  Statistical modelling of covariate distributions allows to generate virtual
populations or to impute missing values in a covariate dataset. Covariate
distributions typically have non-Gaussian margins and show nonlinear
correlation structures, which simple multivariate Gaussian distributions fail
to represent. Prominent non-Gaussian frameworks for covariate distribution
modelling are copula-based models and models based on multiple imputation by
chained equations (MICE). While both frameworks have already found applications
in the life sciences, a systematic investigation of their goodness-of-fit to
the theoretical underlying distribution, indicating strengths and weaknesses
under different conditions, is still lacking. To bridge this gap, we thoroughly
evaluated covariate distribution models in terms of Kullback-Leibler divergence
(KL-D), a scale-invariant information-theoretic goodness-of-fit criterion for
distributions. Methodologically, we proposed a new approach to construct
confidence intervals for KL-D by combining nearest neighbour-based KL-D
estimators with subsampling-based uncertainty quantification. In relevant data
sets of different sizes and dimensionalities with both continuous and discrete
covariates, non-Gaussian models showed consistent improvements in KL-D,
compared to simpler Gaussian or scale transform approximations. KL-D estimates
were also robust to the inclusion of latent variables and large fractions of
missing values. While good generalization behaviour to new data could be seen
in copula-based models, MICE shows a trend for overfitting and its performance
should always be evaluated on separate test data. Parametric copula models and
MICE were found to scale much better with the dataset dimension than
nonparametric copula models. These findings corroborate the potential of
non-Gaussian models for modelling realistic life science covariate
distributions.
