A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models

Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine

“…We provide some theoretical results, as well as practical ones. The first is quite general, valid for any regression function and any criterion based on FIM which guarantees that there is no loss of efficiency when the response variable follows a gamma distribution, and there is assumed to be a heteroscedastic normal distribution with r = 1 in the variance structure given by (5). For the linear quadratic model, analytical results are obtained on computing the optimal design for Poisson and gamma distributions.…”

“…Finally, the 4-parameter Hill model was used to illustrate and quantify the loss of efficiency. Assuming a heteroscedastic normal distribution, taking values close to r = 0 in (5), between about 18% and 25% efficiency is lost for all the drugs looked at in the study when the true distribution is a gamma distribution. Thus, in this case, the usual assumption of normality and homoscedasticity (r = 0) of the response variable is not a good option.…”

“…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. However, there are also papers that use probability distributions different from a normal distribution [1][2][3][4][5][6][7]. At this point, it is important to remember that the probability distribution of the response variable is assumed, on many occasions, from the nature of the experiment to be performed.…”