Population pharmacokinetic-pharmacodynamic modeling of biological agents: when modeling meets reality

The pharmacokinetics (PK) and pharmacodynamics (PD) of many biological agents (biologics) have inherent complexities requiring specialized approaches to develop reliable, unbiased models. Three cases are covered: preponderance of zero values, nonresponder subpopulations, and adaptive dosing. Engineered biologics exhibit high affinity for target receptors. Biologics can saturate receptors, abolishing free receptor levels for protracted periods. Consequently, the distribution of observations can be heavy at, and near, the boundary. A 2-part model (ie, a truncated δ log-normal distribution) may be appropriate. Mixture models identify subpopulations based on bimodal or multimodal distributions of η values. With biologics, PD may be compromised because of lack of receptors, or the PD may be affected because of other events resulting in erratic excursions. Nonresponders exhibit a random walk-around placebo trajectory, resulting in high residual variability. The distributions of etas are often badly skewed or polymodal. An indescribable mixture model separates subjects who are nonresponders, providing diagnostic pharmacologic information on the drug. Many biologics use PD-based adaptive dosing. During model development, data used for model development include adaptive dosing. For simulation, adaptive dosing must be implemented. Failure to account for dose adjustments results in biased or inflated prediction intervals because subjects in the simulated data undergo inappropriate dose adjustments.