Extensions to the two-stage randomized trial design for testing treatment, self-selection, and treatment preference effects to binary outcomes.

While traditional clinical trials seek to determine treatment efficacy within a specified population, they often ignore the role of a patient's treatment preference on his or her treatment response. The two-stage (doubly) randomized preference trial design provides one approach for researchers seeking to disentangle preference effects from treatment effects. Currently, this two-stage design is limited to the design and analysis of continuous outcome variables; in this presentation, we extend this current design to include binary variables. We present test statistics for testing preference, selection, and treatment effects in a two-stage randomized design with a binary outcome measure, with and without stratification. We also derive closed-form sample size formulas to indicate the number of patients needed to detect each effect. A series of simulation studies explore the properties and efficiency of both the unstratified and stratified two-stage randomized trial designs. Finally, we demonstrate the applicability of these methods using an example of a trial of Hepatitis C treatment.