Summary

Statistisk analyse og biologisk tolkning af toksicitetsdata

This project is aimed at studying how the application of simoidal dose-response models (symmetrical and asymmetrical) combined with proper statistical analysis can be used optimize the interpretation of existing experimental data obtained in toxicological and ecotoxicological tests of pesticides. These models are used to describe the dose-response relationships for continuous data, e.g. growth, biomass or enzyme concentration/inhibition, and binomially distributed data, e.g. dead or live animals and plants, mobile or immobile animals. Dose-response curve are either monotonely increasing from a lower to an upper asymptote or decreasing from an upper to a lower asymptote. Usually, we are interested in determining the dose or concentration of a pesticide that yields a 50% reduction in the response relative to the upper and lower asymptotes. This dose or concentration is termed EC50, ED50, LC50, or LD50 depending on whether it is the concentration (EC50, LC50) or dose (ED50, LD50) that is used and whether the endpoint is lethality (LC50, LD50) or other types of effects (EC50, ED50).

For regulatory uses the quantification of toxicity is often related to EC50/LC50/ED50/LD50, but in ecotoxicology also those concentrations/doses yielding low effects, e.g. 10% (EC10/LC10/ED10/LD10), are of interest. All these values are estimates based on a mathematical description of the dose-response relationship combined with a statistical quantification of the variance on parameter estimates. In human toxicology the quantification of doses/concentrations for which no or low effects occurs is also of highly important. Here the use of analysis of variance usually the statistical method recommended for determining the so-called NOEL (No Observable Effect Level). However, by doing so the whole dose-response relationship is not used. By using proper regression a far better basis for interpretation of the experimental results will be obtained.

On the basis of simulations of existing dose-response curves we showed that if there are limits to the number of experimental units, either because of limitation in space, economy or test organisms, the precision of the parameter estimates for toxicity will be improved by reducing the number of replications at each dose and expand the number of doses. In the available data material we showed that the EC50/LD50/EC50 is virtually the same whether one applies a symmetric or an asymmetric dose-response curve. However, the choice of regression model does play a role if the EC10 or EC90 response levels are of interest.

For continuous responses it is important to ensure that there is homogeneity of variance. If this prerequisite does not apply it is required to use an appropriate method to transform data so they comply with this prerequisite. In this report we have used the so-called Box-Cox transformation of both sides of the regression model (also called “Transform-both sides”). The parameter estimates of say EC50 or EC10 do not change dramatically whether we use data with variance heterogeneity or not, but the standard errors of the parameters would not be correct and sometimes will differ considerably from the ones obtained form the analysis with a Box-Cox transformation that takes the heterogeneity of variance into account. The same problems arise when one analyses binomially distributed data as if they are coming from a continuous distribution. As the estimated EC50/ED50/LD50 or EC10/ED10/LD10 and their associated standard errors are of primary importance when registering a pesticide and place it in toxicity classes, it is imperative to apply proper statistical methods.

The report also touches upon semi and non-parametric analysis, i.e. analyses that do not have any a priori functional dose-response specification. Furthermore, the report also looks at various problems with definitions of upper and lower asymptotes and how to compare experiments with several measured responses. One of the examples in the report is a dose-response experiment based upon generation studies in rats were also included. The protocols were designed for a No Observable Effect Level (NOEL) study whilst we analysed them using dose-response regression analysis and obtained more useful information.

It is concluded that in order to exploit the full potential of well-established statistical methods, it is important that regulatory authorities take initiatives to replace obsolete and insufficient methods and concepts, and require that appropriate methods, which account for the statistical properties of the data, must be used.