Table 3.

Multivariate imputation methods and their advantages and disadvantages for Use Case 1, the multivariate descriptor of health.

Method	Description	Advantages	Disadvantages
Multivariate Imputation by Chained Equations (MICE)43	A multiple imputation method using a set of iterative regression models.	Continuous data handling Regressors can also be incomplete Widely used and accepted	Longitudinal data can be a problem Specification of conditional models which may be difficult to know a priori
Nearest Neighbor (NN) estimation	A supervised pattern recognition method based on the distance to each pair of observations based on non-missing variables and imputing based on a weighted mean	Continuous data handling May outperform MICE when transformed data are slightly skewed Consistent with Euclidean distance mp-QIB function Requires only one non-missing value Several modifications and versions to accommodate missingness patterns	Requires specification of a tuning parameter that can have a large effect on the results
Random Forest (RF)44	A sequential, machine learning imputation process that predicts missing data from a training set consisting of observed data	Robust / Non-parametric Good performance in high dimensional QIBs Handles non-linear relationships	Training on observed data Can be severely biased44
Multivariate Normal Imputation (MVNI)45,46	An iterative process that imputes missing data from multivariate normal distribution parameters using an expectation-maximization algorithm.	Performance equal to MICE when data are multivariate normal and no missing patterns Assumption of multivariate normal is given for this Use Case Robust to distribution misspecification	Performance may be degraded for misspecification of multivariate normal data
Selection Model:	Joint distribution of data Y and missingness indicator M is partititioned into f(M,Y|θ, ψ) = f(Y|θ)f(M|Y, ψ).	Under MAR, inference can be based on the likelihood ignoring the missing data mechanism, that is, on f(Yobs|θ) where Yobs are the observed data.	May not be clinically as easily understood as a pattern mixture model because distribution of data not stratified by whether it is missing or not.
Pattern Mixture Model:.	Joint distribution of data Y and missingness indicator M is partititioned into f(M,Y|ξ,ω) = f(Y|M,ξ)f(M|ω)	PMM can be useful for modeling the distribution of data missing not at random (MNAR).	Not as well understood as selection models.
Bayesian inference:	Likelihood given observed data is augmented with draws of missing data from their full conditional posterior predictive distribution given observed data and a sample of the parameter values from their full conditional distribution	Data augmentation simplifies the likelihood and thus the Gibbs sampler or other Monte Carlo Markov Chain algorithm for computing the joint posterior distribution.	Unfamiliarity of Bayesian inference; modeling is required, in particular specification of the prior distribution.
Bootstrap imputation47–49	Methods for bootstrapping after multiple imputation or imputation following bootstrap.	Principled, non-parametric approach for incorporating missing observation uncertainty into analysis.	Implementation varies