Bayesian multi-parameter evidence synthesis to inform decision-making: a case study in metastatic hormone-refractory prostate cancer

In health technology assessment, decisions are based on complex cost-effectiveness models which require numerous input parameters. When not all relevant estimates are available the model may have to be simplified. Multi-parameter evidence synthesis combines data from diverse sources of evidence which results in obtaining estimates required in clinical decision-making that otherwise may not be available. We demonstrate how bivariate meta-analysis can be used to predict an unreported estimate of a treatment effect enabling implementation of a multi-state Markov model, which otherwise needs to be simplified. To illustrate this, we used an example of cost-effectiveness analysis for docetaxel in combination with prednisolone in metastatic hormone-refractory prostate cancer. Bivariate meta-analysis was used to model jointly available data on treatment effects on overall survival and progression-free survival (PFS) to predict the unreported effect on PFS in a study evaluating docetaxel with prednisolone. The predicted treatment effect on PFS enabled implementation of a three-state Markov model comprising of stable disease, progressive disease and dead states, whilst lack of the estimate restricted the model to a two-state model (with alive and dead states). The two-state and three-state models were compared by calculating the incremental cost-effectiveness ratio (which was much lower in the three-state model: £22,148 per QALY gained compared to £30,026 obtained from the two-state model) and the expected value of perfect information (which increased with the three-state model). The three-state model has the advantage of distinguishing surviving patients who progressed from those who did not progress. Hence, the use of advanced meta-analytic techniques allowed obtaining relevant parameter estimates to populate a model describing disease pathway more appropriately, whilst helping to prevent valuable clinical data from being discarded.