Efficient Bayesian joint models for group randomized trials with multiple observation times and multiple outcomes

In this paper, we propose a Bayesian method for group randomized trials with multiple observation times and multiple outcomes of different types. We jointly model these outcomes using latent multivariate normal linear regression, which allows treatment effects to change with time and accounts for (i) intraclass correlation within groups; (ii) the correlation between different outcomes measured on the same subject; and (iii) the over-time correlation of each outcome. Moreover, we develop a set of innovative priors for the variance components, which yield direct inference on the correlations, avoid undesirable constraints, and allow utilization of information from previous studies. We illustrate through simulations that our model can improve estimation efficiency (lower posterior standard deviations) of intraclass correlations and treatment effects relative to single outcome models and models with diffuse priors on the variance components. We also demonstrate the methodology using body composition data collected in the Trial of Activity in Adolescent Girls.