An alternative approach to the optimal design of an LD50 bioassay

In this paper we propose an alternative approach to the optimal design of an LD50 bioassay. We adopt a Bayesian approach to make use of prior information about the location and scale parameters of the tolerance distribution function to select the design parameters (number of doses, total number of animals, centre of doses, space between doses), and we adopt a frequentist approach using the Spearman-Karber statistic to estimate the LD50. We define the optimal design as the one that produces the minimum expected mean squared error E(MSE) with respect to the joint prior distribution of the parameters of the tolerance distribution. For the design parameters investigated, we found: (i) the shape of the E(MSE) is relatively smooth and continuous, the magnitude of which is influenced by the underlying tolerance distribution; (ii) the amount of prior information about the location and scale parameters independently and jointly affect the optimal design; and (iii) as the amount of prior information decreases, one requires more doses and/or animals. Finally, we show the proposed method is robust for an incorrectly assumed tolerance distribution function.