Numeric score-based conditional and overall change-in-status indices for ordered categorical data

• Type of Material: Article
• Authors: Robert Lyles, Emory University; Lawrence L. Kupper, University of North Carolina; Huiman X. Barnhart, Duke University; Sandra L. Martin, University of North Carolina
• Language: English
• Date: 2015-11-30
• Publisher: Wiley
• Publication Version: Author Accepted Manuscript (After Peer Review)
• Copyright Statement: © 2015 John Wiley & Sons, Ltd.
• Final Published Version (URL): http://dx.doi.org/10.1002/sim.6559
• Title of Journal or Parent Work: Statistics in Medicine
• ISSN: 0277-6715
• Volume: 34
• Issue: 27
• Start Page: 3622
• End Page: 3636
• Grant/Funding Information: This research was supported in part by grants from the National Institute of Environmental Health Sciences (5R01ES012458-07), and the National Center for Advancing Translational Sciences (UL1TR000454).
• Keywords: Research & Experimental Medicine; change score; Life Sciences & Biomedicine; ordinal data; Public, Environmental & Occupational Health; CONTINGENCY-TABLES; WEIGHTED KAPPA; INDICATOR; Dirichlet; Science & Technology; Mathematics; Physical Sciences; Statistics & Probability; Medical Informatics; INDEPENDENCE; multinomial; INTERVAL ESTIMATION; Mathematical & Computational Biology
• Research Categories: Health Sciences, General; Biology, Biostatistics

Abstract

Planned interventions and/or natural conditions often effect change on an ordinal categorical outcome (e.g., symptom severity). In such scenarios, it is sometimes desirable to assign a priori scores to observed changes in status, typically giving higher weight to changes of greater magnitude. We define change indices for such data based upon a multinomial model for each row of a c × c table, where the rows represent the baseline status categories. We distinguish an index designed to assess conditional changes within each baseline category from two others designed to capture overall change. One of these overall indices measures expected change across a target population. The other is scaled to capture the proportion of total possible change in the direction indicated by the data, so that it ranges from -1 (when all subjects finish in the least favorable category) to +1 (when all finish in the most favorable category). The conditional assessment of change can be informative regardless of how subjects are sampled into the baseline categories. In contrast, the overall indices become relevant when subjects are randomly sampled at baseline from the target population of interest, or when the investigator is able to make certain assumptions about the baseline status distribution in that population. We use a Dirichlet-multinomial model to obtain Bayesian credible intervals for the conditional change index that exhibit favorable small-sample frequentist properties. Simulation studies illustrate the methods, and we apply them to examples involving changes in ordinal responses for studies of sleep deprivation and activities of daily living.