Sequential Search of an Optimal Dosage, I

Sequential search procedures are described for determining an optimal dosage in the following biomedical problem. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which the proportion of patients whose toxicity level does not cross the allowable limit is γ. We discuss Bayesian and non-Bayesian sequential procedures for searching the optimal dosage, assuming a linear regression between toxicity and dosage, and normal conditional distribution of the toxicity level at each dose, with a known variance.