#### Determination of tolerance dose uncertainties and optimal design of dose response experiments with small animal numbers.

##### Karger, C.P. and Hartmann, G.H.

##### Strahlentherapie Und Onkologie, 177(1), 37-42 (2001).

Background: Dose response experiments aim to determine the complication probability as a function of dose. Adjusting the parameters of the frequently used dose response model P(D) = 1/[1 + (D-50/D)(k)] to the experimental data, 2 intuitive quantities are obtained: the tolerance dose D-50 and the slope parameter k. For mathematical reasons, however, standard statistic software uses a different set of parameters. Therefore, the resulting fit parameters of the statistic software as well as their standard errors have to be transformed to obtain D-50 and k as well as their standard errors. Material and Methods: The influence of the number of dose Levels on the uncertainty of the fit parameters is studied by a simulation for a fixed number of animals. For experiments with small animal numbers, statistical artifacts may prevent the determination of the standard errors of the fit parameters. Consequences on the design of dose response experiments are investigated. Results: Explicit formulas are presented, which allow to calculate the parameters D-50 and k as well as their standard errors from the output of standard statistic software. The simulation shows, that the standard errors of the resulting parameters are indepen dent of the number of dose levels, as long as the total number of animals involved in the experiment, remains constant. Conclusion: Statistical artifacts in experiments containing small animal numbers may be prevented by an adequate design of the experiment. For this, it is suggested to select a higher number of dose levels, rather than using a higher number of animals per dose level.