Score tests for dose effect in the presence of non-responders

When only a certain proportion of subjects respond to treatment ('responders') or may never experience an event of interest (thus 'cured'), mixture models often lead to increased understanding of the treatment or disease process. This paper focuses on hypothesis testing in a dose-response framework and shows that increased power is possible by using a mixture model where both the logit of the response rate and the response mean are linear functions of the dose level. Three score tests are developed for testing an overall effect and permutation methods are used to control the type I error. Extensive simulations establish the power properties of the tests and show that our proposed score test has the best performance. The approach is illustrated by a multi-country clinical trial of rapid acting Intramuscular Olanzapine.