The use of copulas in cost-effectiveness analysis

Abstract

Background: Copula methods have been proposed as a way of modeling dependence between random variables because it lies in the flexibility of the assumption on marginals. As previous authors stated, "A copula is a function which joins or “couples” a multivariate distribution function to its one-dimensional marginal distribution functions. Given that cost and effectiveness are often related to each other and therefore they show statistical dependence, the use of copulas to handle uncertainty caused by sampling variation could be potentially useful when cost-effectiveness analyses (CEA) are performed using patient-level data. The objective of this study was to empirically compare various copula distributions with two traditional methods, namely, the bootstrapping approach and the Bayesian approach assuming that incremental cost and LYs gained are bivariate normally distributed. Methods: The patient-level data from a previously published observational study were analyzed using four copula distributions: independent, Farlie-Gumbel-Morgenstern (FGM), Frank and Clayton copulas. Using the results from the traditional methods previously published, models were compared in terms of incremental cost, incremental life years (LYs) gained and the cost-effectiveness acceptability curves (CEACs) based on the net monetary benefit (NMB). Results: Using the traditional methods provided similar results. The most pronounced impact was the improvement in precision given that the confidence intervals were so much narrower for the copulas methods in comparison to the traditional methods. Consequently, the probability of being optimal derived from the Frank and Clayton copulas were close to 1.0 at a willingness to pay (𝜆) of CA$20,000. By contrast, the traditional methods were optimal for a 𝜆 of $100,000 CAD. Conclusions: The results of this study demonstreate the potential impact and importance of copulas in patient-level cost-effectiveness analysis. This approach could be particularly important in those situations where the data suggests some kind of dependence and some restrictions on the marginals, as observed in our case study.