The Bland-Altman method, which assesses agreement via an assessment set constructed by the difference of the measurement variables, has received great attention. Other assessment approaches have been proposed following the same difference-based framework. However, the exact assessment set constructed by the difference is achievable only for measurements with certain joint distributions. To provide a more general assessment framework, we propose two approaches. First, when the measurement distribution is known, we propose a parametric approach that constructs the assessment set through a measure of closeness corresponding to the distribution. Second, when the measurement distribution is unknown, we propose a nonparametric approach that constructs the assessment set through quantile regression. Both approaches quantify the degree of agreement with the presence of both systematic and random measurement errors, and enable one to go beyond the difference-based approach. Results of simulation and data analyses are presented to compare the two approaches.