**A comparison of methods for handling of data below the limit of quantification in NONMEM VI**

Martin Bergstrand, Elodie Plan, Maria Kjellsson, Mats O Karlsson

Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden

**Introduction:** Common approaches for handling of concentration measurements reported as below the limit of quantification (BLQ), such as discharging the information or substitution with the limit of quantification (LOQ) divided by two, have been shown to introduce bias to parameter estimates [1-3]. In 2001, Stuart Beal published an overview of ways to fit a PK model in the presence of BLQ data [3]. New functionalities in NONMEM VI allow for simplified implementation of some methods presented in the publication. The method referred to as M2 applies conditional likelihood estimation to the observations above LOQ and the likelihood for the data being above LOQ are maximized with respect to the model parameters. This approach can be implemented in NONMEM VI by utilization of the YLO functionality [4]. By simultaneous modeling of continuous and categorical data where the BLQ data are treated as categorical, the likelihood for BLQ data to be indeed BLQ can be maximized with respect to the model parameters. The indicator variable F_FLAG can be used to facilitate this approach in NONMEM VI [4]. This suggested method differs from the one referred to as M3 in the sense that the likelihood is only estimated for BLQ data as opposed to all data.

**Methods:** One hundred simulated population PK data sets, originally provided for comparison of estimation methods in nonlinear mixed effects modeling (PAGE 2005) [5], were analysed with 5 different methods for handling of BLQ data. The simulated datasets was based on a one-compartment model with first order absorption and first order elimination. A second set with 100 data sets was simulated according to a two-compartment intravenous bolus model. The five methods for handling of BLQ data was used; (A) BLQ data omitted (B) First BLQ observation substituted with LOQ/2 (C) YLO functionality (D) F_FLAG functionality (E) Maximum likelihood estimation for all data (M3) [3].

**Results and Discussion:** The over all best performance was seen with method (D). Also method (E) and to some extent (C) showed favorable accuracy for the estimated population parameters and IIV compared to method (A). Method (C) and (E) did however result in several (13-52%) non-successful minimizations, primarily due to rounding error termination. Though parameter estimates following non-successful terminations did not seem to be systematically different. Substitution with LOQ/2 (B) was in one case shown to introduce bias compared to omitting BLQ data.

**References:**

[1] Hing, J.P., et al., Analysis of toxicokinetic data using NONMEM: impact of quantification limit and replacement strategies for censored data. J Pharmacokinet Pharmacodyn, 2001. 28(5): p. 465-79.

[2] Duval, V. and M.O. Karlsson, Impact of omission or replacement of data below the limit of quantification on parameter estimates in a two-compartment model. Pharm Res, 2002. 19(12): p. 1835-40.

[3] Beal, S.L., Ways to fit a PK model with some data below the quantification limit. J Pharmacokinet Pharmacodyn, 2001. 28(5): p. 481-504.

[4] Boeckmann A. J., B.S.L.a.S.L.B., NONMEM Users Guide PartVIII. 1996-2006, NONMEM Project Group,: San Francisco.

[5] Girard P., Mentré F. A comparison of estimation methods in nonlinear mixed effects models using a blind analysis. PAGE 14 (2005) Abstr 834 [www.page-meeting.org/?abstract=834].