Abstract
In optimal experimental design theory it is usually assumed that the response variable follows a normal distribution with constant variance. However, some works assume other probability distributions based on additional information or practitioner’s prior experience. The main goal of this paper is to study the effect, in terms of efficiency, when misspecification in the probability distribution of the response variable occurs. The elemental information matrix, which includes information on the probability distribution of the response variable, provides a generalized Fisher information matrix. This study is performed from a practical perspective, comparing a normal distribution with the Poisson or gamma distribution. First, analytical results are obtained, including results for the linear quadratic model, and these are applied to some real illustrative examples. The nonlinear 4-parameter Hill model is next considered to study the influence of misspecification in a dose-response model. This analysis shows the behavior of the efficiency of the designs obtained in the presence of misspecification, by assuming heteroscedastic normal distributions with respect to the D-optimal designs for the gamma, or Poisson, distribution, as the true one.
Highlights
To obtain optimal designs, it is common to assume a homoscedastic normal distribution of the response variable and under this assumption there is vast literature focused mainly on nonlinear models
This study has been carried out to analyze the effect of misspecification in the probability distribution of the response variable
We measure that effect by calculating the efficiency of the optimal design obtained with an assumed or working distribution compared to that obtained with the true probability distribution
Summary
It is common to assume a homoscedastic normal distribution of the response variable and under this assumption there is vast literature focused mainly on nonlinear models. Present a method to compute the D-optimal designs for Generalized Linear Models with a binary response allowing uncertainty in the link function, ref. [13] study the effect of some drugs which inhibit the growth of tumor cells providing D-optimal designs under the assumption of the response variable follows a heteroscedastic normal distribution with a given structure for the variance.
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