Pharmacodynamic parameter estimation: Population size versus number of samples

Abstract

The purpose of this study was to evaluate the effects of population size, number of samples per individual, and level of interindividual variability (IIV) on the accuracy and precision of pharmacodynamic (PD) parameter estimates. Response data were simulated from concentration input data for an inhibitory sigmoid drug efficacy (E(max)) model using Nonlinear Mixed Effect Modeling, version 5 (NONMEM). Seven designs were investigated using different concentration sampling windows ranging from 0 to 3 EC(50) (EC(50) is the drug concentration at 50% of the E(max)) units. The response data were used to estimate the PD and variability parameters in NONMEM. The accuracy and precision of parameter estimates after 100 replications were assessed using the mean and SD of percent prediction error, respectively. Four samples per individual were sufficient to provide accurate and precise estimate of almost all of the PD and variability parameters, with 100 individuals and IIV of 30%. Reduction of sample size resulted in imprecise estimates of the variability parameters; however, the PD parameter estimates were still precise. At 45% IIV, designs with 5 samples per individual behaved better than those designs with 4 samples per individual. For a moderately variable drug with a high Hill coefficient, sampling from the 0.1 to 1, 1 to 2, 2 to 2.5, and 2.5 to 3 EC(50) window is sufficient to estimate the parameters reliably in a PD study.

Parameter estimation for sigmoid Emax models in exposure-response relationship

“…[11] Both the θ γ and ω γ 2 met the criteria for accuracy and precision at 100 (C max =0.84 EC 50 units) and 200 mg (C max =1.7 EC 50 units) with γ of 2, 100 to 400 mg (C max =0.84 to 3.4 EC 50 units) with γ of 5, and 200 mg (C max =1.7 EC 50 units) with γ of 10. On the other hand, Girgis et al found that all θ γ and ω γ 2 were biased and imprecise when the Hill coefficient was high (γ=6.22), 4 to 5 blood samples were gathered [10] and Pai et al also reported similar results from spare sampling design, when γ were 1 or 2.51. [11] These results suggest that dense sampling design may be essential to get accurate and precise estimates of θ γ and ω γ 2 .…”

“…Simulated concentrations were normalized by true EC 50 (=1000 ng/mL) to identify the generalized exposure-response relationship and then "EC 50 " was used as a unit to express normalized concentrations. [10,11] To evaluate the estimation performance for PD parameters at each dosing scenario, the median values and ranges of normalized maximum concentration (C max ) (normalized by EC 50 ) for single-dose study and normalized steady-state minimum concentration (C min,ss ) and C max,ss for multiple-dose study at each dose level at all values of γ were obtained using individual predicted values, which were calculated from the parameter estimates from 100 simulated subjects and the simulation time points in each scenario.…”

“…The criteria for accuracy and precision were less than or equal to 15% and 35%, respectively. [10][11][12] …”

“…On the other hand, the next two studies used pharmacokinetic sampling designs to investigate pharmacodynamic parameter estimation, as is done in this study. Girgis et al [10] found that the accuracy and precision of the PD parameter estimates got worse as the number of subjects decreased from 100 to 25 with sparse sampling design. Pai et al [11] performed a series of studies that evaluated the effect of octreotide on the insulin-like growth factor-1and the effect of remifentanil on electroencephalogram, which were successfully described using sigmoid E max model with moderate sigmoidicity (γ=2.51) and simple E max model (γ=1), respectively, while the previous study of theophylline-induced eosinopenia was described using a model of high sigmoidicity.…”

“…This is a relatively smaller value than the result form a study which reported that the 2 to 3 EC 50 region is needed to get an unbiased and precise estimate of ω Emax 2 , when γ was 6.22 and blood sampling was sparse. [10] A dense sampling design is recommended to get a precise ωE C50 2 , because it was impossible with sparse sampling design. [11] Both the θ γ and ω γ 2 met the criteria for accuracy and precision at 100 (C max =0.84 EC 50 units) and 200 mg (C max =1.7 EC 50 units) with γ of 2, 100 to 400 mg (C max =0.84 to 3.4 EC 50 units) with γ of 5, and 200 mg (C max =1.7 EC 50 units) with γ of 10.…”