Statistical properties of the least squares estimator of maximum excreted drug amount

Inaccuracy in estimation of the maximum excreted drug amount ($U^{\infty}$) is the main cause of errors in determination of some pharmacokinetic parameters of drugs. Usually, one estimates $U^{\infty}$ using observed values of the cummulative excretion ($U(t)$). This paper uses a new stochastic model to obtain the least squares estimator of $U^{\infty}$. The advantages of the model are that it is applicable for any drug, whose pharmacokinetics may be formalized with a linear $n$-compartment model ($n=1,2,3,...$) with or without phase of absorption and it may be used when the measurements for $U(t)$ are non-equidistant.