Semiparametric regression for assessing agreement using tolerance bands

This article describes a Bayesian semiparametric approach for assessing agreement between two methods for measuring a continuous variable using tolerance bands. A tolerance band quantifies the extent of agreement in methods as a function of a covariate by estimating the range of their differences in a specified large proportion of population. The mean function of differences is modelled using a penalized spline through its mixed model representation. The covariance matrix of the errors may also depend on a covariate. The Bayesian approach is straightforward to implement using the Markov chain Monte Carlo methodology. It provides an alternative to the rather ad hoc frequentist likelihood-based approaches that do not work well in general. Simulation for two commonly used models and their special cases suggests that the proposed Bayesian method has reasonably good frequentist coverage. Two real data sets are used for illustration, and the Bayesian and the frequentist inferences are compared.