On using Lehmann alternatives with nonresponders

The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of responses in the treatment group. It is shown that the locally most powerful test leads to a test statistic that, under the hypothesis of no treatment effect, is the sum of independent pareto random variables whereas under the alternative hypothesis it is the sum of independent random variables from a mixture of two pareto distributions. The limiting distribution of the test statistic under both hypotheses is in the domain of attraction of a stable distribution whose indices are derived. The power of the test is given, and its properties are discussed. A set of data from clinical research involving development of a new drug is used to show application of the procedure and demonstrate its usefulness.