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

Sequential multiple assignment randomized trials (SMARTs) are used to construct data-driven optimal intervention strategies for subjects based on their intervention and covariate histories in different branches of health and behavioral sciences where a sequence of interventions is given to a participant. Sequential intervention strategies are often called dynamic treatment regimes (DTR). In the existing literature, the majority of the analysis methodologies for SMART data assume a continuous primary outcome. However, ordinal outcomes are also quite common in clinical practice. In this work, first, we introduce the notion of generalized odds ratio (GOR) to compare two DTRs embedded in a SMART with an ordinal outcome and discuss some combinatorial properties of this measure. Next, we propose a likelihood-based approach to estimate GOR from SMART data, and derive the asymptotic properties of its estimate. We discuss alternative ways to estimate GOR using concordant-discordant pairs and two-sample U-statistic. We derive the required sample size formula for designing SMARTs with ordinal outcomes based on GOR. A simulation study shows the performance of the estimated GOR in terms of the estimated power corresponding to the derived sample size. The methodology is applied to analyze data from the SMART+ study, conducted in the UK, to improve carbohydrate periodization behavior in athletes using a menu planner mobile application, Hexis Performance. A freely available Shiny web app using R is provided to make the proposed methodology accessible to other researchers and practitioners.