Maximum likelihood estimation of the kappa coefficient from bivariate logistic regression.

We propose a maximum likelihood estimator (MLE) of the kappa coefficient from a 2 x 2 table when the binary ratings depend on patient and/or clinician effects. We achieve this by expressing the logit of the probability of positive rating as a linear function of the subject-specific and the rater-specific covariates. We investigate the bias and variance of the MLE in small and moderate size samples through Monte Carlo simulation and we provide the sample size calculation to detect departure from the null hypothesis H0: kappa = kappa 0 in the direction of H1: kappa > kappa 0.