Design methods for some dose-response models

A recently described design method for one-parameter biomedical models such as limiting or serial dilution assays is generalized to two-parameter models for which the dose-response relationship can be expressed as a linear regression model with parameters alpha (intercept) and beta (slope). Design formulae are proposed for three different cases in which prior information about the unknown regression parameters alpha and beta is available (alpha known, beta known and neither known, respectively). A suitable transformation of the two-parameter model enables the direct application of the one-parameter design method to the first two cases, while the third needs more advanced considerations. Two experimental designs, taken from the literature, are reproduced as closely as possible using the methods described, thus showing under which circumstances these designs are suitable.