informative cluster size (ICS) exists.

We conducted comprehensive Monte Carlo simulation studies to compare the performance of five strategies: complete case analysis (CCA), FCS, FCS+CS (including cluster size (CS) in the imputation model), JM, and JM+CS under various scenarios. We evaluated their performance using a proportional odds logistic regression model estimated with cluster weighted generalized estimating equations (CWGEE).

The simulation results showed that including CS in the imputation model can significantly improve estimation accuracy when ICS exists. FCS provided more accurate and robust estimation than JM, followed by CCA for multilevel ordinal outcomes. We further applied these strategies to a real dental study to assess the association between metabolic syndrome and clinical attachment loss scores. The results based on FCS + CS indicated that the power of the analysis would increase after carrying out the appropriate MI strategy.

MI is an effective tool to increase the accuracy and power of the downstream statistical analysis for missing ordinal outcomes. FCS slightly outperforms JM when imputing multilevel ordinal outcomes. When there is plausible ICS, we recommend including CS in the imputation phase.