A systematic literature review of multivariate normal variance-mean mixture representations in pharmacokinetic studies

Abstract

The NVMM framework is an integrated approach that extends the normal distribution by including heavy-tail properties. In spite rapid methodological advances in this distribution family, large amount of literature only focuses on mixing densities that provide average tail activities which are insufficient in capturing extreme variability that constantly occur in drug pharmacokinetic processes. This study provides an in depth systematic review of literature which focuses on multivariate and few univariate distributions developed using the NVMM approach with particular interest in the baseline distributions such as the normal, Kotz-type, and related distributions. And also, evaluating the different distributions used as mixing variables. This review followed a well-structured PRISMA procedure; the searches for literature related to the study were done with different databases namely PubMed, Web of Science, Google Scholar, Science Direct, and Scopus. From 2,588 retrieved records (between Jan. 1^st, 2000 to Dec. 31^st, 2025), rigorous screening, eligibility criteria, and quality assessment yielded 17 high-quality studies for synthesis. Data extraction focused on distributional structures, mixing variables, estimation methods, and applications. After using the set criteria for selection, 17 literatures were identified and added to the study database for a qualitative synthesis. Our review showed different forms and alternative distributions that could arise from the normal, skew-normal, Kotz, Laplace, skew-Laplace etc using the NVMM framework. The review showed that distribution tail largely depends on the nature of the mixing variable. Finally, the review showed inadequate extreme variability capturing; suggesting the adaptation of a type II extreme-value distribution.