Journal of Data Science

Inter-rater agreement is fundamental to decision making in medicine, psychology, and the social sciences, as it reflects the quality and reliability of rating systems. ICC (intraclass correlation) has been widely used as a measure of inter-rater agreement. To date, there has been no methodological development that properly assesses improvement in ICC for pre–post studies with ordinal ratings. It remain uninvestigated whether/how correlations between pre- and post-intervention scores impact the estimation and comparison of ICC. We present a Bayesian hierarchical probit framework for evaluating changes in ICCs in such settings. The model incorporates rater- and item-level correlations and compares two parameterizations: an “individual components” prior that separately models variances and correlations, and an inverse Wishart prior. Simulation studies show that accounting for pre–post correlation substantially improves estimation accuracy and power to detect changes in agreement, while ignoring it reduces efficiency. Application to a multicenter study on conjunctival inflammation demonstrates that a novel grading scale markedly increased inter-rater agreement. This framework underscores the importance of modeling ordinal outcomes appropriately and provides a flexible Bayesian tool for evaluating the effectiveness of interventions on inter-rater agreement in pre-post studies.