On some properties of a sequential method for estimating ED 50 applied to Quantal Data

Abstract

Recently sequential procedures have been applied to estimate the dose corresponding to the ED 50 (median effective dose) in quantal response data, where subjects are tested one at a time at certain fixed levels (chosen before hand) according to some rule. The primary advantage of these sequential methods is that experimentations on test subjects tend to be concentrated on levels near the ED, 50 which is to be estimated and this naturally increases the accuracy of the estimate. A sequential procedure known as the “Up and Down” method has been developed by Mood and Dixon(c,f,l) in which at any stage of the procedure that level at which the next observation is tested, is determined on the basis of the result of the last trial only. Two other sequential procedures viz. ‘1-rule’ and 3-rule’ and has given some asymptotic properties of these sequential procedures. Of these the ‘3-rules’ seems to have many desirable properties and as such deserves further investigation. In this paper further properties of this rule have been studied. In particular, mention may be made of the problem of estimation of ED, 50 which has not been considered earlier and is presented. Efforts have also been made in this paper to bring out more clearly the operative aspects of this rule by showing that the sequential process involved in the rule can be split into some component parts which are generated by some basic patterns.