BAYESIAN BIVARIATE HIERARCHICAL MODELS FOR ANALYSING COST-EFFECTIVENESS DATA FROM CLUSTER RANDOMIZED TRIALS

PURPOSE: Cost-effectiveness analyses (CEA) may be undertaken alongside cluster randomized trials (CRTs) where randomization is at the level of the cluster (for example the primary care provider) rather than the individual.  Here, an assumption made by traditional analytical methods, that observations are independent, is implausible. This paper develops Bayesian bivariate models for CEA alongside CRTs, and compares the results to those from conventional methods.

 

 METHODS: Bayesian bivariate hierarchical models are attractive for CEA alongside CRTs, as they can allow for any clustering in the data whilst jointly modelling both costs and effects. This paper extends previously published Bayesian bivariate models (Nixon and Thompson 2005) to recognise the specific forms of clustering inherent in CEAs based on CRTs. We develop a flexible set of hierarchical models that allow firstly the mean costs and outcomes in each cluster to differ randomly across clusters, and secondly the standard deviations to differ across clusters. We also consider models that relax normality assumptions by for example, allowing costs to take a gamma distribution.

 We illustrate each model using data from a large (1732 cases, 70 primary care clinics) CRT evaluating alternative interventions in primary care for reducing post-natal depression. Primary care clinics were randomised to provide two different forms of intervention from a health visitor (intervention groups), or usual care (control group). We estimate cost-effectiveness using different bivariate models that recognise or ignore clustering, and compare the results.

 RESULTS:   The main result from the Bayesian bivariate models that ignored clustering was that either intervention reduced costs and was highly cost-effective. However, the Bayesian hierarchical models found that the cost data were strongly clustered within primary care clinics (intra-class correlation = 0.30). When this clustering was allowed for, the reported uncertainty surrounding the incremental cost-effectiveness was much increased. Furthermore, allowing for clustering, substantially changed the point estimates for the incremental cost-effectiveness and altered which intervention was judged relatively cost-effective.

 CONCLUSION:   CEA that use data from CRTs should fully recognise clustering; ignoring clustering can lead to incorrect inferences and recommendations. Bayesian bivariate hierarchical models provide a general, flexible framework for CEA based on CRTs. They allow for clustering, jointly model costs and effects, and make less restrictive assumptions than other alternatives.