This paper by Bland and Altman (2007) discusses methods for analyzing agreement between two measurement methods when multiple observations are taken per individual. The authors describe two scenarios: one where the true value of the measured quantity is constant, and another where it varies. In both cases, the goal is to estimate the 95% limits of agreement, which indicate the range within which the difference between measurements by the two methods is expected to lie for 95% of pairs of future measurements on similar individuals. For the constant value scenario, the authors present a method that accounts for variability in measurements across individuals and within individuals. They use one-way analysis of variance to estimate the variance of differences between methods and adjust for measurement errors. The estimated standard deviation is then used to calculate the 95% limits of agreement. In the varying value scenario, the authors describe a method that accounts for both between-subject and within-subject variability. They use a model that includes the mean difference between methods, a random between-subject effect, and a random error within the subject. The variance is estimated by summing the between-subject and within-subject variances. The standard deviation is then used to calculate the 95% limits of agreement. The authors also discuss the importance of considering the structure of the data when analyzing agreement between methods. They note that ignoring the data structure can lead to incorrect estimates of the limits of agreement. They emphasize the need for methods that take into account the variability within and between subjects to provide more accurate estimates of agreement. The paper provides examples of how these methods can be applied to real data, including data on cardiac ejection fraction measured by two different methods. The authors conclude that the methods described are more accurate than traditional approaches and that further research is needed to improve the analysis of agreement between methods.This paper by Bland and Altman (2007) discusses methods for analyzing agreement between two measurement methods when multiple observations are taken per individual. The authors describe two scenarios: one where the true value of the measured quantity is constant, and another where it varies. In both cases, the goal is to estimate the 95% limits of agreement, which indicate the range within which the difference between measurements by the two methods is expected to lie for 95% of pairs of future measurements on similar individuals. For the constant value scenario, the authors present a method that accounts for variability in measurements across individuals and within individuals. They use one-way analysis of variance to estimate the variance of differences between methods and adjust for measurement errors. The estimated standard deviation is then used to calculate the 95% limits of agreement. In the varying value scenario, the authors describe a method that accounts for both between-subject and within-subject variability. They use a model that includes the mean difference between methods, a random between-subject effect, and a random error within the subject. The variance is estimated by summing the between-subject and within-subject variances. The standard deviation is then used to calculate the 95% limits of agreement. The authors also discuss the importance of considering the structure of the data when analyzing agreement between methods. They note that ignoring the data structure can lead to incorrect estimates of the limits of agreement. They emphasize the need for methods that take into account the variability within and between subjects to provide more accurate estimates of agreement. The paper provides examples of how these methods can be applied to real data, including data on cardiac ejection fraction measured by two different methods. The authors conclude that the methods described are more accurate than traditional approaches and that further research is needed to improve the analysis of agreement between methods.