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Sequential multiple assignment randomized trials (SMARTs) are used toconstruct data-driven optimal intervention strategies for subjects based ontheir intervention and covariate histories in different branches of health andbehavioral sciences where a sequence of interventions is given to aparticipant. Sequential intervention strategies are often called dynamictreatment regimes (DTR). In the existing literature, the majority of theanalysis methodologies for SMART data assume a continuous primary outcome.However, ordinal outcomes are also quite common in clinical practice. In thiswork, first, we introduce the notion of generalized odds ratio (GOR) to comparetwo DTRs embedded in a SMART with an ordinal outcome and discuss somecombinatorial properties of this measure. Next, we propose a likelihood-basedapproach to estimate GOR from SMART data, and derive the asymptotic propertiesof its estimate. We discuss alternative ways to estimate GOR usingconcordant-discordant pairs and two-sample U-statistic. We derive the requiredsample size formula for designing SMARTs with ordinal outcomes based on GOR. Asimulation study shows the performance of the estimated GOR in terms of theestimated power corresponding to the derived sample size. The methodology isapplied to analyze data from the SMART+ study, conducted in the UK, to improvecarbohydrate periodization behavior in athletes using a menu planner mobileapplication, Hexis Performance. A freely available Shiny web app using R isprovided to make the proposed methodology accessible to other researchers andpractitioners.

A Novel Approach To Assess Dynamic Treatment Regimes Embedded In A Smart With An Ordinal Outcome