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

TL;DR

This paper introduces a new likelihood-based method to compare dynamic treatment regimes in SMART trials with ordinal outcomes, including sample size calculation and application to a real study.

Contribution

It develops a generalized odds ratio measure for ordinal outcomes in SMARTs and proposes estimation, asymptotic properties, and sample size formulas for this measure.

Findings

The proposed GOR method effectively compares DTRs with ordinal outcomes.

Simulation results demonstrate accurate power estimation for sample size planning.

Application to the SMART+ study illustrates practical utility and implementation.

Abstract

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.