Reporting Coefficient of Variation for Logit, Box-Cox and Other Non-log-normal Parameters

• Published in: Clinical pharmacokinetics Vol. 63; no. 2; pp. 133 - 135
• Main Author: Prybylski, John P.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2024; Springer Nature B.V
• Subjects: Commentary; Estimates; Expected values; Internal Medicine; Medicine; Medicine & Public Health; Pharmacology/Toxicology; Pharmacotherapy; Random variables
• ISSN: 0312-5963; 1179-1926; 1179-1926
• DOI: 10.1007/s40262-023-01343-2

The coefficient of variation, typically given in percent (CV%), is the standard deviation of a random variable X divided by the mean of X. Standard deviation is calculated as the square root of the variance (Var), and both mean and Var can be determined by the moments of the distribution describing X. The expected values, E, of various powers of X are used to determine the moments. The expected value of X which is subject to an invertible transformation function, F-1 (Fy) = X (where Tx is the transformed value with a continuous range) and raised to some power n for moment calculation, are found with the integration in Eq. 2, where ц is in the transformed domain and ω2 is the variance. The R programming language, for example, contains optimized functions to compute all parts of Eq. 2 rapidly and accurately. [...]the CV% for non-log-normal transforms can be easily reported.