Agreement is an important concept in medical and behavioral sciences, in particular in clinical decision making where disagreements possibly imply a different patient management. The concordance correlation coefficient is an appropriate measure to quantify agreement between two scorers on a quantitative scale. However, this measure is based on the first two moments, which could poorly summarize the shape of the score distribution on bounded scales. Bounded outcome scores are common in medical and behavioral sciences. Typical examples are scores obtained on visual analog scales and scores derived as the number of positive items on a questionnaire. These kinds of scores often show a non-standard distribution, like a J- or U-shape, questioning the usefulness of the concordance correlation coefficient as agreement measure. The logit-normal distribution has shown to be successful in modeling bounded outcome scores of two types: (1) when the bounded score is a coarsened version of a latent score with a logit-normal distribution on the [0,1] interval and (2) when the bounded score is a proportion with the true probability having a logit-normal distribution. In the present work, a model-based approach, based on a bivariate generalization of the logit-normal distribution, is developed in a Bayesian framework to assess the agreement on bounded scales. This method permits to directly study the impact of predictors on the concordance correlation coefficient and can be simply implemented in standard Bayesian softwares, like JAGS and WinBUGS. The performances of the new method are compared to the classical approach using simulations. Finally, the methodology is used in two different medical domains: cardiology and rheumatology.
Keywords: Likert scale; Limited scale; concordance; intraclass correlation coefficient; logistic transform.