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Impact of low percentage of data below the quantification limit on parameter estimates of pharmacokinetic models

  • Xu Steven Xu
  • Adrian Dunne
  • Holly Kimko
  • Partha Nandy
  • An Vermeulen
Article

Abstract

The objectives of the simulation study were to evaluate the impact of BQL data on pharmacokinetic (PK) parameter estimates when the incidence of BQL data is low (e.g. ≤10%), and to compare the performance of commonly used modeling methods for handling BQL data such as data exclusion (M1) and likelihood-based method (M3). Simulations were performed by adapting the method of a recent publication by Ahn et al. (J Phamacokinet Pharmacodyn 35(4):401–421, 2008). The BQL data in the terminal elimination phase were created at frequencies of 1, 2.5, 5, 7.5, and 10% based on a one- and a two-compartment model. The impact of BQL data on model parameter estimates was evaluated based on bias and imprecision. The simulations demonstrated that for the one-compartment model, the impact of ignoring the low percentages of BQL data (≤10%) in the elimination phase was minimal. For the two-compartment model, when the BQL incidence was less than 5%, omission of the BQL data generally did not inflate the bias in the fixed-effect parameters, whereas more pronounced bias in the estimates of inter-individual variability (IIV) was observed. The BQL data in the elimination phase had the greatest impact on the volume of distribution estimate of the peripheral compartment of the two-compartment model. The M3 method generally provided better parameter estimates for both PK models than the M1 method. However, the advantages of the M3 over the M1 method varied depending on different BQL censoring levels, PK models and parameters. As the BQL percentages decreased, the relative gain of the M3 method based on more complex likelihood approaches diminished when compared to the M1 method. Therefore, it is important to balance the trade-off between model complexity and relative gain in model improvement when the incidence of BQL data is low. Understanding the model structure and the distribution of BQL data (percentage and location of BQL data) allows selection of an appropriate and effective modeling approach for handling low percentages of BQL data.

Keywords

Pharmacokinetics Parameter estimate BQL 

Notes

Acknowledgments

All authors are employees of Johnson & Johnson Pharmaceutical Research & Development. Steven Xu is an adjunct assistant professor in the School of Public Health at the University of Medicine and Dentistry of New Jersey.

Supplementary material

10928_2011_9201_MOESM1_ESM.ppt (106 kb)
Supplementary Figure 1. Relative bias (%) for parameter estimates of the one-compartment model (additive residual error) at different BQL levels with M1 (°) and M3 (×) methods (N=1,000; successful minimizations only). The vertical lines represent the relative bias for parameter estimates based on the complete datasets without BQL censoring. (PPT 106 kb)
10928_2011_9201_MOESM2_ESM.ppt (106 kb)
Supplementary Figure 2. Root relative mean square error (%) for parameter estimates of the one-compartment model (additive residual error) at different BQL levels with M1 (°) and M3 (×) methods (N=1,000; successful minimizations only). The vertical lines represent the Root relative mean square errors for parameter estimates based on the complete datasets without BQL censoring. (PPT 106 kb)
10928_2011_9201_MOESM3_ESM.ppt (174 kb)
Supplementary Figure 3. Relative bias (%) for parameter estimates of the two-compartment model (additive residual error) at different BQL levels with M1 (°) and M3 (×) methods (N=1,000; successful minimizations only). The vertical lines represent the relative bias for parameter estimates based on the complete datasets without BQL censoring. (PPT 174 kb)
10928_2011_9201_MOESM4_ESM.ppt (117 kb)
Supplementary Figure 4. Root relative mean square error (%) for parameter estimates of the two compartment model (additive residual error) at different BQL levels with M1 (°) and M3 (×) methods (N=1,000; successful minimizations only). The vertical lines represent the Root relative mean square errors for parameter estimates based on the complete datasets without BQL censoring. (PPT 117 kb)

References

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Xu Steven Xu
    • 1
  • Adrian Dunne
    • 2
    • 3
  • Holly Kimko
    • 1
  • Partha Nandy
    • 1
  • An Vermeulen
    • 2
  1. 1.Clinical Pharmacology, Advanced PK-PD Modeling and SimulationJohnson & Johnson Pharmaceutical R&DRaritanUSA
  2. 2.Clinical Pharmacology, Advanced PK-PD Modeling and SimulationJanssen Research & DevelopmentBeerseBelgium
  3. 3.School of Mathematical SciencesUniversity College DublinDublinIreland

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