Assessment of dosing impact on intra-individual variability in estimation of parameters for basic indirect response models

The application of D-optimization and the assessment of bias and precision of parameter estimates for four basic pharmacodynamic (PD) indirect response (IDR) models for ascending doses was examined using simulated data. While D-optimization provided four sampling times, each IDR model was used to generate eight data points per dose level. The PD parameters were: input rate constant (k _in), disposition rate constant (k _out), capacity constant (I _max or S _max), and sensitivity constant (IC ₅₀ or SC ₅₀). A monoexponential pharmacokinetic function was applied with single doses increased by a factor of 10 to generate responses that vary from weak to fully saturable. For each dose, 100 replications of response data were simulated using independent normally distributed errors of CV = 20%. The original IDR model was fitted and PD parameters estimated. Histograms and descriptive statistics were generated. All parameters exhibited asymmetric distributions with positive coefficients of skewness except for I _max. Higher doses resulted in unbiased estimates of all PD parameters. The precision of parameter estimates improved with increasing doses except for IC ₅₀ and SC ₅₀ indicating that a single dose experimental design cannot be corrected by increasing dose in order to improve precision of estimates of IC ₅₀ or SC ₅₀. Highest variability was for IC ₅₀ and SC ₅₀ parameters. This study provides new insights into optimum study designs and recovery of parameters for basic IDR models.