Shared genetic aetiology may explain the co-occurrence of diseases in individuals more often than expected by chance. On identifying associated variants shared between two traits, one objective is to determine whether such overlap may be explained by specific genomic characteristics (eg, functional annotation). In clinical studies, inter-rater agreement approaches assess concordance among expert opinions on the presence/absence of a complex disease for each subject. We adapt a two-stage inter-rater agreement model to the genetic association setting to identify features predictive of overlap variants, while accounting for their marginal trait associations. The resulting corrected overlap and marginal enrichment test (COMET) also assesses enrichment at the individual trait level. Multiple categories may be tested simultaneously and the method is computationally efficient, not requiring permutations to assess significance. In an extensive simulation study, COMET identifies features predictive of enrichment with high power and has well-calibrated type I error. In contrast, testing for overlap with a single-trait enrichment test has inflated type I error. COMET is applied to three glycaemic traits using a set of functional annotation categories as predictors, followed by further analyses that focus on tissue-specific regulatory variants. The results support previous findings that regulatory variants in pancreatic islets are enriched for fasting glucose-associated variants, and give insight into differences/similarities between characteristics of variants associated with glycaemic traits. Also, despite regulatory variants in pancreatic islets being enriched for variants that are marginally associated with fasting glucose and fasting insulin, there is no enrichment of shared variants between the traits.