Comparison of Dynamic Treatment Regimes with An Ordinal Outcome
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Sequential multiple assignment randomized trials (SMART) are used to develop optimal treatment strategies for patients based on their medical histories in different branches of medical and behavioral sciences where a sequence of treatments are given to the patients; such sequential treatment strategies are often called dynamic treatment regimes. In the existing literature, the majority of the analysis methodologies for SMART studies assume a continuous primary outcome. However, ordinal outcomes are also quite common in medical practice; for example, the quality of life (poor, moderate, good) is an ordinal variable. In this work, first, we develop the notion of dynamic generalized odds-ratio (dGOR) to compare two dynamic treatment regimes embedded in a 2-stage SMART with an ordinal outcome. We propose a likelihood-based approach to estimate dGOR from SMART data. Next, we discuss some results related to dGOR and derive the asymptotic properties of it's estimate. We derive the required sample size formula. Then, we extend the proposed methodology to a K-stage SMART. Finally, we discuss some alternative ways to estimate dGOR using concordant-discordant pairs and multi-sample U-statistic. A simulation study shows the performance of the estimated dGOR in terms of the estimated power corresponding to the derived sample size. We analyze data from STAR*D, a multistage randomized clinical trial for treating major depression, to illustrate the proposed methodology. A freely available online tool using R statistical software is provided to make the proposed method accessible to other researchers and practitioners.
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