Design and Analysis of Switchback Experiments

Iavor Bojinov (), David Simchi-Levi () and Jinglong Zhao ()
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Iavor Bojinov: Technology and Operations Management Unit, Harvard Business School, Boston, Massachusetts 02163
David Simchi-Levi: Institute for Data, Systems, and Society, Department of Civil and Environmental Engineering, and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Jinglong Zhao: Operations and Technology Management Department, Questrom School of Business, Boston University, Boston, Massachusetts 02215

Management Science, 2023, vol. 69, issue 7, 3759-3777

Abstract: Switchback experiments, where a firm sequentially exposes an experimental unit to random treatments, are among the most prevalent designs used in the technology sector, with applications ranging from ride-hailing platforms to online marketplaces. Although practitioners have widely adopted this technique, the derivation of the optimal design has been elusive, hindering practitioners from drawing valid causal conclusions with enough statistical power. We address this limitation by deriving the optimal design of switchback experiments under a range of different assumptions on the order of the carryover effect—the length of time a treatment persists in impacting the outcome. We cast the optimal experimental design problem as a minimax discrete optimization problem, identify the worst-case adversarial strategy, establish structural results, and solve the reduced problem via a continuous relaxation. For switchback experiments conducted under the optimal design, we provide two approaches for performing inference. The first provides exact randomization-based p -values, and the second uses a new finite population central limit theorem to conduct conservative hypothesis tests and build confidence intervals. We further provide theoretical results when the order of the carryover effect is misspecified and provide a data-driven procedure to identify the order of the carryover effect. We conduct extensive simulations to study the numerical performance and empirical properties of our results and conclude with practical suggestions.

Keywords: design of experiments; discrete optimization; central limit theorem; switchback experiments (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:69:y:2023:i:7:p:3759-3777

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