Impact of omission or replacement of data below the limit of quantification on parameter estimates in a two-compartment model

Abstract

Purpose: To evaluate the influence of omission and replacement approaches for data below the limit of quantification (LOQ) on the estimation of pharmacokinetic parameters for two-compartment models when using nonlinear mixed-effect models.

Method: Nine data sets were simulated according to a two-compartment intravenous bolus model with interindividual and residual variabilities, and a sparse sampling strategy was adopted. The data sets differed with respect to area-under-the-curve (AUC) ratio (0.1. 0.2, 0.3) and half-life ratio (0.03, 0.1, 0.3) between the distribution and elimination phases. For each of the nine data sets, six reduced data sets were created by omitting 5%, 10%, 20%, 30%, 40%, or 50% of the lowest concentration values. For each of the reduced data sets only one simple correction procedure to handle observations below LOQ was applied. All the values below the LOQ were deleted, and the first one was replaced by half of the LOQ value. Population parameters were estimated for each of the 117 resulting data sets (one initial, six reduced, and six "corrected" data sets for each of the nine cases). This approach was also applied on a real data set of patients administered multiple i.v. bolus doses.

Results: For many of the data sets, particularly when a large fraction of the data was omitted, one or several population parameters were biased. When there was bias, clearance (CL) usually was underestimated, whereas peripheral volume was overestimated. The parameters related to the distribution phase (central volume and intercompartmental clearance) were less affected, and changes were not systematic. The correction procedure markedly decreased overall bias on the fixed effect of the parameters. Results for the real data were similar.

Conclusion: Omission of data below the LOQ value may induce a not negligible bias on fixed-effect parameter estimates. The influence of the omission of values below LOQ was related to the underlying shape of the concentration-time profile and fraction of omitted observations. The use of a simple replacement rule seems to reduce this bias in estimates but needs further investigation.