Estimating area under the curve and relative exposure in a pharmacokinetic study with data below quantification limit

Area under the drug-concentration-over-time curve (AUC) is an important endpoint for many phase I/II clinical trials and laboratory assays. Drug concentrations are measured using laboratory assays with a lower limit of quantification (LLOQ). How to calculate AUC when some drug concentration data are below the LLOQ remains as a challenge. In this article, we develop a maximum likelihood method to estimate AUC and relative exposure (i.e., ratio of two AUCs) when data below LLOQ exists. We also compare the proposed method to several commonly used methods, including imputation with model-predicted values or ad hoc values (i.e., LLOQ, LLOQ/2, or zero) through a simulation study. The proposed method gives unbiased inference. Commonly used methods can provide biased estimation, especially when a large proportion of data is below LLOQ. Application to a case study is also presented.