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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.

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