Measuring inter-rater reliability for nominal data – which coefficients and confidence intervals are appropriate?

TLDR

Reliability of measurements is essential for medical research, and for nominal data Fleiss' kappa and Krippendorff's alpha are the most flexible reliability measures with respect to number of raters and categories. The study aims to determine which reliability measures and confidence intervals best assess inter‑rater reliability for nominal data across various scenarios. We performed a large simulation study evaluating the precision and empirical coverage of asymptotic and bootstrap confidence intervals for Fleiss' K and Krippendorff's alpha, compared them in a real‑world case study, and provided an R script for calculation. In simulations, Krippendorff's alpha gave stable estimates with missing data, while Fleiss' K’s asymptotic CI had low coverage; bootstrap CIs for both measures achieved nominal coverage, and for complete nominal data both measures with bootstrap CIs are suitable, whereas for missing data or higher‑order data Krippendorff's alpha is recommended.

Abstract

Reliability of measurements is a prerequisite of medical research. For nominal data, Fleiss' kappa (in the following labelled as Fleiss' K) and Krippendorff's alpha provide the highest flexibility of the available reliability measures with respect to number of raters and categories. Our aim was to investigate which measures and which confidence intervals provide the best statistical properties for the assessment of inter-rater reliability in different situations.We performed a large simulation study to investigate the precision of the estimates for Fleiss' K and Krippendorff's alpha and to determine the empirical coverage probability of the corresponding confidence intervals (asymptotic for Fleiss' K and bootstrap for both measures). Furthermore, we compared measures and confidence intervals in a real world case study.Point estimates of Fleiss' K and Krippendorff's alpha did not differ from each other in all scenarios. In the case of missing data (completely at random), Krippendorff's alpha provided stable estimates, while the complete case analysis approach for Fleiss' K led to biased estimates. For shifted null hypotheses, the coverage probability of the asymptotic confidence interval for Fleiss' K was low, while the bootstrap confidence intervals for both measures provided a coverage probability close to the theoretical one.Fleiss' K and Krippendorff's alpha with bootstrap confidence intervals are equally suitable for the analysis of reliability of complete nominal data. The asymptotic confidence interval for Fleiss' K should not be used. In the case of missing data or data or higher than nominal order, Krippendorff's alpha is recommended. Together with this article, we provide an R-script for calculating Fleiss' K and Krippendorff's alpha and their corresponding bootstrap confidence intervals.