MvLognCorrEst: an R package for sampling from multivariate lognormal distributions and estimating correlations from uncomplete correlation matrix. (June 2023) - Carlo, Alessandro De; Tosca, Elena Maria; Melillo, Nicola; Magni, Paolo
Highlights: Pharmacometrics leverages Modeling and Simulations to support drug development. Considering correlations between model parameters enhances the reliability of simulation results. Extracting samples of correlated lognormally distributed model parameter can be tough. Correlation matrices can have some unknown values which should be properly managed. The developed mvLognCorrest R package allows to easily address all these issues. Abstract: Background and Objective: Pharmacometrics (PMX) is a quantitative discipline which supports decision-making processes in all stages of drug development. PMX leverages Modeling and Simulations (M&S), which represents a powerful tool to characterize and predict the behavior and the effect of a drug. M&S-based methods, such as Sensitivity Analysis (SA) and Global Sensitivity Analysis (GSA), are gaining interest in PMX as they allow the evaluation of model-informed inference quality. Simulations should be correctly designed to obtain reliable results. Neglecting correlations between model parameters can significantly alter the results of simulations. However, the introduction of a correlation structure between model parameters can cause some issues. Sampling from a multivariate lognormal distribution, which is the typically distribution assumed for PMX model parameters, is not straightforward when a correlation structure is introduced. Indeed, correlations need to respect some constraints which depend by the CVs (i.e., coefficients of variation) of lognormal variables. In addition, when correlation matrices have some unspecified values, they should be properly fixed preserving the positive semi-definiteness of the correlation structure. In this paper, we present mvLognCorrEst, an R package developed to address these issues. Methods: The proposed sampling strategy was based on reconducting the extraction from the multivariate lognormal distribution of interest to the underlying Normal distribution. However, with high lognormal CVs, a positive semi-definite Normal covariance matrix cannot be obtained due to the violation of some theoretical constraints. In these cases, the Normal covariance matrix was approximated to its nearest positive definite matrix using Frobenius norm as matrix distance. For the estimation of unknown correlations terms, the graph theory was used to represent the correlation structure as weighed undirected graph. Plausible value ranges for the unspecified correlations were derived considering the paths between variables. Then, their estimation was performed by solving a constrained optimization problem. Results: Package functions are presented and applied on a real case study, that is the GSA of a PMX model that has been recently developed to support preclinical oncological studies. Conclusions: mvLognCorrEst package is an R tool to support simulation-based analysis for which sampling from multivariate lognormal distributions with correlated variables and/or estimation of partially defined correlation matrix are required.