Design and Analysis of Multi-Arm Trials with a Common Control Using Order Restrictions

Abstract

Trials for comparing I treatments with a control are considered, where the aim is to identify one treatment (if at least one exists) which is better than control. Tests are developed which use all of the data simultaneously, rather than combining separate tests of a single arm versus control. The null hypothesis H0 : i 0 is tested against H1 : i > 0 for at least one i, where i represents the scaled di erence in response between treatment i and the control, i = 1; : : : ; I, and, if rejected, the best treatment is selected. A likelihood ratio test (LRT) is developed using order restricted inference, a family of tests is de ned and it is shown that the LRT and Dunnett-type tests are members of this family. Tests are compared by simulation, both under normality and for binary data, an exact test being developed for the latter case. The LRT compares favourably with other tests in terms of power and a simple loss function. Proportions of subjects on the control close to ( p I ð€€€1)=(I ð€€€1) are found to maximise the power and minimise the expected loss. Two-stage adaptive designs for comparing two experimental arms with a control are developed, in which the trial is stopped early if the di erence between the best treatment and the control is less than C1; otherwise, it continues, with one arm if one experimental treatment is better than the other by at least C2, or with both arms otherwise. Values of the constants C1 and C2 are compared and the adaptive design is found to be more powerful than the xed design. The new tests can make a contribution to improving the analysis of multi-arm clinical trials and further research in their application is recommended.