BAYESIAN PROCEDURES FOR SELECTING THE BEST POPULATION OF (k + 1) NORMAL POPULATIONS

Afaf M. Mady (Egypt)

Received October 16, 2008

Abstract

Mady [3] introduced two simple procedures for dealing with patients who arrive during the waiting period, caused by the lag, between the trial and treatment stages for designing an optimal clinical trial when a total of N patients with a disease are to be treated with one of  medical treatments. The relative performance of the procedures in the Bayesian framework is discussed when the responses to  treatments  are normally distributed with unknown means  and a common known variance  We notice that when  the formulae for the expected regret function for Procedures 1 and 2 performed by Mady are not equivalent with those of Langenberg and Srinivasan [2]. We found that the reason for this situation is as fallows. Mady expressed the expected regret function in terms of the true difference  while Langenberg and Srinivasan expressed the same function in terms of the absolute difference  That is, we must differentiate between two cases: (i)  (ii)  as the probability of selecting the inferior population has a different formual in each case. This paper will express the expected regret function using Procedures 1 and 2 in terms of the absolute value of the true difference between the treatments  instead of  where  and  are the unknown means of treatments  and  respectively. The consideration of this modification leads to major changes in the results.

Keywords and phrases: Bayesian approach, decision theory, delayed observations.