Bayesian Analysis of Latent Trait Hierarchical Models for Multiple Binary Outcomes in Cluster Randomized Clinical Trials

In clinical trials, multiple endpoints for treatment efficacy often are obtained, and in addition, data may be collected hierarchically. Statistical analyses become very challenging for this multidimensional hierarchical data, particularly with data collected at more than two levels. We propose a latent variable approach to assess an intervention effect on multiple binary outcomes from three-level hierarchical data. This approach incorporates the correlation structure into one or more latent outcomes, and simultaneously regresses the latent outcome(s) on observed covariates. Random effects are included to model the hierarchical structure. Parameters estimation is done using a fully Bayesian approach implemented in WinBUGS. We first illustrate the approach in a cluster randomized clinical trial of three interventions to improve the processes of care for outpatients with pneumonia. Four binary outcomes are collected at the patient-level and clustered at the provider and clinic site levels. Simulation studies are conducted to check the algorithm and computational implementation. Then, we extend the one latent trait model to a two-latent trait model using eight outcomes from both outpatient and inpatient care. This latent modeling approach provides a comprehensive way to analyze multivariate hierarchical data. The method not only allows assessment of intervention effects with respect to multiple outcomes, but also assesses the relationship between outcomes, identifies those outcomes that carry the most information about the latent trait(s), and provides a summary measure of the "quality of care" at each clinical site.This work extends existing methods to model multivariate binary endpoints in a cluster-randomized clinical trial. The public health significance of this study is the potential usefulness of this approach to quantify intervention (or exposure) effects with regard to multiple outcomes in hierarchical data setting, which arises frequently in medical and epidemiologic studies