Population Pharmacodynamics: Strategies for Concentration- and Effect-Controlled Clinical Trials

Abstract

OBJECTIVE: To explore and evaluate various strategies for drug concentration- and effect-controlled clinical trials, respectively, in the context of studies of population pharmacodynamics (concentration—effect relationships). METHODS: The relative utility of drug concentration- and pharmacologic effect-controlled, randomized clinical trials with two or three concentration—effect measurements for each subject has been explored by computer simulation. The basis for these simulations was a sigmoid-E_max (maximum effect) pharmacodynamic model with E_max = 100%, EC₅₀ (drug concentrations required to produce an effect intensity of 50%) = 10 concentration units, gamma = 2, and no hysteresis. E_max and gamma were held constant whereas EC₅₀ was assumed to be log-normally distributed with a 26% coefficient of variation of the natural log-normalized data. A smaller random variability and variability due to measurement error also were incorporated in the simulations. To explore the implications of variable and unknown and gamma values, the suitability of linear and log—linear interpolation procedures for two-point concentration—effect data in different regions of the sigmoid-E_max curve was compared. RESULTS: Pharmacologic effect-controlled clinical trials with 300 hypothetical subjects and targeted effect intensities of 25% and 75% yielded very good estimates of drug concentrations required to produce effect intensities of 35%, 50%, and 65%, whereas concentration-controlled trials yielded much poorer estimates. Moreover, the concentration-controlled trials, despite optimum choice of targeted concentrations, yielded a large number of data points with poor information content (effect intensities of 85%). Determinations based on targeted effect intensities of 25% and 75% yielded better estimates of individual EC₅₀ values than those targeted for 25% and 50% or 50% and 75% effect intensity. Results were not significantly improved by adding a third measurement (targeted to 50% effect) to the 25% and 75% effect design. Estimations of drug concentrations required to produce an effect intensity of 50%, based on log—linear interpolation of exact concentration—effect data at 25% and 75%, yielded exact results independent of gamma value (0.5–8.0) whereas linear interpolation produced large overestimates at gamma = 0.5 or 1.0 but satisfactory estimates at gamma ≤ 2.0. Similar calculations for an effect intensity of 15% based on exact concentration—effect data at 5% and 25% yielded reasonably good estimates by both methods of interpolation over a wide range of gamma values. A review of the clinical literature showed that gamma values are usually 2 or higher. CONCLUSIONS: Population pharmacodynamic studies of reversibly acting drugs without pharmacodynamic hysteresis or time dependency (e.g., tolerance) can be successfully conducted using a pharmacologic effect-controlled randomized clinical trial design with only two properly selected target effect intensities per subject.