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Efficient designs for estimation in the power logistic quantal response model. (English) Zbl 0823.62087
Summary: A convenient three-parameter class of asymmetric dose-response models can be obtained by raising the logistic response function to the power $$m$$, for $$m>0$$. For these models, called power logistic quantal response models, $$D$$-optimal two point designs for various choices of $$m$$ are numerically derived. We then investigate design efficiencies and design robustness to misspecification of the three model parameters for two point designs relative to the $$D$$-optimal two point design.
It turns out that if the experimenter assumes an incorrect value of $$m$$ when determining a design, the loss of efficiency incurred as a result is fairly small for a wide range of $$m$$, assuming no error in the initial values of the other parameters. Moreover, the effects of poor initial values of the other parameters seem more serious when $$m$$ is large than when $$m$$ is small, so that special care should be taken when $$m$$ is large.

##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis 62K05 Optimal statistical designs