SMART Binary: New Sample Size Planning Resources for SMART Studies with Binary Outcome Measurements

Abstract

Sequential Multiple-Assignment Randomized Trials (SMARTs) play an increasingly important role in psychological and behavioral health research. This experimental approach enables researchers to answer scientific questions about how to sequence and match interventions to the unique, changing needs of individuals. A variety of sample size planning resources for SMART studies have been developed, enabling researchers to plan SMARTs for addressing different types of scientific questions. However, relatively limited attention has been given to planning SMARTs with binary (dichotomous) outcomes, which often require higher sample sizes relative to continuous outcomes. Existing resources for estimating sample size requirements for SMARTs with binary outcomes do not consider the potential to improve power by including a baseline measurement and/or multiple repeated outcome measurements. The current paper addresses this issue by providing sample size planning simulation procedures and approximate formulas for two-wave repeated measures binary outcomes (i.e., two measurement times for the outcome variable, before and after intervention delivery). The simulation results agree well with the formulas. We also discuss how to use simulations to calculate power for studies with more than two outcome measurement occasions. Results show that having at least one repeated measurement of the outcome can substantially improve power under certain conditions.

Keywords:

• Sequential multiple assignment randomized trials (SMARTs)
• adaptive interventions
• binary outcome
• power
• sample size

Article information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was supported by Grants R01 DA039901, P30 DA029926, R01 DA015186, and P50 DA039838 from the National Institutes of Health.

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The authors would like to thank Nick Seewald and Jamie Yap for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors' institutions or the National Institutes of Health is not intended and should not be inferred.

Author note

This research was supported by awards R01 DA039901, P30 DA029926, R01 DA015186, and P50 DA039838 from the National Institutes of Health. The content is solely the responsibility of the authors and does not necessarily represent the official views of the funding institutions as mentioned above. The authors thank Nick Seewald and Jamie Yap for their helpful advice and input. We have no known conflict of interest to disclose. Correspondence concerning this paper may be sent to John Dziak, [email protected], or to Inbal Nahum-Shani, [email protected]. The first and last authors contributed equally. The first author gratefully acknowledges the Methodology Center and Edna Bennett Pierce Prevention Center at The Pennsylvania State University, where he did most of the research and writing for this manuscript, and especially thanks Prevention Research Center director Stephanie Lanza for her support.

The analyses reported here were not preregistered. No empirical dataset was used. Simulation code is available at https://github.com/d3lab-isr/Binary_SMART_Power_Simulations.