Bayesian analysis of a multivariate null intercept errors-in-variables regression model

Longitudinal data are of great interest in analysis of clinical trials. In many practical situations the covariate can not be measured precisely and a natural alternative model is the errors-in-variables regression models. In this paper we study a null intercept errors-in-variables regression model with a structure of dependency between the response variables within the same group. We apply the model to real data presented in Hadgu and Koch (Hadgu, A., Koch, G. (1999). Application of generalized estimating equations to a dental randomized clinical trial. J. Biopharmaceutical Statistics 9(1):161-178). In that study volunteers with preexisting dental plaque were randomized to two experimental mouth rinses (A and B) or a control mouth rinse with double blinding. The dental plaque index was measured for each subject in the beginning of the study and at two follow-up times, which leads to the presence of an interclass correlation. We propose the use of a Bayesian approach to model a multivariate null intercept errors-in-variables regression model to the longitudinal data. The proposed Bayesian approach accommodates the correlated measurements and incorporates the restriction that the slopes must lie in the (0, 1) interval. A Gibbs sampler is used to perform the computations.