Bayesian hierarchical analysis of within‐units variances in repeated measures experiments

We develop hierarchical Bayesian models for biomedical data that consist of multiple measurements on each individual under each of several conditions. The focus is on investigating differences in within‐subject variation between conditions. We present both population‐level and individual‐level comparisons. We extend the partial likelihood models of Chinchilli et al. with a unique Bayesian hierarchical framework for variance components and associated degrees of freedom. We use the Gibbs sampler to estimate posterior marginal distributions for the parameters of the Bayesian hierarchical models. The application involves a comparison of two cholesterol analysers each applied repeatedly to a sample of subjects. Both the partial likelihood and Bayesian approaches yield similar results, although confidence limits tend to be wider under the Bayesian models.