title: Numeric score-based conditional and overall change-in-status indices for ordered categorical data.
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.
authors.affiliation: Department of Biostatistics and Bioinformatics, The Rollins School of Public Health of Emory University, 1518 Clifton Rd. N.E., Mailstop 1518-002-3AA, Atlanta, 30322, GA, U.S.A.
authors.forename: Robert H
authors.identifier: http://orcid.org/0000-0001-7883-6404
authors.initials: RH
authors.lastname: Lyles
authors.affiliation: Department of Biostatistics, Gillings School of Global Public Health, The University of North Carolina at Chapel Hill, Chapel Hill, 27599-7420, NC, U.S.A.
authors.forename: Lawrence L
authors.initials: LL
authors.lastname: Kupper
authors.affiliation: Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, 27710, NC, U.S.A.
authors.forename: Huiman X
authors.initials: HX
authors.lastname: Barnhart
authors.affiliation: Department of Maternal and Child Health, Gillings School of Global Public Health, The University of North Carolina at Chapel Hill, Chapel Hill, 27599-7445, NC, U.S.A.
authors.forename: Sandra L
authors.initials: SL
authors.lastname: Martin
mesh_terms: D000203:Activities of Daily Living; D000368:Aged; D001499:Bayes Theorem; D003198:Computer Simulation; D016001:Confidence Intervals; D006801:Humans; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000706:statistics & numerical data*; D012892:Sleep Deprivation; D013548:Sweden
keywords: Dirichlet; change score; multinomial; ordinal data