A common approach to the design of phase II clinical trials in oncology is to conduct a two-stage trial so as to control type I and type II error rates. A number of researchers have proposed methods for the design of such trials when the response can take one of a number of ordered values such as tumor response, stable disease or progressive disease. In this case, the problem may be formulated as that of testing a complex null hypothesis. Control of the type I error rate thus requires specification of the null region and construction of a test that limits the maximum error rate over this region. In this paper we propose that the null region should be bounded by a line in the two-dimensional parameter space for the setting with a response with three levels and more generally by a plane or hyperplane. We then propose a test based on the likelihood ratio statistic and show how this may be calculated in this case for a three-level response. The method is illustrated using an example of a clinical trial to evaluate a new treatment for breast cancer.