Testing the individual effective dose hypothesis.

The assumption of the individual effective dose is the basis for the probit method used for analyzing dose or concentration-response data. According to this assumption, each individual has a uniquely innate tolerance expressed as the individual effective dose (IED) or the smallest dose that is sufficient to kill the individual. An alternative to IED, stochasticity suggests that individuals do not have uniquely innate tolerance; deaths result from random processes occurring among similar individuals. Although the probit method has been used extensively in toxicology, the underlying assumption has not been tested rigorously. The goal of the present study was to test which assumption, IED or stochasticity, best explained the response of Daphnia magna exposed to multiple pulses of copper sulfate (CuSO4 ) over 24 d. Daphnia magna were exposed to subsequent age-dependent 24-h median lethal concentrations (LC50s) of copper (Cu). Age-dependent 24-h LC50 values and Cu depuration test were determined prior to the 24-d bioassay. The LC50 values were inversely related to organism age. The Cu depuration of D. magna did not depend on age or Cu concentration, and 5 d was sufficient recovery time. Daphnia magna were exposed to 4 24-h Cu exposures, and surviving organisms after each exposure were transferred to Cu-free culture media for recovery before the next exposure. Stochasticity appropriately explained the survival and reproduction response of D. magna exposed to Cu.

Statistical methodology to determine kinetically derived maximum tolerated dose in repeat dose toxicity studies.

Several statistical approaches were evaluated to identify an optimum method for determining a point of nonlinearity (PONL) in toxicokinetic data. (1) A second-order least squares regression model was fit iteratively starting with data from all doses. If the second order term was significant (α<0.05), the dataset was reevaluated with successive removal of the highest dose until the second-order term became non-significant. This dose, whose removal made the second order term non-significant, is an estimate of the PONL. (2) A least squares linear model was fit iteratively starting with data from all doses except the highest. The mean response for the omitted dose was compared to the 95% prediction interval. If the omitted dose falls outside the confidence interval it is an estimate of the PONL. (3) Slopes of least squares linear regression lines for sections of contiguous doses were compared. Nonlinearity was suggested when slopes of compared sections differed. A total of 33 dose-response datasets were evaluated. For these toxicokinetic data, the best statistical approach was the least squares regression analysis with a second-order term. Changing the α level for the second-order term and weighting the second-order analysis by the inverse of feed consumption were also considered. This technique has been shown to give reproducible identification of nonlinearities in TK datasets.