Analyses of 20 imputed complete datasets, generated by using multivariate normal imputation, 33 provided results that indicated essentially the same conclusions as the complete case analyses reported here.
For longitudinal analyses involving hospital survivors, ten multiply imputated datasets were generated under a multivariate normal model using Markov chain Monte Carlo methods in the SAS function PROC_MI.
We carried out multiple imputation analyses with 5 imputed datasets based on Rubin's multivariate normal model [ 37] to assess potential biases due to missing values in our data.
To assess the performances of the different methods in detection of associations in a similar-sized dataset, we simulated 500 datasets with 500 individuals and 300 covariates, sampled from a multivariate normal distribution (the simulation process is detailed in Additional file 1).
The imputation procedure used an iterative Markov chain Monte Carlo method based on a multivariate normal regression [ 62] and involved replacing each missing value in the dataset with a set of 20 plausible values that represented the uncertainty about the right value to impute [ 61].
While on the left panel, the three species of iris share a same copula, on the right panel, the three species are generated as a multivariate normal with parameters estimated from the three species of iris in the original dataset.
We will therefore draw simulated iris from a multivariate normal distribution with parameters equal to the estimated mean and covariance obtained from the original Iris dataset.
Review of multivariate normal distribution theory.
Multivariate distributions: joint, conditional, and marginal distributions, independence, transformations, Multinomial, Multivariate Normal.
Three different methods for monthly dataset imputation were selected: AMÉLIA II – runs the bootstrap Expectation Maximization algorithm, MICE – runs an algorithm via Multivariate Imputation by Chained Equations and MTSDI – an Expectation Maximization algorithm-based method for imputation of missing values in multivariate normal time series.
