Analysis of toxicokinetic data using NONMEM: impact of quantification limit and replacement strategies for censored data

Abstract

The purpose of this study was to examine how best to incorporate plasma samples which fall below an assay's lower limit of quantification into the process of toxicokinetic data modeling. Secondly to establish what proportion of data can be below the quantification limit without compromising NONMEM's parameter estimates. Using pharmacokinetic parameters determined in a rat toxicokinetic study we simulated datasets that might emerge from similar experiments in which only one sample was obtained per individual. A number of quantification limits were used which resulted in increasing proportions of data values being treated as if they were below the limit of quantification (BQL). For each quantification level we incorporated BQL data into our analyses in number of ways. We compared these analysis methods with respect to how well the underlying parameter values were retrieved. Omitting BQL data values or entering them as zero led to inaccurate and biased study results. We found that incorporating BQL values using more complex substitution methods via a mixed effects model produced more reliable and less biased parameter estimates. The four substitution methods that we investigated performed similarly. Parameter estimates became less reliable and more biased as the quantification level was increased depending on the method of BQL value incorporation. Naive methods of BQL data handling can produce unreliable and biased parameter estimates. An alternative is to incorporate BQL values into a population-type model, our results showed this method to be preferable. We found it advisable that the proportion of BQL data should not exceed one third and, if possible should be less than one quarter.