In this paper, we check the accuracy of an approximate variance for the area under the concentration curve (AUC). Based on the model function of a random effects model, an analytic expression for the AUC can be obtained. Then an approximate variance for the AUC can be derived after the linearisation of it using the Taylor series expansion. This variance is used in the construction of confidence interval to check the accuracy of the approximation made. We assume that the data on concentration are collected with the advancement of a dose-finding study. Following the allocation of the lowest dose to a cohort of patients, the concentration of drug in the blood samples is measured at the locally D-optimum time points. The successive doses for the cohorts are determined by the popular continual reassessment method. Four PK proles, along with three plausible dose-response scenarios, are investigated through a simulation study. The numerical findings assure the quality of the approximated variance.