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

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.