Bayesian Cost-Effectiveness Analysis Using Individual-Level Data is Sensitive to the Choice of Uniform Priors on the Standard Deviations for Costs in Log-Normal Models.

Background: Bayesian cost-effectiveness analysis (CEA) requires the specification of prior distributions for all parameters to be empirically estimated via Bayes' rule. When costs are modelled via Log-Normal distributions, Uniform prior distributions are commonly applied on the logarithm-scale standard deviations for costs due to the ease of implementation. However, the consequences of placing wide Uniform priors on standard deviations of log costs for the interpretation of original-scale CEA results remain unclear. The purpose of our study is to explore the impact of using Uniform priors for the standard deviations of cost data on CEA conclusions when costs are assumed to be log-normally distributed.

Methods: The analysis has been performed using individual-level cost-utility data from a randomised controlled trial. Costs are initially jointly modelled with quality-adjusted life years (QALYs) using Log-Normal and Beta distributions, respectively. Uniform prior distributions with different upper bounds are applied to log-scale standard deviations in the cost Log-Normal model. We compare the performance of Uniform priors under the Log-Normal distribution with other distributional assumptions for costs. A simulation study has then been conducted to explore the impact of these models and prior choices on cost estimates in CEAs.

Results: Results show that the choice of Uniform priors on standard deviations of log costs in a Log-Normal model can substantially induce large fluctuations in cost estimates, and thus potentially affect the final estimates of the intervention being cost-effective compared with other distributional assumptions. This is potentially driven by the occurrence of zero values in cost data.

Conclusion: Bayesian CEAs may be sensitive to the choice of upper bounds of the Uniform priors for the standard deviations of log costs in Log-Normal models, particularly when data contain zero values. Our results suggest that caution should be taken when Uniform distributions with large upper bounds are used.