The present method allows to detect outlying observations in data which may be described by a deterministic function plus a stochastic component. This type of functional relationship often occurs in experimental data, in toxicological research, for instance. The Hampel identifier, an outlier identification method designed for location-scale models, is modified to account for the special structure of the data. Simulated standardisation values for the procedure are given for sample sizes from 16 to 21. The procedure is applied to a toxicological study with one of the basic petrochemical compounds ethylene (ethene). This study was designed to determine the individual and population parameters, i. e. the parameters which describe the general behaviour of the investigated process in the whole population, as well as the intra- and interindividual variability of the processes of inhalation, exhalation, and metabolic elimination of the chemical ethylene in male Sprague- Dawley rats. The results are discussed for various methods determining the functional relationship and for two possible approaches of applying the outlier identification method, one based on the simulated (exact) standardisation values for all sample sizes, the other based on taking a tabled value corresponding to the sample size 'nearest' to the real sample.
Outliers Hampel identifier toxicokinetics nonlinear hierarchical models population parameters EM algorithm ethylene