Optimal designs when the variance is a function of the mean

We develop locally D-optimal designs for nonlinear models when the variance of the response is a function of its mean. Using the two-parameter Michaelis-Menten model as an example, we show that the optimal design depends on both the type of heteroscedasticity and the magnitude of the variation. In addition, our results suggest that the homoscedastic D-optimal design has high efficiency under a broad class of heteroscedastic patterns and that it is fairly insensitive to nominal values of the parameters.