Improved rounding methods for binary and ordinal variables under multivariate normal imputation

[Truncated] Missing data are common in epidemiological studies. Multivariate normal imputa- tion (MVNI) is a popular method of handling missing data that imputes missing values assuming a multivariate normal distribution. This presents a dilemma when imputing categorical variables as these are not normally distributed. Should the continuous imputations be rounded, and if so, which rounding method should be used?

The objective of this study is to evaluate and compare existing methods and develop new methods of rounding categorical variables under MVNI. We focus on missingness in covariates rather than outcome variables. This is because MVNI generally has little or no bene t over complete case analysis if missingness is in an outcome variable only.

A number of different rounding methods have been proposed for binary variables, including simple rounding, adaptive rounding and calibration. However, no studies to date have compared adaptive rounding with calibration. We performed a large simulation study in Stata to compare the above rounding methods with unrounded MVNI, and with a new method that we developed called proportional rounding. Proportional rounding produced similar results to adaptive rounding and calibration but was faster and easier to implement.

To date, several rounding methods have been proposed for ordinal variables. Distance-based rounding (DBR) and projected distance-based rounding (PDBR) are indicator-based methods, while crude rounding, calibration and mean indicator- based rounding (MIBR) are continuous methods. Previous studies have demon- strated the inadequacy of DBR, PDBR and crude rounding for rounding categorical variables with up to seven categories. Calibration and MIBR perform well in some settings but they are two-stage methods that are time-consuming to implement, par- ticularly for large data sets. An alternative method of imputing ordinal variables is fully conditional speci cation (FCS). There have been no studies to date comparing FCS with MVNI-based rounding methods for ordinal exposure variables.