Transl Clin Pharmacol.  2017 Jun;25(2):74-84. 10.12793/tcp.2017.25.2.74.

Parameter estimation for sigmoid E(max) models in exposure-response relationship

  • 1Department of Clinical Pharmacology, Pusan National University Hospital, Busan 49241, Republic of Korea.
  • 2(Bio)Medical Research Institute, Pusan National University Hospital, Busan 49241, Republic of Korea.


The purpose of this simulation study is to explore the limitation of the population PK/PD analysis using data from a clinical study and to help to construct an appropriate PK/PD design that enable precise and unbiased estimation of both fixed and random PD parameters in PK/PD analysis under different doses and Hill coefficients. 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 1-compartment PK model and sigmoid E(max) model. 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 E(max) model were accurately and precisely estimated when the C(max) was more than 85% of ECâ‚…â‚€, except for typical value and inter-individual variability of ECâ‚…â‚€ which were poorly estimated at low Hill coefficients. For the multiple dose studies, the parameter estimation performance was not good. This simulation study demonstrated the effect of the relative range of sampled concentrations to ECâ‚…â‚€ and sigmoidicity on the parameter estimation performance using dense sampling design.


pharmacodynamic parameter estimation; exposure-response relationship; PK/PD modeling and simulation; stochastic simulation and estimation; sigmoid E(max) Model

MeSH Terms

Bias (Epidemiology)
Clinical Study
Colon, Sigmoid*


  • Figure 1 Relative bias (upper) and relative root mean square error (lower) of pharmacokinetic parameters estimates for the single-dose scenarios (a) and the multiple-dose scenarios (b).

  • Figure 2 Effects versus concentrations/EC50 plots relevant to each simulation scenario for the single-dose scenarios (a) and the multiple-dose scenarios (b).

  • Figure 3 Relative bias (a) and relative root mean square error (b) of pharmacodynamic parameters estimates for the single-dose scenarios.


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