A Pragmatic Approach to Handling Censored Data Below the Lower Limit of Quantification in Pharmacokinetic Modeling

Proper handling of data below the lower limit of quantification (BLQ) is crucial for accurate pharmacokinetic parameter estimation. The M3 method proposed by Beal uses a likelihood-based approach that is precise but has been reported to suffer from numerical issues in converging. Common alternatives include ignoring the BLQs (M1), imputing half of the lower limit of quantification and ignoring trailing BLQs (M6) or imputing zero (M7). The imputation methods fail to account for the additional uncertainty affecting imputed observations. We used NONMEM with FOCE-I/Laplace to compare the stability, bias, and precision of methods M1, M3, M6, M7, and modified versions M6+ and M7+ that inflate the additive residual error for BLQs. Real and simulated datasets with a two-compartment model were used to assess stability through parallel retries with perturbed initial estimates. The resulting differences in objective function values (OFV) were compared. Bias and precision were evaluated on simulated data using stochastic simulations and estimations. M3 yielded different OFV across retries (+/- 14.7), though the parameter estimates were similar. All other methods, except M7 (+/- 130), were stable. M3 demonstrated the best bias and precision (average rRMSE 18.7%), but M6+ and M7+ performed comparably (26.0% and 23.3%, respectively). The unstable OFV produced by M3 represents a challenge when used to guide model development. Imputation methods showed superior stability, and including inflated additive error improved bias and precision to levels comparable with M3. For these reasons, M7+ (of simpler implementation than M6+) is an attractive alternative to M3, especially during model development.