Happy Djokoto 1, Adrien Olama 1, Camille Massaux 1, Grace Shalom Govere 1, Hélène Haguet 1, Lisa Hanquet 1, Reagan Kilela Songela 3, Lisa Wellin 1, Jean-Michel Dogné 1,2, Flora T. Musuamba 1,2,3
1 Clinical Pharmacology and toxicology research unit, Faculty of medicine, University of Namur (Namur, Belgium), 2 Federal Agency for Medicines and Health Products (FAMHP) (Brussels, Belgium), 3 Faculté de Sciences Pharmaceutiques, Université de Lubumbashi (Lubumbashi, Democratic Republic of the Congo)
Introduction/objectives :
The analysis of pharmacokinetic (PK) clinical data is frequently complicated by censored observations, which may affect data representativeness and the reliability of parameter estimation. Censoring occurs when measured concentrations fall below the lower limit of quantification (LLOQ)[1, 2] or above the upper limit of quantification (ULOQ)[3]. LLOQ and ULOQ censoring can arise simultaneously in clinical studies characterized by wide exposure variability, such as paediatric populations spanning broad developmental stages or studies involving IV bolus administration. In such settings, early peak concentrations and late elimination-phase samples may exceed the assay’s quantification limits at opposite ends of the concentration range. Appropriate statistical handling of such data is therefore essential for accurate PK parameter estimation. The M3 method[4, 5] is widely regarded as a robust approach for handling censored observations in nonlinear mixed-effects modeling. However, despite its theoretical advantages, a high proportion of censored data may compromise estimation stability and increase bias and imprecision.
The objectives of this study were to evaluate the impact of increasing proportions of censored data on estimation stability, bias, and imprecision and to quantify the expected deviation from true parameter values when applying the M3 method under high censoring conditions. This work aims to provide quantitative insight into the behavior of the M3 method under substantial censoring, supporting a more nuanced interpretation of model-based results.
Methods:
NONMEM (Laplace estimation) was used to evaluate the performance of the M3 approach under imposed varying proportions of censored data, ranging from 0% to 90%. Data can be either ULOQ or LLOQ or both. An Paediatric extravascular population PK model[6] was implemented, and stochastic simulation and estimation (SSE) was performed with 500 replicates per scenario. Estimation stability was assessed using the proportion of runs with successful minimization and model convergence across scenarios. Bias and imprecision were quantified by comparing estimated parameters to their true values using relative bias (RBias) and relative root mean square error (RRMSE), respectively. In addition, shrinkage for Clerance (CL) was recorded.
Results:
Overall, the M3 method showed good performance and stable estimation when the proportion of censored observations remained below 50%. Bias and imprecision increased once censoring exceeded 50%, with a more pronounced deterioration when censoring was driven by concentrations above the ULOQ rather than below the LLOQ. Parameters related to the Maturation (Hill coefficient and TM50) were more strongly affected under ULOQ censoring than under LLOQ censoring. CL shrinkage also increased markedly beyond 50% censoring in ULOQ-driven scenarios.
As expected, the probability of successful minimization decreased as the proportion of censored observations increased, with a stronger decline in ULOQ-only scenarios. At 50% censoring, the proportion of successful minimization was approximately 50% under ULOQ-only censoring, compared with 95% under LLOQ-only censoring.
Across scenarios where ≥50% of observations were outside the quantification range, the typical clearance (TVCL) exhibited RBias ranging from 25% to over 50% and a RRMSE ranging from 1.2 to over 2.4 regardless of whether censoring originated from LLOQ, ULOQ, or both. Typical volume (TVV) estimates were comparatively stable when censoring was driven only by LLOQ. However, when ULOQ censoring was present at ≥50%, TVV showed substantially larger degradation, with RBias and RRMSE ranging from 41% to 2000% and 93 to over 200, respectively. These results highlight that heavy ULOQ censoring can have a disproportionate impact on estimation stability and precision compared with LLOQ censoring, and they underscore the sensitivity of inference to the loss (or censoring) of information around peak concentrations.
Conclusion:
This SSE study shows that the M3 method provides reliable and stable parameter estimation when the proportion of censored observations remains below 50%. Above this threshold, estimation stability decreases, and both bias and imprecision increase, particularly when censoring is driven by ULOQ values. ULOQ censoring had a high impact on key parameters, including maturation parameters (Hill and TM50) and typical volume, highlighting the importance of information around peak concentrations. These findings provide quantitative insight into the expected magnitude of estimation degradation under high censoring conditions and support a cautious interpretation of model-based results when a substantial fraction of observations lies outside the quantification range. Although these conclusions are supported within the structural model evaluated, further investigations across models of varying structural complexity are required to assess the generalizability of these findings.
References:
[1] H. Humbert, M. D. Cabiac, J. Barradas, and C. Gerbeau, “Evaluation of pharmacokinetic studies: is it useful to take into account concentrations below the limit of quantification?,” Pharm Res, vol. 13, no. 6, pp. 839-45, Jun 1996, doi: 10.1023/a:1016088609005.
[2] D. B. Hibbert, E.-H. Korte, and U. Örnemark, “Metrological and quality concepts in analytical chemistry (IUPAC Recommendations 2021),” Pure and Applied Chemistry, vol. 93, no. 9, pp. 997-1048, 2021, doi: doi:10.1515/pac-2019-0819.
[3] FDA. Bioanalytical Method Validation of ANDAsWhat the Assessor Looks For. Available: //efaidnbmnnnibpcajpcglclefindmkaj/https://www.fda.gov/media/135129/download
[4] M. Bergstrand and M. O. Karlsson, “Handling data below the limit of quantification in mixed effect models,” AAPS J, vol. 11, no. 2, pp. 371-80, Jun 2009, doi: 10.1208/s12248-009-9112-5.
[5] M. Wijk, R. E. Wasmann, K. R. Jacobson, E. M. Svensson, and P. Denti, “A Pragmatic Approach to Handling Censored Data Below the Lower Limit of Quantification in Pharmacokinetic Modeling,” CPT Pharmacometrics Syst Pharmacol, vol. 14, no. 6, pp. 1042-1049, Jun 2025, doi: 10.1002/psp4.70015.
[6] A. R. Maharaj et al., “Population pharmacokinetics of olanzapine in children,” Br J Clin Pharmacol, vol. 87, no. 2, pp. 542-554, Feb 2021, doi: 10.1111/bcp.14414.
Reference: PAGE 34 (2026) Abstr 12018 [www.page-meeting.org/?abstract=12018]
Poster: Methodology - Other topics