A multivariate hierarchical Bayesian approach to measuring agreement in repeated measurement method comparison studies

Adopting the Bland-Altman framework, but using Bayesian methods, we present this statistical machinery. Two multivariate hierarchical Bayesian models are advocated, one which assumes that the underlying values for subjects remain static (exchangeable replicates) and one which assumes that the underlying values can change between repeated measurements (non-exchangeable replicates).We illustrate the salient advantages of these models using two separate datasets that have been previously analysed and presented; (i) assuming static underlying values analysed using both multivariate hierarchical Bayesian models, and (ii) assuming each subject's underlying value is continually changing quantity and analysed using the non-exchangeable replicate multivariate hierarchical Bayesian model.These easily implemented models allow for full parameter uncertainty, simultaneous method comparison, handle unbalanced or missing data, and provide estimates and credible regions for all the parameters of interest. Computer code for the analyses in also presented, provided in the freely available and currently cost free software package WinBUGS.Accurate measurement of the variable of interest is fundamentally important in any health research or practice setting. However, it is widely recognised that measurements simultaneously made on the same subject or specimen by different instruments, methods or observers invariably yield different empirical values. As such, evaluation of measurement quality is a central issue in deciding the utility of any instrument, method or observer [1]. Measurement validity and reproducibility are essential elements in determining this quality. Validity is the degree to which a measurement measures what it purports to measure and reproducibility is the degree to which a measurement provides the same result each time it is performed on a given subject or specimen [2]. Reproducibility is invariably assessed using agreement analysis of within (intra) and between (inte