Robustness of κ -type coefficients for clinical agreement

Abstract

The degree of inter-rater agreement is usually assessed through $\kappa$ -type coefficients and the extent of agreement is then characterized by comparing the value of the adopted coefficient against a benchmark scale. Through two motivating examples, it is displayed the different behavior of some $\kappa$ -type coefficients due to asymmetric distribution of marginal frequencies over categories. In order to investigate the robustness of four $\kappa$ -type coefficients for nominal and ordinal classifications and of an inferential benchmarking procedure that, differently from straightforward benchmarking, does not neglect the influence of the experimental conditions, an extensive Monte Carlo simulation study has been conducted. The robustness has been investigated for several scenarios, differing for sample size, rating scale dimension, number of raters, frequency distribution of rater classifications, pattern of agreement across raters. Simulation results reveal an higher paradoxical behavior of Fleiss kappa and Conger kappa with ordinal rather than nominal classifications; the coefficients robustness improves with increasing sample size and number of raters for both nominal and ordinal classifications whereas robustness improves with rating scale dimension only for nominal classifications. By identifying the scenarios (ie, minimum sample size, number of raters, rating scale dimension) with acceptable robustness, this study provides guidelines about the design of robust agreement studies.

Keywords: $\kappa$ -type coefficients; Monte Carlo simulation; inter-rater agreement; paradoxical behavior; robustness.