Abstract
Many existing methods for estimating agreement correct for chance agreement by adjusting the observed proportion agreement by the probability of chance agreement based on different assumptions. These assumptions may not always be appropriate, as demonstrated by pathologists' ratings of kidney biopsy descriptors. We propose a novel agreement statistic that accounts for the empirical probability of chance agreement, estimated by collecting additional data on rater uncertainty for each rating. A standard error estimator for the proposed statistic is derived. Simulation studies show that in most cases, our proposed statistic is unbiased in estimating the probability of agreement after removing chance agreement.