Bayesian inference for longitudinal data with non-parametric treatment effects

We consider inference for longitudinal data based on mixed-effects models with a non-parametric Bayesian prior on the treatment effect. The proposed non-parametric Bayesian prior is a random partition model with a regression on patient-specific covariates. The main feature and motivation for the proposed model is the use of covariates with a mix of different data formats and possibly high-order interactions in the regression. The regression is not explicitly parameterized. It is implied by the random clustering of subjects. The motivating application is a study of the effect of an anticancer drug on a patient's blood pressure. The study involves blood pressure measurements taken periodically over several 24-h periods for 54 patients. The 24-h periods for each patient include a pretreatment period and several occasions after the start of therapy.