Open AccessVariability in the Log Domain and Limitations to Its Approximation by the Normal Distribution
Author(s) -
ElassaissSchaap Jeroen,
Duisters Kevin
Publication year - 2020
Publication title -
cpt: pharmacometrics and systems pharmacology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.53
H-Index - 37
ISSN - 2163-8306
DOI - 10.1002/psp4.12507
Subject(s) - log normal distribution , omega , mathematics , standard deviation , context (archaeology) , normal distribution , distribution (mathematics) , statistics , similarity (geometry) , statistical physics , computer science , mathematical analysis , physics , artificial intelligence , geography , quantum mechanics , archaeology , image (mathematics)
Pharmacometric models using lognormal distributions have become commonplace in pharmacokinetic–pharmacodynamic investigations. The extent to which it can be interpreted by traditional description of variability through the normal distribution remains elusive. In this tutorial, the comparison is made using formal approximation methods. The quality of the resulting approximation was assessed by the similarity of prediction intervals (PIs) to true values, illustrated using 80% PIs. Approximated PIs were close to true values when lognormal standard deviation (omega) was smaller than about 0.25, depending mostly on the desired precision. With increasing omega values, the precision of approximation worsens and starts to deteriorate at omega values of about 1. With such high omega values, there is no resemblance between the lognormal and normal distribution anymore. To support dissemination and interpretation of these nonlinear properties, some additional statistics are discussed in the context of the three regions of behavior of the lognormal distribution.