Cross-calibration of Stroke disability measures: Bayesian analysis of longitudinal ordinal categorical data using negative dependence

It is common to assess disability of stroke patients using standardized scales, such as the Rankin Stroke Outcome Scale (RS) and the Barthel Index (BI). The RS, which was designed for applications to stroke, is based on assessing directly the global conditions of a patient. The BI, which was designed for more general applications, is based on a series of questions about the patient's ability to carry out 10 basic activities of daily living. Because both scales are commonly used, but few studies use both, translating between scales is important in gaining an overall understanding of the efficacy of alternative treatments, and in developing prognostic models that combine several datasets. The objective of our analysis is to provide a tool for translating between BI and RS. Specifically, we estimate the conditional probability distributions of each given the other. Subjects consisted of 459 individuals who sustained a stroke and who were recruited for the Kansas City Stroke Study from 1995 to 1998. We assessed patients with BI and RS measures 1, 3, and 6 months after stroke. In addition, we included data from the Framingham study, in the form of a table cross-classifying patients by RS and coarsely aggregated BI. Our statistical estimation approach is motivated by several goals: (a) overcoming the difficulty presented by the fact that our two sources report data at different resolutions; (b) smoothing the empirical counts to provide estimates of probabilities in regions of the table that are sparsely populated; (c) avoiding estimates that would conflict with medical knowledge about the relationship between the two measures; and (d) estimating the relationship between RS and BI at three months after the stroke, while borrowing strength from measurements made at 1 month and 6 months. We address these issues via a Bayesian analysis combining data augmentation and constrained semiparametric inference. Our results provide the basis for comparing and integrating the results of clinical trials using different disability measures, and integrating clinical trials results into a comprehensive decision model for the assessment of long-term implications and cost-effectiveness of stroke prevention and acute treatment interventions. In addition, our results indicate that the degree of agreement between the two measures is less strong than commonly reported, and emphasize the importance of trial designs that include multiple assessments of outcome.