Estimation the withdrawal period for veterinary drugs used in food producing animals

A theoretical background of three methods for the estimation of the withdrawal period for veterinary drugs used in food producing animals is described. The three methods considered were: 1. Decision rule: The time in which the residues in all tissues of all observed animals are below the respective maximum residue levels (MRLs), plus a safety span, is considered the withdrawal period. This rule is unacceptable in terms of statistical inference because of the impossibility of assessing the uncertainty of the results. 2. Linear regression: It fits a regression model to estimate the withdrawal period as the upper limit of the 95 or 99% tolerance interval (with 95% confidence). When departures from basic assumptions of the model cannot be overcome with a log(e) transformation, other transformations (the power family where each observation is raised to some power) might also be contemplated. 3. Non-parametric approach: The withdrawal period is the time in which a given percentage of at least 95% of the animals have residues below the MRL (with a 5% risk). This method is based on the binomial distribution (making the original response dicothomic). It reduces the theoretical assumptions, but increases the requirements for sample sizes, unless either the percentage of risk, or the violation rate or both are reconsidered. Two examples that illustrate the use of these methods are presented with different percentages of tolerance limits, risk levels and percentiles. The withdrawal period estimated is different for the three methods being less for method 2, more for method I and longest for method 3. (C) 2003 Elsevier Science B.V. All rights reserved.