Designing One Sided Group Sequential Clinical Trials To Detect A Mixture Alternative

Group sequential designs play an important role in monitoring clinical trials. In this dissertation, we consider the construction of one-sided group sequential designs where the stopping rule includes boundaries for early stopping to accept for futility and to reject for efficacy. The traditional assumption that all patients have the same likelihood of benefiting from the treatment is sometimes unrealistic and it can underestimate the required sample size. This motivates us to power the design for an alternative where the treatment group observations come from a mixture of normal distributions. For the proposed setting, we use standardized test statistics based on sample means. Stopping boundaries and arm size for the design are determined by Type I and Type II error spending equations. The unknown variance case is discussed, and we introduce the group sequential t-test for the mixture setting. With the mixture model, we discuss a more general definition of treatment effect. The maximum likelihood estimator and method of moment estimator for the treatment effect are discussed.