Incorporation of concentration data below the limit of quantification in population pharmacokinetic analyses

<jats:title>Abstract</jats:title><jats:p>Handling of data below the lower limit of quantification (<jats:styled-content style="fixed-case">LLOQ</jats:styled-content>), below the limit of quantification (<jats:styled-content style="fixed-case">BLOQ</jats:styled-content>) in population pharmacokinetic (<jats:styled-content style="fixed-case">PopPK</jats:styled-content>) analyses is important for reducing bias and imprecision in parameter estimation. We aimed to evaluate whether using the concentration data below the <jats:styled-content style="fixed-case">LLOQ</jats:styled-content> has superior performance over several established methods. The performance of this approach (“All data”) was evaluated and compared to other methods: “Discard,” “<jats:styled-content style="fixed-case">LLOQ</jats:styled-content>/2,” and “<jats:styled-content style="fixed-case">LIKE</jats:styled-content>” (likelihood‐based). An analytical and residual error model was constructed on the basis of in‐house analytical method validations and analyses from literature, with additional included variability to account for model misspecification. Simulation analyses were performed for various levels of <jats:styled-content style="fixed-case">BLOQ</jats:styled-content>, several structural <jats:styled-content style="fixed-case">PopPK</jats:styled-content> models, and additional influences. Performance was evaluated by relative root mean squared error (<jats:styled-content style="fixed-case">RMSE</jats:styled-content>), and run success for the various <jats:styled-content style="fixed-case">BLOQ</jats:styled-content> approaches. Performance was also evaluated for a real <jats:styled-content style="fixed-case">PopPK</jats:styled-content> data set. For all <jats:styled-content style="fixed-case">PopPK</jats:styled-content> models and levels of censoring, <jats:styled-content style="fixed-case">RMSE</jats:styled-content> values were lowest using “All data.” Performance of the “<jats:styled-content style="fixed-case">LIKE</jats:styled-content>” method was better than the “<jats:styled-content style="fixed-case">LLOQ</jats:styled-content>/2” or “Discard” method. Differences between all methods were small at the lowest level of <jats:styled-content style="fixed-case">BLOQ</jats:styled-content> censoring. “<jats:styled-content style="fixed-case">LIKE</jats:styled-content>” method resulted in low successful minimization (<50%) and covariance step success (<30%), although estimates were obtained in most runs (~90%). For the real <jats:styled-content style="fixed-case">PK</jats:styled-content> data set (7.4% <jats:styled-content style="fixed-case">BLOQ</jats:styled-content>), similar parameter estimates were obtained using all methods. Incorporation of <jats:styled-content style="fixed-case">BLOQ</jats:styled-content> concentrations showed superior performance in terms of bias and precision over established <jats:styled-content style="fixed-case">BLOQ</jats:styled-content> methods, and shown to be feasible in a real <jats:styled-content style="fixed-case">PopPK</jats:styled-content> analysis.</jats:p>