One- and Two-Stage Models for Comparing an Experimental Treatment with a Standard.

Optimal one- and two-stage plans are developed for selecting one of two medical treatments, an experimental treatment A or a standard treatment B. The response to treatment is normally distributed with unknwon mean mu sub A or mu sub B and known variance sigma squared. It is assumed mu sub A or mu sub B but that treatment A is worthwhile adopting only if mu sub A - mu sub B or a, where a is fixed. The only cost considered is the ethical one of treating a patient with the wrong treatment. Out of a total of N patients with the disease in question, a fraction 2P of them is to be placed in a clinical trial comparing the two treatments, with the winning treatment to be given to the remaining N1-2P patients. Optimal values of P are found for both a one-stage and a two-stage plan, with the latter showing a modest improvement in expected net gain. The case in which mu sub B is known is also considered, and the resultant improvement in expected net gain over the case mu sub B unknown is found to moderate for a one-stage trial. Author