Concordance correlation coefficient applied to discrete data

In any field in which decisions are subject to measurements, interchangeability between the methods used to obtain these measurements is essential. To consider methods as interchangeable, a certain degree of agreement is needed between the measurements they provide. The concordance correlation coefficient is an index that assesses the strength of agreement and it has been widely applied in situations in which measurements are made on a continuous scale. Recently the concordance correlation coefficient has been defined as a specific intraclass correlation coefficient estimated by the variance components of a Normal-Normal mixed linear model. Although this coefficient was defined for the continuous scale case, it may also be used with a discrete scale. In this case the data are often transformed and normalized, and the concordance correlation is applied. This study discusses the expression of the concordance correlation coefficient for discrete Poisson data by means of the Poisson-Normal generalized linear mixed model. The behaviour of the concordance correlation coefficient estimate is assessed by means of a simulation study, in which the estimates were compared using four models: three Normal-Normal mixed models with raw data, log-transformed data and square-root transformed data, and the Poisson-Normal generalized linear mixed model. An example is provided in which two different methods are used to measure CD34+ cells.