Pharmacometric and statistical considerations for dose optimization

Abstract

The probability of target attainment (PTA) is a common metric in drug dose optimization, but it requires a specific known target concentration threshold. Such target thresholds are not always available for some treatments, and patient and disease groups, particularly when treating children. This study performed pharmacokinetic and pharmacokinetic-pharmacodynamic (PKPD) simulations to explore different statistical approaches for determining the optimal dose for unknown PK and PKPD targets. To determine an optimal dose, PK and PKPD outcomes in typical patients with a standard adult dosing regimen were simulated and set as the reference profile, and compared to simulated outcomes for different dosing regimens in the population of interest. Statistical distances between the empirical cumulative distribution functions of the outcomes from all possible dosing regimens were calculated and compared to the reference profile. An optimal dose for known PK and PKPD target outcomes was selected to maintain the outcome above the assigned target, while optimal dosing in a population of interest with an unknown target was selected to generate equivalent PK and PKPD outcomes as the typical population. All of the dose optimization methods with commonly used PK and PKPD models and covariates were implemented as an open source freely available Shiny web-application. The developed pharmacometric method for dose optimization in populations with known and unknown target levels were robust and reproducible, and the implementation of a freely accessible Shiny web-application ensures widespread use and could be a useful tool for dose optimization in populations of interest.

FIGURE 1

Methodological frameworks of dose optimization for known PK or PKPD targets (left panel) and unknown PK or PKPD targets (right panel). Dose optimization of known targets is determined by the probability of the target attainment (PTA), whereas dose optimization of the unknown targets is based on the distance between the ECDF of the target profile in a reference population after a standard dose (solid black line) and ECDF of each possible dose in the population of interest (solid color lines). The dose with the minimum distance to the target profile will be assigned as an optimal dose.

FIGURE 2

Probability density function (a) and empirical cumulative distribution function (b) of AUC_LAST between a reference population (blue lines) and a population of interest (red lines).

FIGURE 3

Statistical sensitivity of dose optimization for an unknown target outcome, stratified by different levels of the possible tablet strengths, that is, ±20% (a) and ±50% (b). Each panel shows a different level of inter‐individual variability (from 20% to 100%) in underlying model parameters. Colored lines represent the different statistical calculations for the distance between two ECDFs.