Methods for covariate adjustment in cost-effectiveness analysis that use cluster randomised trials

Statistical methods have been developed for cost-effectiveness analyses of cluster randomised trials (CRTs) where baseline covariates are balanced. However, CRTs may show systematic differences in individual and cluster-level covariates between the treatment groups. This paper presents three methods to adjust for imbalances in observed covariates: seemingly unrelated regression with a robust standard error, a 'two-stage' bootstrap approach combined with seemingly unrelated regression and multilevel models. We consider the methods in a cost-effectiveness analysis of a CRT with covariate imbalance, unequal cluster sizes and a prognostic relationship that varied by treatment group. The cost-effectiveness results differed according to the approach for covariate adjustment. A simulation study then assessed the relative performance of methods for addressing systematic imbalance in baseline covariates. The simulations extended the case study and considered scenarios with different levels of confounding, cluster size variation and few clusters. Performance was reported as bias, root mean squared error and CI coverage of the incremental net benefit. Even with low levels of confounding, unadjusted methods were biased, but all adjusted methods were unbiased. Multilevel models performed well across all settings, and unlike the other methods, reported CI coverage close to nominal levels even with few clusters of unequal sizes.