Multivariate generalised linear mixed-effects models for analysis of clinical trial-based cost-effectiveness data

Economic evaluations conducted alongside randomised controlled trials are a popular vehicle for generating high-quality evidence on the incremental cost-effectiveness of competing healthcare interventions. Typically, in these studies, resource use (and by extension, economic costs) and clinical (or preference-based health) outcomes data are collected prospectively for trial participants to estimate the joint distribution of incremental costs and incremental benefits associated with the intervention. In this paper, we extend the generalised linear mixed-model framework to enable simultaneous modelling of multiple outcomes of mixed data types, such as those typically encountered in trial-based economic evaluations, taking into account correlation of outcomes due to repeated measurements on the same individual and other clustering effects. We provide new wrapper functions to estimate the models in Stata and R by maximum and restricted maximum quasi-likelihood and compare the performance of the new routines with alternative implementations across a range of statistical programming packages. Empirical applications using observed and simulated data from clinical trials suggest the new methods produce broadly similar results compared with Stata’s merlin and gsem commands and a Bayesian implementation in WinBUGS. We highlight that, although these empirical applications primarily focus on trial-based economic evaluations, the new methods presented can be generalised to other health economic investigations characterised by multivariate hierarchical data structures