Avoiding drug residues: a multivariate approach to estimating withdrawal intervals in edible tissues of goats following extra label administration of flunixin meglumine.

Introduction: Flunixin meglumine is a non-steroidal anti-inflammatory drug (NSAID) commonly used extra-label in goats, necessitating the determination of an extended withdrawal interval (WDI) to minimize the risk of violative residues at slaughter. Current U.S. Food and Drug Administration (FDA) guidance estimates WDIs using univariate ordinary least squares (OLS) regression applied to concentrations at or above the limit of detection (LOD), defining the WDI as the time at which the upper bound of the 95% confidence interval for the 99% quantile falls below a specified tolerance. However, residue concentrations measured across multiple tissues from the same animal may be correlated, and excluding observations below the LOD may distort estimates by removing information from the terminal depletion phase. Materials and methods: We propose a multivariate linear regression (MvLR) framework that jointly models inter-tissue dependence while accommodating left-censored observations. Regression parameters are estimated using OLS and generalized least squares (GLS) under the uncensored MvLR model, and via an expectation conditional-maximization (ECM) algorithm under a censored MvLR formulation. Withdrawal intervals are computed using the multivariate t-distribution to obtain the upper limit of the 95% confidence interval for the 99% quantile across tissues. The methods are illustrated using tissue-residue data from 20 Boer goats administered flunixin meglumine at 2.2 mg/kg, with five animals euthanized at each of four post-treatment time points (24, 48, 72, and 96 h) and are further evaluated in a simulation study. Results: The simulation results indicate that the ECM-based censored MvLR approach yields stable parameter estimation and reliable WDI inference in the presence of censoring. Applying this framework to the goat residue data suggests that a withdrawal interval of at least 10 days is recommended to ensure that residues across all tissues fall below conservative safety thresholds. Discussion: These findings suggest that a multivariate censored modeling framework can improve WDI estimation by accounting for inter-tissue correlation and incorporating observations below the LOD, addressing key limitations of current univariate FDA-style approaches.