The AAPS Journal

, 11:535 | Cite as

Population Pharmacodynamic Parameter Estimation from Sparse Sampling: Effect of Sigmoidicity on Parameter Estimates

  • Sudhakar M. Pai
  • Suzette GirgisEmail author
  • Vijay K. Batra
  • Ihab G. Girgis
Research Article


The objective of this stimulation study was to evaluate effect of simoidicity of the concentration–effect (CE) relationship on the efficiency of population parameter estimation from sparse sampling and is a continuation of previous work that addressed the effect of sample size and number of samples on parameters estimation from sparse sampling for drugs with CE relationship characterized by high sigmoidicity (γ > 5). The findings are based on observed CE relationships for two drugs, octreotide and remifentanil, characterized by simple E max and sigmoid E max models (γ = ~2.5), respectively. For each model, CE profiles (100 replicates of 100 subjects each) were simulated for several sampling designs, with four or five samples/individual randomly obtained from within sampling windows based on EC50-normalized plasma drug concentrations, PD parameters based on observed population mean values, and inter-individual and residual variability of 30% and 25%, respectively. The CE profiles were fitted using non-linear mixed effect modeling with the first-order conditional estimation method; variability parameters were described by an exponential error model. The results showed that, for the sigmoid E max model, designs with four or five samples reliably estimated the PD parameters (EC50, E max, E 0, and γ), whereas the five-sample design, with two samples in the 2–3 E max region, provided in addition more reliable estimates of inter-individual variability; increasing the information content of the EC50 region was not critical as long as this region was covered by a single sample in the 0.5–1.5 EC50 window. For the simple E max model, because of the shallower profile, enriching the EC50 region was more important. The impact of enrichment of appropriate regions for the two models can be explained based on the shape (sigmoidicity) of the concentration–effect relationships, with shallower CE profiles requiring data enrichment in the EC50 region and steeper curves less so; in both cases, the E max region needs to be adequately delineated, however. The results provide a general framework for population parameter estimation from sparse sampling in clinical trials when the underlying CE profiles have different degrees of sigmoidicity.

Key words

clinical trials PK-PD simulations population PK-PD modeling sparse sampling 





Baseline response


Drug concentration at 50% of the E max


Drug efficacy


The sigmoidicity constant






Sample size




Non-linear mixed effect modeling








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Copyright information

© American Association of Pharmaceutical Scientists 2009

Authors and Affiliations

  • Sudhakar M. Pai
    • 1
  • Suzette Girgis
    • 2
    Email author
  • Vijay K. Batra
    • 3
  • Ihab G. Girgis
    • 4
  1. 1.Clinical PharmacologyAkros Pharma, Inc.PrincetonUSA
  2. 2.Global Clinical PharmacologyJohnson & Johnson Pharmaceutical Research & DevelopmentTitusvilleUSA
  3. 3.Drug DevelopmentRanbaxy Laboratories LimitedGurgaonIndia
  4. 4.Clinical Biostatistics-Advanced Modeling & SimulationJohnson & Johnson Pharmaceutical Research & DevelopmentRaritanUSA

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