The concordance correlation coefficient (CCC) is an index that assesses the agreement between continuous measures made by different observers. At least four methods are used to estimate the CCC: two (Lin's method, Variance Components) which are defined on the basis that data are normally distributed, and the two others (U-statistics, GEE) which do not assume any particular distribution of the data. Here the four methods are compared with skewed data from a model in which the subject means follow a log-normal distribution while the within-subject variability is assumed to be normally distributed. An example of alcohol consumption is considered and a simulation study is performed.