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J Pharmacokinet Pharmacodyn. 2008 Aug;35(4):401-21. doi: 10.1007/s10928-008-9094-4. Epub 2008 Aug 7.

Likelihood based approaches to handling data below the quantification limit using NONMEM VI.

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Pharmacometrics R & D, ICON Development Solutions, Ellicott City, MD, USA.

Erratum in

  • J Pharmacokinet Pharmacodyn. 2010 Jun;37(3):305-8.



To evaluate the likelihood-based methods for handling data below the quantification limit (BQL) using new features in NONMEM VI.


A two-compartment pharmacokinetic model with first-order absorption was chosen for investigation. Methods evaluated were: discarding BQL observations (M1), discarding BQL observations but adjusting the likelihood for the remaining data (M2), maximizing the likelihood for the data above the limit of quantification (LOQ) and treating BQL data as censored (M3), and like M3 but conditioning on the observation being greater than zero (M4). These four methods were compared using data simulated with a proportional error model. M2, M3, and M4 were also compared using data simulated from a positively truncated normal distribution. Successful terminations and bias and precision of parameter estimates were assessed.


For the data simulated with a proportional error model, the overall performance was best for M3 followed by M2 and M1. M3 and M4 resulted in similar estimates in analyses without log transformation. For data simulated with the truncated normal distribution, M4 performed better than M3.


Analyses that maximized the likelihood of the data above the LOQ and treated BQL data as censored provided the most accurate and precise parameter estimates.

[Indexed for MEDLINE]

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