Parameter estimation performance for sigmoid emax models in exposure-response Relationship

Abstract

Drug exposures are not often high enough to estimate maximum effect (Emax) to avoid drug toxicity, bring about difficulties in estimating unbiased and precise PD parameter estimates or inevitably simplified models such as linear model and log-linear model. The purpose of this simulation study is to investigate the accuracy and precision of PD parameter estimates in PK/PD analysis under different doses and Hill coefficients in case of dense PK sampling design in human pharmacology study. Seven escalating doses of virtual drugs with equal potency and efficacy but with five different Hill coefficients were used in simulations of single and multiple dose scenarios with dense sampling design. A total of 70 scenarios with 100 subjects were simulated and estimated 100 times applying one compartment PK model with first-order absorption and sigmoid Emax model using SSE (Stochastic simulation and estimation) of PSN (Perl-speaks-NONMEM) and first order conditional estimation with interaction (FOCE-I) method in NONMEM (version 7.2).The bias and precision of the parameter estimates in each scenario were assessed using relative bias and relative root mean square error. For the single dose scenarios, most PD parameters of sigmoid Emax model were accurately and precisely estimated when the Cmax was attained more than 85%of EC50, except for typical value and inter-individual variability of EC50 which were poorly estimated at low Hill coefficients. For the multiple dose studies, the parameter estimation performance was not good. This simulation study quantitatively demonstrated the effect of the relative range of sampled concentrations to EC50 and sigmoidicity on the PD parameter estimation performance using dense sampling design. This study can be useful in designing a clinical study to evaluate PK/PD relationship for new drug development or drug repositioning.