An Integrated Formulation for Comparing Treatments with Binary Response with a Control

The problem of comparing k(≧2) bernoulli rates of success with a control is considered. An one-stage decision procedure is proposed for either (1) choosing the best among several experimental treatments and the control treatment when the best is significantly superior or (2) selecting a random size subset that contains the best experimental treatment if it is better than the control when the difference between the best and the remaining treatments is not significant. We integrate two traditional formulations, namely, the indifference (IZ) approach and the subset selection (SS) approach, by seperating the parameter space into two disjoint sets, the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best experimental treatment for a correct selection (CS₁) but in the IZ we define any selected subset to be correct (CS₂) if it contains the best experimental treatment which is also better than the control. We propose a procedure R to guarantee lower bounds P₁* for P(CS₁≧PZ) and P₂* for P(CS₂≧IZ) simultaneously. A brief table on the common sample size and the procedure parameters is presented to illustrate the procedure R.