We consider the problem of studying several dose combinations of two drugs for a therapeutic endpoint in a multilevel factorial clinical trial. Two test statistics are constructed to test whether there exists at least one dose combination that is more effective than its component doses. Their distributions involve nuisance parameters quantifying the mean differences among the doses of the two component drugs. It is shown that their power functions achieve maxima as all the nuisance parameters approach infinity in absolute value. The significance levels of the two tests are derived and two alpha-level tests are proposed. Tables are given to provide the alpha-level critical values for these tests and to gain insights into their power performances.

For factorial clinical trials in which two monotherapy treatments under study can interact only in the presence of treatment effects for each treatment, the always-pooled test statistic using data from all four groups has a correct size in detecting the simple effect of an individual treatment used alone. However, this test statistic may have an unbounded bias in estimation of the simple effect. The never-pooled test statistic that uses only data from the treatment group not receiving the other treatment has poor precision for estimating the simple effect. Two alternative test statistics under consideration are the two-stage statistic involving a preliminary test of treatment interaction and the maximum test statistic taking the larger of the always-pooled and the never-pooled statistics. The power, bias, and mean square error of all four tests are compared. When negative interactions exist, the two-stage and maximum statistics are generally superior to the always-pooled statistic and compare reasonably well with the never-pooled statistic; the maximum statistic seems slightly more favorable than the two-stage statistic. The two-stage statistic is the best choice when a treatment interaction can be large.