Inter-individual variability (IIV)
Inter-individual variability is the spread of a PK parameter between patients, usually modeled as log-normal. Its variance ω² on the log scale corresponds to a coefficient of variation of about √(exp(ω²) − 1).
Definition
Inter-individual variability (IIV, also between-subject variability) is how much a PK parameter such as clearance differs between patients. In a population model it is a random effect, usually log-normal: the individual's parameter is the typical value times exp(η), with η normally distributed with variance ω².
Conversion to a coefficient of variation
For a log-normal distribution, CV ≈ √(exp(ω²) − 1). A variance of 0.134 corresponds to a CV of about 38%.
Not residual error
IIV describes differences between patients in the parameters. Residual error describes the remaining difference between each observation and the model prediction for that patient. They are estimated separately.
On this site
The reimplemented pembrolizumab model has an IIV of 38% CV on clearance and 21% CV on volume, and the simulated spread of exposure in the anti-PD-1 analysis comes from these values together with body weight. The mosunetuzumab reimplementation checks that the covariance matrix of the random effects is positive definite before simulating. See also population PK models.
Frequently asked questions
How do I convert ω² to a percent CV?
CV ≈ √(exp(ω²) − 1). For ω² = 0.134 this gives about 38%.
Is IIV the same as variability in the measurements?
No. IIV is the spread of the true parameter between patients; measurement and model misfit are the residual error.