Residuals and outliers in replicate design crossover studies

Outliers in bioequivalence trials may arise through various mechanisms, requiring different interpretation and handling of such data points. For example, regulatory authorities might permit exclusion from analysis of outliers caused by product or process failure, while exclusion of outliers caused by subject-by-treatment interaction generally is not acceptable. In standard 2 x 2 crossover studies it is not possible to distinguish between relevant types of outliers based on statistical criteria alone. However, in replicate design (2-treatment, 4-period) crossover studies three types of outliers can be distinguished: (i) Subject outliers are usually unproblematic, at least regarding the analysis of bioequivalence, and may require no further action; (ii) Subject-by-formulation outliers may affect the outcome of the bioequivalence test but generally cannot simply be removed from analysis; and (iii) Removal of single-data-point outliers from analysis may be justified in certain cases. As a very simple but effective diagnostic tool for the identification and classification of outliers in replicate design crossover studies we propose to calculate and plot three types of residual corresponding to the three different types of outliers that can be distinguished. The residuals are obtained from four mutually orthogonal linear contrasts of the four data points associated with each subject. If preferred, outlier tests can be applied to the resulting sets of residuals after suitable standardization.