Simple, robust and near optimal designs for the estimation of log-logistic dose response functions

Experimental designs in dose response experiments often use simple setups where the dose levels are increased by a fixed factor on the log scale. More efficient or even formally optimal experimental designs exist for this context, but these are often unpopular among applied scientists as they usually depend on the true value of some of the parameters and also frequently propose using only a small number of distinct dose levels. On the other hand, more generally optimal designs such as quasi-bayesian designs are often quite complicated, and still require specifying an a-priori distribution of parameters. In this paper we propose a single graphical representation which shows the performance of any given experimental design under a wide range of possible parameters. Using this representation, we propose four different possible designs which are both simple and still provide reasonable efficiency under many parameter constellations, without needing anything but the most coarse prior knowledge about these parameters. Specifically, our recommended design proposes 10 different dose levels in total, 8 main doses spaced equally around the most likely ED50 value, exactly one natural log step apart, and one more set of observations each under control, and under the maximum technically feasible dose. The available observations should be distributed among these dose levels so that each of the main dose levels is assigned roughly [Formula: see text] of the observations, while control and maxdose are assigned roughly [Formula: see text] of the observations, rounding when necessary.