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Stat Med. 2018 Sep 30;37(22):3147-3178. doi: 10.1002/sim.7830. Epub 2018 May 31.

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

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Department of Biostatistics, Yale School of Public Health, New Haven, CT 06510, USA.


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.


binomial outcome; doubly randomized; preference; sample size; two-stage clinical trials


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